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FrequencyOfOccurenceOfSpaceGroups

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Claudio Bantaloukas edited this page Nov 2, 2021 · 1 revision

Frequency of Occurrence of Space Groups

This appendix lists space groups by their frequency of occurrence in organic and organometallic crystal structures.

Space Groups Listed by Frequency of Occurrence

This table lists all space groups that occur at least 40 times in the Cambridge Structural Database (CSD), arranged in descending order of frequency. Since there were already over 250,000 structures in the CSD when this list was compiled, any space group not included in the table is very uncommon. Only the symbol for the standard setting is given for each space group in the list.

Number Symbol Occurrences Number Symbol Occurrences
14 P21/c 73151 2 P-1 41639
19 P212121 18216 15 C2/c 15150
4 P21 11572 61 Pbca 7768
33 Pna21 3157 62 Pnma 3128
9 Cc 2075 1 P1 1848
60 Pbcn 1841 5 C2 1702
29 Pca21 1474 11 P21/m 1350
13 P2/c 1064 12 C2/m 1053
148 R-3 1044 18 P21212 970
7 Pc 760 56 Pccn 720
43 Fdd2 684 88 I41/a 671
92 P41212 522 20 C2221 393
36 Cmc21 362 64 Cmca 334
82 I-4 330 176 P63/m 325
146 R3 311 96 P43212 290
114 P-421c 289 57 Pbcm 285
86 P42/n 275 161 R3c 271
63 Cmcm 270 76 P41 240
167 R-3c 236 205 Pa3 226
152 P3121 222 85 P4/n 213
41 Aba2 211 147 P-3 194
31 Pmn21 188 70 Fddd 180
58 Pnnm 173 144 P31 168
52 Pnna 166 173 P63 149
45 Iba2 143 198 P213 143
169 P61 132 145 P32 131
8 Cm 126 87 I4/m 122
122 I-42d 114 78 P43 113
154 P3221 106 165 P-3c1 100
72 Ibam 99 59 Pmmn 92
68 Ccca 92 170 P65 90
155 R32 87 142 I41/acd 86
110 I41cd 85 130 P4/ncc 85
166 R-3m 84 54 Pcca 81
129 P4/nmm 79 160 R3m 78
55 Pbam 74 34 Pnn2 72
113 P-421m 71 143 P3 70
163 P-31c 62 225 Fm3m 62
121 I-42m 57 80 I41 56
79 I4 55 81 P-4 55
217 I-43m 55 23 I222 54
3 P2 53 10 P2/m 53
186 P63mc 53 118 P-4n2 49
126 P4/nnc 49 127 P4/mbm 49
194 P63/mmc 49 26 Pmc21 48
159 P31c 48 73 Ibca 47
178 P6122 47 94 P42212 46
136 P42/mnm 46 32 Pba2 44
17 P2221 43 40 Ama2 42

Chiral (Sohnke) Space Groups Listed by Frequency of Occurrence

This table lists all Sohnke space groups (i.e. space groups in which enantiomerically pure substances can crystallise) that occur at least 40 times in the Cambridge Structural Database (CSD), arranged in descending order of frequency. Since there were over 250,000 structures in the CSD when this list was compiled, any space group not in the table is very uncommon. Only the symbol for the standard setting is given for each space group in the list.

Number Symbol Occurrences Number Symbol Occurrences
19 P212121 18216 4 P21 11572
1 P1 1848 5 C2 1702
18 P21212 970 92 P41212 522
20 C2221 393 146 R3 311
96 P43212 290 76 P41 240
152 P3121 222 144 P31 168
173 P63 149 198 P213 143
169 P61 132 145 P32 131
78 P43 113 154 P3221 106
170 P65 90 155 R32 87
143 P3 70 80 I41 56
79 I4 55 23 I222 54
3 P2 53 178 P6122 47
94 P42212 46 17 P2221 43

Space Group Listing for DASH

The Entry Number is an internal identifier used by DASH. The corresponding space group number, setting and symbol are shown in the second column of the table. Within a DASH .sdi file, the space group is stored as:

SpaceGroup entry_number sg#:setting symbol

For example:
SpaceGroup 39 4:b P 1 21 1
or
SpaceGroup 52 9:b3 I 1 a 1

Entry Number SG #:setting Symbol
1 1 P 1
2 2 P -1
3 3:a P 2 1 1
4 4:a P 21 1 1
5 5:a1 B 2 1 1
6 5:a2 C 2 1 1
7 5:a3 I 2 1 1
8 6:a P m 1 1
9 7:a1 P b 1 1
10 7:a2 P n 1 1
11 7:a3 P c 1 1
12 8:a1 B m 1 1
13 8:a2 C m 1 1
14 8:a3 I m 1 1
15 9:a1 B b 1 1
16 9:a2 C n 1 1
17 9:a3 I c 1 1
18 9:-a1 C c 1 1
19 9:-a2 B n 1 1
20 9:-a3 I b 1 1
21 10:a P 2/m 1 1
22 11:a P 21/m 1 1
23 12:a1 B 2/m 1 1
24 12:a2 C 2/m 1 1
25 12:a3 I 2/m 1 1
26 13:a1 P 2/b 1 1
27 13:a2 P 2/n 1 1
28 13:a3 P 2/c 1 1
29 14:a1 P 21/b 1 1
30 14:a2 P 21/n 1 1
31 14:a3 P 21/c 1 1
32 15:a1 B 2/b 1 1
33 15:a2 C 2/n 1 1
34 15:a3 I 2/c 1 1
35 15:-a1 C 2/c 1 1
36 15:-a2 B 2/n 1 1
37 15:-a3 I 2/b 1 1
38 3:b P 1 2 1
39 4:b P 1 21 1
40 5:b1 C 1 2 1
41 5:b2 A 1 2 1
42 5:b3 I 1 2 1
43 6:b P 1 m 1
44 7:b1 P 1 c 1
45 7:b2 P 1 n 1
46 7:b3 P 1 a 1
47 8:b1 C 1 m 1
48 8:b2 A 1 m 1
49 8:b3 I 1 m 1
50 9:b1 C 1 c 1
51 9:b2 A 1 n 1
52 9:b3 I 1 a 1
53 9:-b1 A 1 a 1
54 9:-b2 C 1 n 1
55 9:-b3 I 1 c 1
56 10:b P 1 2/m 1
57 11:b P 1 21/m 1
58 12:b1 C 1 2/m 1
59 12:b2 A 1 2/m 1
60 12:b3 I 1 2/m 1
61 13:b1 P 1 2/c 1
62 13:b2 P 1 2/n 1
63 13:b3 P 1 2/a 1
64 14:b1 P 1 21/c 1
65 14:b2 P 1 21/n 1
66 14:b3 P 1 21/a 1
67 15:b1 C 1 2/c 1
68 15:b2 A 1 2/n 1
69 15:b3 I 1 2/a 1
70 15:-b1 A 1 2/a 1
71 15:-b2 C 1 2/n 1
72 15:-b3 I 1 2/c 1
73 3:c P 1 1 2
74 4:c P 1 1 21
75 5:c1 A 1 1 2
76 5:c2 B 1 1 2
77 5:c3 I 1 1 2
78 6:c P 1 1 m
79 7:c1 P 1 1 a
80 7:c2 P 1 1 n
81 7:c3 P 1 1 b
82 8:c1 A 1 1 m
83 8:c2 B 1 1 m
84 8:c3 I 1 1 m
85 9:c1 A 1 1 a
86 9:c2 B 1 1 n
87 9:c3 I 1 1 b
88 9:-c1 B 1 1 b
89 9:-c2 A 1 1 n
90 9:-c3 I 1 1 a
91 10:c P 1 1 2/m
92 11:c P 1 1 21/m
93 12:c1 A 1 1 2/m
94 12:c2 B 1 1 2/m
95 12:c3 I 1 1 2/m
96 13:c1 P 1 1 2/a
97 13:c2 P 1 1 2/n
98 13:c3 P 1 1 2/b
99 14:c1 P 1 1 21/a
100 14:c2 P 1 1 21/n
101 14:c3 P 1 1 21/b
102 15:c1 A 1 1 2/a
103 15:c2 B 1 1 2/n
104 15:c3 I 1 1 2/b
105 15:-c1 B 1 1 2/b
106 15:-c2 A 1 1 2/n
107 15:-c3 I 1 1 2/a
108 16 P 2 2 2
109 17 P 2 2 21
110 17:cab P 21 2 2
111 17:bca P 2 21 2
112 18 P 21 21 2
113 18:cab P 2 21 21
114 18:bca P 21 2 21
115 19 P 21 21 21
116 20 C 2 2 21
117 20:cab A 21 2 2
118 20:bca B 2 21 2
119 21 C 2 2 2
120 21:cab A 2 2 2
121 21:bca B 2 2 2
122 22 F 2 2 2
123 23 I 2 2 2
124 24 I 21 21 21
125 25 P m m 2
126 25:cab P 2 m m
127 25:bca P m 2 m
128 26 P m c 21
129 26:ba-c P c m 21
130 26:cab P 21 m a
131 26:-cba P 21 a m
132 26:bca P b 21 m
133 26:a-cb P m 21 b
134 27 P c c 2
135 27:cab P 2 a a
136 27:bca P b 2 b
137 28 P m a 2
137 28:ba-c P b m 2
139 28:cab P 2 m b
140 28:-cba P 2 c m
141 28:bca P c 2 m
142 28:a-cb P m 2 a
143 29 P c a 21
144 29:ba-c P b c 21
145 29:cab P 21 a b
146 29:-cba P 21 c a
147 29:bca P c 21 b
148 29:a-cb P b 21 a
149 30 P n c 2
150 30:ba-c P c n 2
151 30:cab P 2 n a
152 30:-cba P 2 a n
153 30:bca P b 2 n
154 30:a-cb P n 2 b
155 31 P m n 21
156 31:ba-c P n m 21
157 31:cab P 21 m n
158 31:-cba P 21 n m
159 31:bca P n 21 m
160 31:a-cb P m 21 n
161 32 P b a 2
162 32:cab P 2 c b
163 32:bca P c 2 a
164 33 P n a 21
165 33:ba-c P b n 21
166 33:cab P 21 n b
167 33:-cba P 21 c n
168 33:bca P c 21 n
169 33:a-cb P n 21 a
170 34 P n n 2
171 34:cab P 2 n n
172 34:bca P n 2 n
173 35 C m m 2
174 35:cab A 2 m m
175 35:bca B m 2 m
176 36 C m c 21
177 36:ba-c C c m 21
178 36:cab A 21 m a
179 36:-cba A 21 a m
180 36:bca B b 21 m
181 36:a-cb B m 21 b
182 37 C c c 2
183 37:cab A 2 a a
184 37:bca B b 2 b
185 38 A m m 2
186 38:ba-c B m m 2
187 38:cab B 2 m m
188 38:-cba C 2 m m
189 38:bca C m 2 m
190 38:a-cb A m 2 m
191 39 A b m 2
192 39:ba-c B m a 2
193 39:cab B 2 c m
194 39:-cba C 2 m b
195 39:bca C m 2 a
196 39:a-cb A c 2 m
197 40 A m a 2
198 40:ba-c B b m 2
199 40:cab B 2 m b
200 40:-cba C 2 c m
201 40:bca C c 2 m
202 40:a-cb A m 2 a
203 41 A b a 2
204 41:ba-c B b a 2
205 41:cab B 2 c b
206 41:-cba C 2 c b
207 41:bca C c 2 a
208 41:a-cb A c 2 a
209 42 F m m 2
210 42:cab F 2 m m
211 42:bca F m 2 m
212 43 F d d 2
213 43:cab F 2 d d
214 43:bca F d 2 d
215 44 I m m 2
216 44:cab I 2 m m
217 44:bca I m 2 m
218 45 I b a 2
219 45:cab I 2 c b
220 45:bca I c 2 a
221 46 I m a 2
222 46:ba-c I b m 2
223 46:cab I 2 m b
224 46:-cba I 2 c m
225 46:bca I c 2 m
226 46:a-cb I m 2 a
227 47 P m m m
228 48:1 P n n n:1
229 48:2 P n n n:2
230 49 P c c m
231 49:cab P m a a
232 49:bca P b m b
233 50:1 P b a n:1
234 50:2 P b a n:2
235 50:1cab P n c b:1
236 50:2cab P n c b:2
237 50:1bca P c n a:1
238 50:2bca P c n a:2
239 51 P m m a
240 51:ba-c P m m b
241 51:cab P b m m
242 51:-cba P c m m
243 51:bca P m c m
244 51:a-cb P m a m
245 52 P n n a
246 52:ba-c P n n b
247 52:cab P b n n
248 52:-cba P c n n
249 52:bca P n c n
250 52:a-cb P n a n
251 53 P m n a
252 53:ba-c P n m b
253 53:cab P b m n
254 53:-cba P c n m
255 53:bca P n c m
256 53:a-cb P m a n
257 54 P c c a
258 54:ba-c P c c b
259 54:cab P b a a
260 54:-cba P c a a
261 54:bca P b c b
262 54:a-cb P b a b
263 55 P b a m
264 55:cab P m c b
265 55:bca P c m a
266 56 P c c n
267 56:cab P n a a
268 56:bca P b n b
269 57 P b c m
270 57:ba-c P c a m
271 57:cab P m c a
272 57:-cba P m a b
273 57:bca P b m a
274 57:a-cb P c m b
275 58 P n n m
276 58:cab P m n n
277 58:bca P n m n
278 59:1 P m m n:1
279 59:2 P m m n:2
280 59:1cab P n m m:1
281 59:2cab P n m m:2
282 59:1bca P m n m:1
283 59:2bca P m n m:2
284 60 P b c n
285 60:ba-c P c a n
286 60:cab P n c a
287 60:-cba P n a b
288 60:bca P b n a
289 60:a-cb P c n b
290 61 P b c a
291 61:ba-c P c a b
292 62 P n m a
293 62:ba-c P m n b
294 62:cab P b n m
295 62:-cba P c m n
296 62:bca P m c n
297 62:a-cb P n a m
298 63 C m c m
299 63:ba-c C c m m
300 63:cab A m m a
301 63:-cba A m a m
302 63:bca B b m m
303 63:a-cb B m m b
304 64 C m c a
305 64:ba-c C c m b
306 64:cab A b m a
307 64:-cba A c a m
308 64:bca B b c m
309 64:a-cb B m a b
310 65 C m m m
311 65:cab A m m m
312 65:bca B m m m
313 66 C c c m
314 66:cab A m a a
315 66:bca B b m b
316 67 C m m a
317 67:ba-c C m m b
318 67:cab A b m m
319 67:-cba A c m m
320 67:bca B m c m
321 67:a-cb B m a m
322 68:1 C c c a:1
323 68:2 C c c a:2
324 68:1ba-c C c c b:1
325 68:2ba-c C c c b:2
326 68:1cab A b a a:1
327 68:2cab A b a a:2
328 68:1-cba A c a a:1
329 68:2-cba A c a a:2
330 68:1bca B b c b:1
331 68:2bca B b c b:2
332 68:1a-cb B b a b:1
333 68:2a-cb B b a b:2
334 69 F m m m
335 70:1 F d d d:1
336 70:2 F d d d:2
337 71 I m m m
338 72 I b a m
339 72:cab I m c b
340 72:bca I c m a
341 73 I b c a
342 73:ba-c I c a b
343 74 I m m a
344 74:ba-c I m m b
345 74:cab I b m m
346 74:-cba I c m m
347 74:bca I m c m
348 74:a-cb I m a m
349 75 P 4
350 76 P 41
351 77 P 42
352 78 P 43
353 79 I 4
354 80 I 41
355 81 P -4
356 82 I -4
357 83 P 4/m
358 84 P 42/m
359 85:1 P 4/n:1
360 85:2 P 4/n:2
361 86:1 P 42/n:1
362 86:2 P 42/n:2
363 87 I 4/m
364 88:1 I 41/a:1
365 88:2 I 41/a:2
366 89 P 4 2 2
367 90 P 42 1 2
368 91 P 41 2 2
369 92 P 41 21 2
370 93 P 42 2 2
371 94 P 42 21 2
372 95 P 43 2 2
373 96 P 43 21 2
374 97 I 4 2 2
375 98 I 41 2 2
376 99 P 4 m m
377 100 P 4 b m
378 101 P 42 c m
379 102 P 42 n m
380 103 P 4 c c
381 104 P 4 n c
382 105 P 42 m c
383 106 P 42 b c
384 107 I 4 m m
385 108 I 4 c m
386 109 I 41 m d
387 110 I 41 c d
388 111 P -4 2 m
389 112 P -4 2 c
390 113 P -4 21 m
391 114 P -4 21 c
392 115 P -4 m 2
393 116 P -4 c 2
394 117 P -4 b 2
395 118 P -4 n 2
396 119 I -4 m 2
397 120 I -4 c 2
398 121 I -4 2 m
399 122 I -4 2 d
400 123 P 4/m m m
401 124 P 4/m c c
402 125:1 P 4/n b m:1
403 125:2 P 4/n b m:2
404 126:1 P 4/n n c:1
405 126:2 P 4/n n c:2
406 127 P 4/m b m
407 128 P 4/m n c
408 129:1 P 4/n m m:1
409 129:2 P 4/n m m:2
410 130:1 P 4/n c c:1
411 130:2 P 4/n c c:2
412 131 P 42/m m c
413 132 P 42/m c m
414 133:1 P 42/n b c:1
415 133:2 P 42/n b c:2
416 134:1 P 42/n n m:1
417 134:2 P 42/n n m:2
418 135 P 42/m b c
419 136 P 42/m n m
420 137:1 P 42/n m c:1
421 137:2 P 42/n m c:2
422 138:1 P 42/n c m:1
423 138:2 P 42/n c m:2
424 139 I 4/m m m
425 140 I 4/m c m
426 141:1 I 41/a m d:1
427 141:2 I 41/a m d:2
428 142:1 I 41/a c d:1
429 142:2 I 41/a c d:2
430 143 P 3
431 144 P 31
432 145 P 32
433 146:H R 3:H
434 147 P -3
435 148:H R -3:H
436 149 P 3 1 2
437 150 P 3 2 1
438 151 P 31 1 2
439 152 P 31 2 1
440 153 P 32 1 2
441 154 P 32 2 1
442 155:H R 32:H
443 156 P 3 m 1
444 157 P 3 1 m
445 158 P 3 c 1
446 159 P 3 1 c
447 160:H R 3 m:H
448 161:H R 3 c:H
449 162 P -3 1 m
450 163 P -3 1 c
451 164 P -3 m 1
452 165 P -3 c 1
453 166:H R -3 m:H
454 167:H R -3 c:H
455 146:R R 3:R
456 148:R R -3:R
457 155:R R 32:R
458 160:R R 3 m:R
459 161:R R 3 c:R
460 166:R R -3 m:R
461 167:R R -3 c:R
462 168 P 6
463 169 P 61
464 170 P 65
465 171 P 62
466 172 P 64
467 173 P 63
468 174 P -6
469 175 P 6/m
470 176 P 63/m
471 177 P 6 2 2
472 178 P 61 2 2
473 179 P 65 2 2
474 180 P 62 2 2
475 181 P 64 2 2
476 182 P 63 2 2
477 183 P 6 m m
478 184 P 6 c c
479 185 P 63 c m
480 186 P 63 m c
481 187 P -6 m 2
482 188 P -6 c 2
482 189 P -6 2 m
484 190 P -6 2 c
485 191 P 6/m m m
486 192 P 6/m c c
487 193 P 63/m c m
488 194 P 63/m m c
489 195 P 2 3
490 196 F 2 3
491 197 I 2 3
492 198 P 21 3
493 199 I 21 3
494 200 P m -3
495 201:1 P n -3:1
496 201:2 P n -3:2
497 202 F m -3
498 203:1 F d -3:1
499 203:2 F d -3:2
500 204 I m -3
501 205 P a -3
502 206 I a -3
503 207 P 4 3 2
504 208 P 42 3 2
505 209 F 4 3 2
506 210 F 41 3 2
507 211 I 4 3 2
508 212 P 43 3 2
509 213 P 41 3 2
510 214 I 41 3 2
511 215 P -4 3 m
512 216 F -4 3 m
513 217 I -4 3 m
514 218 P -4 3 n
515 219 F -4 3 c
516 220 I -4 3 d
517 221 P m -3 m
518 222:1 P n -3 n:1
519 222:2 P n -3 n:2
520 223 P m -3 n
521 224:1 P n -3 m:1
522 224:2 P n -3 m:2
523 225 F m -3 m
524 226 F m -3 c
525 227:1 F d -3 m:1
526 227:2 F d -3 m:2
527 228:1 F d -3 c:1
528 228:2 F d -3 c:2
529 229 I m -3 m
530 230 I a -3 d
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