Finite Group Databasebeta

← #11757058

Subgroups — #11757058

Order 960.

1620 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D15C211yesmaximal, characteristic, complemented
2C5×D3×#41C211yesmaximal, characteristic, complemented
3C3×D5×#41C211yesmaximal, characteristic, complemented
4#92035C211yesmaximal, characteristic, complemented
5#92030C211yesmaximal, characteristic, complemented
6#92029C211yesmaximal, characteristic, complemented
7#92028C211yesmaximal, characteristic, complemented
8#92027C213yesmaximal, complemented
9#92026C213yesmaximal, complemented
10#92025C213yesmaximal, complemented
11#92020C213yesmaximal, complemented
12#92016C213yesmaximal, complemented
13D3×#709C213yesmaximal, complemented
14D5×#235C213yesmaximal, complemented
15C2×#6771C213yesmaximal, complemented
16#66283—31nomaximal, Hall
17C3×C5×#41C2211yescharacteristic, complemented
18#6821C2211yescharacteristic, complemented
19Q8×D15C2211yescharacteristic, complemented
20#6819C2213yescomplemented
21D4×D15C2213yescomplemented
22#6817C2213yescomplemented
23C2×C4×D15C2213yescomplemented
24C5×#239C2211yescharacteristic, complemented
25C5×D3×Q8C2211yescharacteristic, complemented
26C5×#237C2213yescomplemented
27C5×D3×D4C2213yescomplemented
28C5×#235C2213yescomplemented
29C2×C4×C5×D3C2213yescomplemented
30C3×#713C2211yescharacteristic, complemented
31C3×Q8×D5C2211yescharacteristic, complemented
32C3×#711C2213yescomplemented
33C3×D4×D5C2213yescomplemented
34C3×#709C2213yescomplemented
35C2×C3×C4×D5C2213yescomplemented
36#6790C2216yescomplemented
37D3×C22⋊D5C2216yescomplemented
38D5×#67C2216yescomplemented
39C2×#1204C2213yescomplemented
40C2×#1203C2213yescomplemented
41C2×#1202C2213yescomplemented
42C2×#1201C2213yescomplemented
43#6782C2216yescomplemented
44#6780C2216yescomplemented
45#6779C2216yescomplemented
46#6777C2213yescomplemented
47D3×D20C2213yescomplemented
48D5×D12C2213yescomplemented
49C4×D3×D5C2216yescomplemented
50#6773C2213yescomplemented
51#6772C2213yescomplemented
52#6771C2211yescharacteristic, complemented
53#6771C2213yescomplemented
54#6771C2213yescomplemented
55#6771C2213yescomplemented
56#6771C2213yescomplemented
57#6771C2213yescomplemented
58#6771C2213yescomplemented
59#6771C2213yescomplemented
60D15⋊Q8C2213yescomplemented
61#6769C2213yescomplemented
62#6768C2213yescomplemented
63D3×Dic10C2213yescomplemented
64#6766C2213yescomplemented
65#6765C2213yescomplemented
66D5×Dic6C2213yescomplemented
67#5964—51nomaximal, Hall
68C2×C5×#41—31no—
69#4150—31no—
70#4150—33no—
71#4149—31no—
72#4149—33no—
73D5×#41—31no—
74D5×#41—33no—
75D5×#41—33no—
76D5×#41D311yescharacteristic, complemented
77#4147—31no—
78#4147—31no—
79#4144—33no—
80#4144—33no—
81C2×#709—33no—
82C2×#709—33no—
83C22×D15C2313yes—
84C22×C5×D3C2313yes—
85C22×C3×D5C2313yes—
86C2×D3×D5C2316yes—
87C3×C5×Q8C2311yescharacteristic
88C3×C5×D4C2313yes—
89C2×C3×C4×C5C2313yes—
90#1220C2316yes—
91C2×Dic15C2313yes—
92D60C2313yes—
93C4×D15C2313yes—
94C4×D15C2313yes—
95C4×D15C2311yescharacteristic
96C4×D15C2313yes—
97Dic30C2313yes—
98C5×#67C2316yes—
99C2×C5×Dic3C2313yes—
100C5×D12C2313yes—
101C4×C5×D3C2313yes—
102C4×C5×D3C2313yes—
103C4×C5×D3C2311yescharacteristic
104C4×C5×D3C2313yes—
105C5×Dic6C2313yes—
106C3×C22⋊D5C2316yes—
107C2×C3×Dic5C2313yes—
108C3×D20C2313yes—
109C3×C4×D5C2313yes—
110C3×C4×D5C2311yescharacteristic
111C3×C4×D5C2313yes—
112C3×C4×D5C2313yes—
113C3×Dic10C2313yes—
114#1204C2313yes—
115#1204C2313yes—
116#1204C2313yes—
117#1204C2311yescharacteristic
118#1203C2313yes—
119#1203C2313yes—
120#1203C2311yescharacteristic
121#1203C2313yes—
122#1202C2313yes—
123#1202C2311yescharacteristic
124#1202C2313yes—
125#1202C2313yes—
126#1201C2313yes—
127#1201C2311yescharacteristic
128#1201C2313yes—
129#1201C2313yes—
130#1200C2316yes—
131D3×Dic5C2316yes—
132D5×Dic3C2316yes—
133C2×C3×#41—51no—
134#1010—51no—
135#1010—53no—
136#1009—51no—
137#1009—53no—
138D3×#41—51no—
139D3×#41—53no—
140D3×#41—53no—
141D3×#41D511yescharacteristic, complemented
142#1007—51no—
143#1007—51no—
144#1004—53no—
145#1004—53no—
146C2×#235—53no—
147C2×#235—53no—
148C5×#41—31no—
149C5×#41—33no—
150C5×#41—33no—
151C5×#41C2×D311yescharacteristic, complemented
152C2×C5×Q8—31no—
153C2×C5×D4—33no—
154C22×C4×C5—33no—
155C2×C22⋊D5—33no—
156C2×C22⋊D5—36no—
157C2×C22⋊D5—33no—
158#713—31no—
159#713—33no—
160#713—33no—
161#713C2×D311yescharacteristic, complemented
162Q8×D5—31no—
163Q8×D5—33no—
164Q8×D5—33no—
165Q8×D5C2×D311yescharacteristic, complemented
166#711—33no—
167#711—36no—
168#711—36no—
169#711—33no—
170#711—33no—
171#711C2×D313yescomplemented
172D4×D5—36no—
173D4×D5—33no—
174D4×D5—36no—
175D4×D5—33no—
176D4×D5—33no—
177D4×D5C2×D313yescomplemented
178#709—33no—
179#709—36no—
180#709—33no—
181#709—33no—
182#709—31no—
183#709—33no—
184#709—33no—
185#709—33no—
186#709—33no—
187#709—33no—
188#709—33no—
189#709—33no—
190#709C2×D313yescomplemented
191C2×D20—33no—
192C2×D20—33no—
193C2×C4×D5—33no—
194C2×C4×D5—36no—
195C2×C4×D5C2×D313yescomplemented
196C2×Dic10—33no—
197C2×Dic10—33no—
198#585—151noSylow
199C22×C3×C5C2413yes—
200C2×D15—43no—
201C2×D15C2413yes—
202C2×D15C2411yescharacteristic
203C2×C5×D3—43no—
204C2×C5×D3C2413yes—
205C2×C5×D3C2411yescharacteristic
206C2×C3×D5—43no—
207C2×C3×D5C2413yes—
208C2×C3×D5C2411yescharacteristic
209D3×D5—46no—
210C3×C4×C5C2413yes—
211C3×C4×C5C2411yescharacteristic
212Dic15C2413yes—
213Dic15C2411yescharacteristic
214C3×Dic5C2413yes—
215C3×Dic5C2411yescharacteristic
216C5×Dic3C2413yes—
217C5×Dic3C2411yescharacteristic
218C3×#41—51no—
219C3×#41—53no—
220C3×#41—53no—
221C3×#41C2×D511yescharacteristic, complemented
222C2×C3×Q8—51no—
223C2×C3×D4—53no—
224C22×C3×C4—53no—
225C2×#67—53no—
226C2×#67—56no—
227C2×#67—53no—
228#239—51no—
229#239—53no—
230#239—53no—
231#239C2×D511yescharacteristic, complemented
232D3×Q8—51no—
233D3×Q8—53no—
234D3×Q8—53no—
235D3×Q8C2×D511yescharacteristic, complemented
236#237—53no—
237#237—56no—
238#237—56no—
239#237—53no—
240#237—53no—
241#237C2×D513yescomplemented
242D3×D4—56no—
243D3×D4—53no—
244D3×D4—56no—
245D3×D4—53no—
246D3×D4—53no—
247D3×D4C2×D513yescomplemented
248#235—53no—
249#235—56no—
250#235—53no—
251#235—53no—
252#235—51no—
253#235—53no—
254#235—53no—
255#235—53no—
256#235—53no—
257#235—53no—
258#235—53no—
259#235—53no—
260#235C2×D513yescomplemented
261C2×D12—53no—
262C2×D12—53no—
263C2×C4×D3—53no—
264C2×C4×D3—56no—
265C2×C4×D3C2×D513yescomplemented
266C2×Dic6—53no—
267C2×Dic6—53no—
268C23×C5—33no—
269C22×D5—33no—
270C22×D5—36no—
271C22×D5C22×D313yes—
272C5×Q8—33no—
273C5×Q8C22×D311yescharacteristic
274C5×D4—36no—
275C5×D4—33no—
276C5×D4C22×D313yes—
277C2×C4×C5—33no—
278C2×C4×C5—33no—
279C2×C4×C5—33no—
280C2×C4×C5—31no—
281C2×C4×C5—33no—
282C2×C4×C5C22×D313yes—
283C22⋊D5—36no—
284C22⋊D5—33no—
285C22⋊D5—31no—
286C22⋊D5—33no—
287C22⋊D5—33no—
288C22⋊D5—31no—
289C22⋊D5—33no—
290C22⋊D5—33no—
291C22⋊D5—33no—
292C22⋊D5C22×D316yes—
293C2×Dic5—33no—
294C2×Dic5—36no—
295C2×Dic5C22×D313yes—
296D20—33no—
297D20—31no—
298D20—33no—
299D20—33no—
300D20—33no—
301D20C22×D313yes—
302C4×D5—36no—
303C4×D5—31no—
304C4×D5—33no—
305C4×D5—33no—
306C4×D5—33no—
307C4×D5—36no—
308C4×D5C22×D313yes—
309C4×D5C22×D311yescharacteristic
310C4×D5C22×D313yes—
311C4×D5C22×D313yes—
312Dic10—33no—
313Dic10—31no—
314Dic10—33no—
315Dic10—33no—
316Dic10—33no—
317Dic10C22×D313yes—
3182−1+4—151no—
3192−1+4—151no—
3202−1+4—151no—
3212−1+4—153no—
322H(5,𝔽2)—153no—
323H(5,𝔽2)—153no—
324H(5,𝔽2)—153no—
325H(5,𝔽2)—151no—
326C2×#41—31no—
327C2×#41—51no—
328C2×#41—153no—
329C2×#41—153no—
330C2×#41—153no—
331C2×#41—153no—
332C2×#41—151no—
333C2×C3×C5—23no—
334C2×C3×C5C2511yescharacteristic
335D15—23no—
336D15—21no—
337C3×D5—23no—
338C3×D5—21no—
339C5×D3—23no—
340C5×D3—21no—
341C23×C3—53no—
342C22×D3—53no—
343C22×D3—56no—
344C22×D3C22×D513yes—
345C3×Q8—53no—
346C3×Q8C22×D511yescharacteristic
347C3×D4—56no—
348C3×D4—53no—
349C3×D4C22×D513yes—
350C2×C3×C4—53no—
351C2×C3×C4—53no—
352C2×C3×C4—53no—
353C2×C3×C4—51no—
354C2×C3×C4—53no—
355C2×C3×C4C22×D513yes—
356#67—56no—
357#67—53no—
358#67—51no—
359#67—53no—
360#67—53no—
361#67—51no—
362#67—53no—
363#67—53no—
364#67—53no—
365#67C22×D516yes—
366C2×Dic3—53no—
367C2×Dic3—56no—
368C2×Dic3C22×D513yes—
369D12—53no—
370D12—51no—
371D12—53no—
372D12—53no—
373D12—53no—
374D12C22×D513yes—
375C4×D3—56no—
376C4×D3—51no—
377C4×D3—53no—
378C4×D3—53no—
379C4×D3—53no—
380C4×D3—56no—
381C4×D3C22×D513yes—
382C4×D3C22×D511yescharacteristic
383C4×D3C22×D513yes—
384C4×D3C22×D513yes—
385Dic6—53no—
386Dic6—51no—
387Dic6—53no—
388Dic6—53no—
389Dic6—53no—
390Dic6C22×D513yes—
391C22×C5—33no—
392C22×C5—31no—
393C22×C5—123no—
394C22×C5C23×D313yes—
395C2×D5—33no—
396C2×D5—31no—
397C2×D5—43no—
398C2×D5—126no—
399C2×D5—123no—
400C2×D5C23×D313yes—
401C2×D5C23×D311yescharacteristic
402C4×C5—31no—
403C4×C5—33no—
404C4×C5C23×D313yes—
405C4×C5C23×D311yescharacteristic
406Dic5—33no—
407Dic5—31no—
408Dic5C23×D311yescharacteristic
409Dic5C23×D313yes—
410#41—31no—
411#41—33no—
412#41—33no—
413#41—51no—
414#41—53no—
415#41—53no—
416#41—151no—
417#41—153no—
418#41—153no—
419#41—153no—
420#41—153no—
421#41—153no—
422#41—153no—
423#41—153no—
424#41—156no—
425#41—153no—
426#41—153no—
427#41—156no—
428#41—153no—
429#41—153no—
430#41—156no—
431#41—153no—
432#41—153no—
433#41—151no—
434#41—153no—
435#41—153no—
436#41D3×D511yescharacteristic, complemented
437C2×Q8—31no—
438C2×Q8—51no—
439C2×Q8—153no—
440C2×Q8—153no—
441C2×Q8—153no—
442C2×Q8—153no—
443C2×Q8—151no—
444C2×D4—33no—
445C2×D4—53no—
446C2×D4—153no—
447C2×D4—153no—
448C2×D4—153no—
449C2×D4—153no—
450C2×D4—156no—
451C2×D4—153no—
452C2×D4—156no—
453C2×D4—156no—
454C2×D4—153no—
455C2×D4—153no—
456C22×C4—33no—
457C22×C4—53no—
458C22×C4—156no—
459C22×C4—153no—
460C3×C5#58511yescharacteristic, complemented, Hall
461C22×C3—53no—
462C22×C3—51no—
463C22×C3—203no—
464C22×C3C23×D513yes—
465C2×D3—43no—
466C2×D3—53no—
467C2×D3—51no—
468C2×D3—206no—
469C2×D3—203no—
470C2×D3C23×D513yes—
471C2×D3C23×D511yescharacteristic
472C3×C4—51no—
473C3×C4—53no—
474C3×C4C23×D513yes—
475C3×C4C23×D511yescharacteristic
476Dic3—53no—
477Dic3—51no—
478Dic3C23×D511yescharacteristic
479Dic3C23×D513yes—
480C2×C5—23no—
481C2×C5—63no—
482C2×C5—61no—
483C2×C5C24×D311yescharacteristic
484D5—21no—
485D5—23no—
486D5—63no—
487D5—61no—
488C23—33no—
489C23—53no—
490C23—156no—
491C23—153no—
492Q8—33no—
493Q8—53no—
494Q8—151no—
495Q8—153no—
496Q8—153no—
497Q8—153no—
498Q8—153no—
499Q8C2×D3×D511yescharacteristic
500D4—36no—
501D4—33no—
502D4—56no—
503D4—53no—
504D4—151no—
505D4—153no—
506D4—153no—
507D4—153no—
508D4—151no—
509D4—153no—
510D4—153no—
511D4—153no—
512D4—151no—
513D4—153no—
514D4—153no—
515D4—153no—
516D4—156no—
517D4—153no—
518D4C2×D3×D513yes—
519C2×C4—33no—
520C2×C4—33no—
521C2×C4—33no—
522C2×C4—31no—
523C2×C4—33no—
524C2×C4—53no—
525C2×C4—53no—
526C2×C4—53no—
527C2×C4—51no—
528C2×C4—53no—
529C2×C4—156no—
530C2×C4—156no—
531C2×C4—156no—
532C2×C4—153no—
533C2×C4—153no—
534C2×C4—153no—
535C2×C4—153no—
536C2×C4—151no—
537C2×C4C2×D3×D513yes—
538C2×C3—23no—
539C2×C3—103no—
540C2×C3—101no—
541C2×C3C24×D511yescharacteristic
542D3—21no—
543D3—23no—
544D3—103no—
545D3—101no—
546C5#596411yescharacteristic, complemented, Sylow
547C22—31no—
548C22—33no—
549C22—51no—
550C22—53no—
551C22—123no—
552C22—153no—
553C22—151no—
554C22—203no—
555C22—603no—
556C22—606no—
557C22C22×D3×D513yes—
558C4—31no—
559C4—33no—
560C4—51no—
561C4—53no—
562C4—153no—
563C4—151no—
564C4C22×D3×D513yes—
565C4C22×D3×D511yescharacteristic
566C3#6628311yescharacteristic, complemented, Sylow
567C2—23no—
568C2—61no—
569C2—63no—
570C2—101no—
571C2—103no—
572C2—301no—
573C2—303no—
574C2C23×D3×D511yescharacteristic
subgroupG/H
centerC4C22×D3×D5
commutator, socle, cosocleC2×C3×C5C25
FrattiniC2C23×D3×D5
FittingC3×C5×#41C22
hypercenter#41D3×D5
hypocenterC3×C5#585
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ #41

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #41×D15C2semidirect
2. C5×D3×#41C2semidirect
3. C3×D5×#41C2semidirect
4. #92035C2semidirect
5. #92030C2semidirect
6. #92029C2semidirect
7. #92028C2semidirect
8. #92027C2semidirect
9. #92026C2semidirect
10. #92025C2semidirect
11. #92020C2semidirect
12. #92016C2semidirect
13. D3×#709C2semidirect
14. D5×#235C2semidirect
15. C2×#6771C2semidirect
17. C3×C5×#41C22semidirect
18. #6821C22semidirect
19. Q8×D15C22semidirect
20. #6819C22semidirect
21. D4×D15C22semidirect
22. #6817C22semidirect
23. C2×C4×D15C22semidirect
24. C5×#239C22semidirect
25. C5×D3×Q8C22semidirect
26. C5×#237C22semidirect
27. C5×D3×D4C22semidirect
28. C5×#235C22semidirect
29. C2×C4×C5×D3C22semidirect
30. C3×#713C22semidirect
31. C3×Q8×D5C22semidirect
32. C3×#711C22semidirect
33. C3×D4×D5C22semidirect
34. C3×#709C22semidirect
35. C2×C3×C4×D5C22semidirect
36. #6790C22semidirect
37. D3×C22⋊D5C22semidirect
38. D5×#67C22semidirect
39. C2×#1204C22semidirect
40. C2×#1203C22semidirect
41. C2×#1202C22semidirect
42. C2×#1201C22semidirect
43. #6782C22semidirect
44. #6780C22semidirect
45. #6779C22semidirect
46. #6777C22semidirect
47. D3×D20C22semidirect
48. D5×D12C22semidirect
49. C4×D3×D5C22semidirect
50. #6773C22semidirect
51. #6772C22semidirect
52. #6771C22semidirect
53. #6771C22semidirect
54. #6771C22semidirect
55. #6771C22semidirect
56. #6771C22semidirect
57. #6771C22semidirect
58. #6771C22semidirect
59. #6771C22semidirect
60. D15⋊Q8C22semidirect
61. #6769C22semidirect
62. #6768C22semidirect
63. D3×Dic10C22semidirect
64. #6766C22semidirect
65. #6765C22semidirect
66. D5×Dic6C22semidirect
76. D5×#41D3semidirect
141. D3×#41D5semidirect
151. C5×#41C2×D3semidirect
161. #713C2×D3semidirect
165. Q8×D5C2×D3semidirect
171. #711C2×D3semidirect
177. D4×D5C2×D3semidirect
190. #709C2×D3semidirect
195. C2×C4×D5C2×D3semidirect
221. C3×#41C2×D5semidirect
231. #239C2×D5semidirect
235. D3×Q8C2×D5semidirect
241. #237C2×D5semidirect
247. D3×D4C2×D5semidirect
260. #235C2×D5semidirect
265. C2×C4×D3C2×D5semidirect
436. #41D3×D5semidirect
460. C3×C5#585semidirect
546. C5#5964semidirect
566. C3#66283semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×D152
C5×D3×#412
C3×D5×#412
#920352
#920302
#920292
#920282
#920272
#920262
#920252
#920202
#920162
D3×#7092
D5×#2352
C2×#67712
#662833
#59645