Finite Group Databasebeta

← #11755329

Subgroups — #11755329

Order 960.

524 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×D15C211yesmaximal, characteristic, complemented
2#92016C211yesmaximal, characteristic, complemented
3C5×#950C211yesmaximal, characteristic, complemented
4C3×#4096C211yesmaximal, characteristic, complemented
5#91524C211yesmaximal, characteristic, complemented
6#91522C211yesmaximal, characteristic, complemented
7#91512C211yesmaximal, characteristic, complemented
8#91506C211yesmaximal, characteristic, complemented
9#91500C211yesmaximal, characteristic, complemented
10#91498C211yesmaximal, characteristic, complemented
11#91488C211yesmaximal, characteristic, complemented
12#91482C211yesmaximal, characteristic, complemented
13#91311C211yesmaximal, characteristic, complemented
14#91303C211yesmaximal, characteristic, complemented
15C2×#6651C211yesmaximal, characteristic, complemented
16#66102—31nomaximal, Hall
17C3×C5×#41C2211yescharacteristic, complemented
18#6821C2211yescharacteristic
19Q8×D15C2211yescharacteristic, complemented
20#6819—21no—
21#6819C2211yescharacteristic
22D4×D15—21no—
23D4×D15C2211yescharacteristic, complemented
24#6817—21no—
25#6817C2211yescharacteristic, complemented
26C2×C4×D15—21no—
27C2×C4×D15C2211yescharacteristic
28C5×#235C2211yescharacteristic, complemented
29C3×#709C2211yescharacteristic, complemented
30#6790—21no—
31#6780—21no—
32#6777C2211yescharacteristic, complemented
33C4×D3×D5—21no—
34#6771—21no—
35D15⋊Q8C2211yescharacteristic, complemented
36#6768C2211yescharacteristic
37#6766C2211yescharacteristic
38C5×#216C2211yescharacteristic, complemented
39C5×#215C2211yescharacteristic, complemented
40C5×#214C2211yescharacteristic, complemented
41C5×#213C2211yescharacteristic, complemented
42C2×C5×C3⋊C8C2211yescharacteristic, complemented
43C3×#689C2211yescharacteristic, complemented
44C3×#688C2211yescharacteristic, complemented
45C3×#687C2211yescharacteristic, complemented
46C3×#686C2211yescharacteristic, complemented
47C2×C3×#168C2211yescharacteristic, complemented
48#6663C2211yescharacteristic, complemented
49#6662C2211yescharacteristic, complemented
50#6660C2211yescharacteristic, complemented
51#6659C2211yescharacteristic, complemented
52#6658C2211yescharacteristic, complemented
53#6657C2211yescharacteristic, complemented
54#6654C2211yescharacteristic, complemented
55#6653C2211yescharacteristic, complemented
56#6651C2211yescharacteristic, complemented
57#6651C2211yescharacteristic, complemented
58#6651C2211yescharacteristic, complemented
59#6651C2211yescharacteristic, complemented
60#5768—51nomaximal, Hall
61D5×#41—31no—
62D5×#41—31no—
63C5×#135—31no—
64#4096—31no—
65#4096D311yescharacteristic, complemented
66#4064—31no—
67#4064—31no—
68#4061—31no—
69#4061—31no—
70#4060—31no—
71#4060—31no—
72#4057—31no—
73#4057—31no—
74#4050—31no—
75C2×#676—31no—
76C22×D15—21no—
77C22×D15D411yescharacteristic
78C2×D3×D5—21no—
79C3×C5×Q8C2311yescharacteristic
80C3×C5×D4—21no—
81C3×C5×D4C2311yescharacteristic
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5C2311yescharacteristic
84#1220—21no—
85#1220—21no—
86#1220—21no—
87C2×Dic15—21no—
88C2×Dic15D411yescharacteristic
89D60—21no—
90D60C2311yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15D411yescharacteristic
95C4×D15D411yescharacteristic
96C4×D15C2311yescharacteristic
97C4×D15C2311yescharacteristic
98Dic30—21no—
99Dic30C2311yescharacteristic
100C5×#67—21no—
101C5×D12C2311yescharacteristic
102C4×C5×D3—21no—
103C5×Dic6C2311yescharacteristic
104C3×C22⋊D5—21no—
105C3×D20C2311yescharacteristic
106C3×C4×D5—21no—
107C3×Dic10C2311yescharacteristic
108#1204—21no—
109#1203—21no—
110#1202—21no—
111#1201—21no—
112#1200—21no—
113D3×Dic5—21no—
114D5×Dic3—21no—
115C3×#168C2311yescharacteristic
116C3×#168C2311yescharacteristic
117C5×C3⋊C8C2311yescharacteristic
118C5×C3⋊C8C2311yescharacteristic
119D3×#41—51no—
120D3×#41—51no—
121C3×#135—51no—
122#950—51no—
123#950D511yescharacteristic, complemented
124#918—51no—
125#918—51no—
126#915—51no—
127#915—51no—
128#914—51no—
129#914—51no—
130#911—51no—
131#911—51no—
132#904—51no—
133C2×ΓL(1,𝔽25)—51no—
134C5×#41—31no—
135C5×#41C2×D311yescharacteristic, complemented
136#713—31no—
137#713—31no—
138Q8×D5—31no—
139Q8×D5—31no—
140#711—31no—
141#711—31no—
142#711—61no—
143#711—61no—
144D4×D5—31no—
145D4×D5—31no—
146D4×D5—61no—
147D4×D5—61no—
148#709—31no—
149#709—61no—
150#709—61no—
151#709C2×D311yescharacteristic, complemented
152C2×C4×D5—31no—
153C2×C4×D5—61no—
154C2×C4×D5—61no—
155C5×Q16—31no—
156C5×SD16—31no—
157C5×SD16—31no—
158C5×D8—31no—
159C2×C5×C8—31no—
160#689—31no—
161#689C2×D311yescharacteristic, complemented
162#688—31no—
163#688C2×D311yescharacteristic, complemented
164#687—31no—
165#687C2×D311yescharacteristic, complemented
166#686—31no—
167#686C2×D311yescharacteristic, complemented
168C2×#168C2×D311yescharacteristic, complemented
169Dic20—31no—
170D40—31no—
171#677—31no—
172#677—31no—
173#676—31no—
174#676—31no—
175#676—31no—
176#676—31no—
177#575—151noSylow
178C22×C3×C5—21no—
179C22×C3×C5C2×D411yescharacteristic
180C2×D15—21no—
181C2×D15—41no—
182C2×D15—42no—
183C2×D15C2×D411yescharacteristic
184C2×D15C2×D411yescharacteristic
185C2×C5×D3—21no—
186C2×C3×D5—21no—
187D3×D5—42no—
188C3×C4×C5—21no—
189C3×C4×C5C2×D411yescharacteristic
190C3×C4×C5C2411yescharacteristic
191Dic15—21no—
192Dic15C2×D411yescharacteristic
193Dic15C2×D411yescharacteristic
194C3×Dic5—21no—
195C5×Dic3—21no—
196C3×#41—51no—
197C3×#41C2×D511yescharacteristic, complemented
198#239—51no—
199#239—51no—
200D3×Q8—51no—
201D3×Q8—51no—
202#237—51no—
203#237—51no—
204#237—101no—
205#237—101no—
206D3×D4—51no—
207D3×D4—51no—
208D3×D4—101no—
209D3×D4—101no—
210#235—51no—
211#235—101no—
212#235—101no—
213#235C2×D511yescharacteristic, complemented
214C2×C4×D3—51no—
215C2×C4×D3—101no—
216C2×C4×D3—101no—
217C3×Q16—51no—
218C3×SD16—51no—
219C3×SD16—51no—
220C3×D8—51no—
221C2×C3×C8—51no—
222#216—51no—
223#216C2×D511yescharacteristic, complemented
224#215—51no—
225#215C2×D511yescharacteristic, complemented
226#214—51no—
227#214C2×D511yescharacteristic, complemented
228#213—51no—
229#213C2×D511yescharacteristic, complemented
230C2×C3⋊C8C2×D511yescharacteristic, complemented
231Dic12—51no—
232D24—51no—
233#204—51no—
234#204—51no—
235ΓL(1,𝔽25)—51no—
236ΓL(1,𝔽25)—51no—
237ΓL(1,𝔽25)—51no—
238ΓL(1,𝔽25)—51no—
239C22×D5—31no—
240C22×D5—61no—
241C22×D5—61no—
242C5×Q8—31no—
243C5×Q8C22×D311yescharacteristic
244C5×D4—21no—
245C5×D4—31no—
246C5×D4—61no—
247C5×D4C22×D311yescharacteristic
248C2×C4×C5—21no—
249C2×C4×C5—61no—
250C2×C4×C5C22×D311yescharacteristic
251C22⋊D5—21no—
252C22⋊D5—61no—
253C22⋊D5—61no—
254C22⋊D5—61no—
255C22⋊D5—61no—
256C22⋊D5—61no—
257C2×Dic5—31no—
258C2×Dic5—61no—
259C2×Dic5—61no—
260D20—31no—
261D20—61no—
262D20—61no—
263D20C22×D311yescharacteristic
264C4×D5—21no—
265C4×D5—31no—
266C4×D5—31no—
267C4×D5—31no—
268C4×D5—31no—
269C4×D5—61no—
270C4×D5—61no—
271C4×D5—61no—
272C4×D5—61no—
273C4×D5—61no—
274Dic10—31no—
275Dic10—61no—
276Dic10—61no—
277Dic10C22×D311yescharacteristic
278C5×C8—31no—
279C5×C8—31no—
280#168C22×D311yescharacteristic
281#168C22×D311yescharacteristic
282C2×#41—151no—
283C2×#41—151no—
284#137—151no—
285#137—151no—
286#137—151no—
287#137—151no—
288AGL(1,ℤ/8)—151no—
289AGL(1,ℤ/8)—151no—
290AGL(1,ℤ/8)—151no—
291AGL(1,ℤ/8)—151no—
292#135—31no—
293#135—51no—
294#135—151no—
295#135—151no—
296C2×M16—151no—
297C2×C3×C5—21no—
298C2×C3×C5—41no—
299C2×C3×C5C22×D411yescharacteristic
300D15—21no—
301D15—21no—
302D15—41no—
303C3×D5—41no—
304C5×D3—41no—
305C22×D3—51no—
306C22×D3—101no—
307C22×D3—101no—
308C3×Q8—51no—
309C3×Q8C22×D511yescharacteristic
310C3×D4—21no—
311C3×D4—51no—
312C3×D4—101no—
313C3×D4C22×D511yescharacteristic
314C2×C3×C4—21no—
315C2×C3×C4—101no—
316C2×C3×C4C22×D511yescharacteristic
317#67—21no—
318#67—101no—
319#67—101no—
320#67—101no—
321#67—101no—
322#67—101no—
323C2×Dic3—51no—
324C2×Dic3—101no—
325C2×Dic3—101no—
326D12—51no—
327D12—101no—
328D12—101no—
329D12C22×D511yescharacteristic
330C4×D3—21no—
331C4×D3—51no—
332C4×D3—51no—
333C4×D3—51no—
334C4×D3—51no—
335C4×D3—101no—
336C4×D3—101no—
337C4×D3—101no—
338C4×D3—101no—
339C4×D3—101no—
340Dic6—51no—
341Dic6—101no—
342Dic6—101no—
343Dic6C22×D511yescharacteristic
344C3×C8—51no—
345C3×C8—51no—
346C3⋊C8C22×D511yescharacteristic
347C3⋊C8C22×D511yescharacteristic
348C22×C5—21no—
349C22×C5—61no—
350C22×C5D3×D411yescharacteristic
351C2×D5—21no—
352C2×D5—31no—
353C2×D5—31no—
354C2×D5—61no—
355C2×D5—122no—
356C2×D5—121no—
357C2×D5—122no—
358C4×C5—21no—
359C4×C5—61no—
360C4×C5D3×D411yescharacteristic
361C4×C5C23×D311yescharacteristic
362Dic5—21no—
363Dic5—31no—
364Dic5—31no—
365Dic5—61no—
366#41—31no—
367#41—51no—
368#41—151no—
369#41—151no—
370#41—151no—
371#41—151no—
372#41—151no—
373#41—301no—
374#41—301no—
375#41—301no—
376#41—301no—
377#41D3×D511yescharacteristic, complemented
378C2×Q8—151no—
379C2×Q8—151no—
380C2×D4—151no—
381C2×D4—151no—
382C2×D4—301no—
383C2×D4—301no—
384C22×C4—151no—
385C22×C4—301no—
386C22×C4—301no—
387Q16—31no—
388Q16—51no—
389Q16—151no—
390Q16—151no—
391SD16—31no—
392SD16—31no—
393SD16—51no—
394SD16—51no—
395SD16—151no—
396SD16—151no—
397SD16—151no—
398SD16—151no—
399D8—31no—
400D8—51no—
401D8—151no—
402D8—151no—
403M16—151no—
404M16—151no—
405M16—151no—
406M16—151no—
407C2×C8—31no—
408C2×C8—51no—
409C3×C5#57511yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—101no—
412C22×C3D4×D511yescharacteristic
413C2×D3—21no—
414C2×D3—51no—
415C2×D3—51no—
416C2×D3—101no—
417C2×D3—202no—
418C2×D3—201no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—101no—
422C3×C4D4×D511yescharacteristic
423C3×C4C23×D511yescharacteristic
424Dic3—21no—
425Dic3—51no—
426Dic3—51no—
427Dic3—101no—
428C2×C5—21no—
429C2×C5—41no—
430C2×C5—121no—
431C2×C5C2×D3×D411yescharacteristic
432D5—41no—
433D5—61no—
434D5—61no—
435D5—121no—
436C23—151no—
437C23—301no—
438C23—301no—
439Q8—31no—
440Q8—51no—
441Q8—151no—
442Q8—301no—
443Q8—301no—
444Q8C2×D3×D511yescharacteristic
445D4—21no—
446D4—31no—
447D4—51no—
448D4—61no—
449D4—101no—
450D4—151no—
451D4—301no—
452D4—301no—
453D4—301no—
454D4—301no—
455D4—301no—
456D4—301no—
457D4—301no—
458D4C2×D3×D511yescharacteristic
459C2×C4—21no—
460C2×C4—61no—
461C2×C4—101no—
462C2×C4—151no—
463C2×C4—151no—
464C2×C4—151no—
465C2×C4—151no—
466C2×C4—151no—
467C2×C4—301no—
468C2×C4—301no—
469C2×C4—301no—
470C2×C4—301no—
471C2×C4—301no—
472C2×C4—301no—
473C2×C4—301no—
474C2×C4C2×D3×D511yescharacteristic
475C8—31no—
476C8—31no—
477C8—51no—
478C8—51no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—201no—
482C2×C3C2×D4×D511yescharacteristic
483D3—41no—
484D3—101no—
485D3—101no—
486D3—201no—
487C5#576811yescharacteristic, complemented, Sylow
488C22—21no—
489C22—61no—
490C22—101no—
491C22—151no—
492C22—151no—
493C22—301no—
494C22—601no—
495C22—602no—
496C22—602no—
497C22#679011yescharacteristic
498C4—21no—
499C4—61no—
500C4—101no—
501C4—151no—
502C4—151no—
503C4—301no—
504C4#679011yescharacteristic
505C4C22×D3×D511yescharacteristic
506C3#6610211yescharacteristic, complemented, Sylow
507C2—21no—
508C2—41no—
509C2—121no—
510C2—201no—
511C2—301no—
512C2—301no—
513C2—601no—
514C2C2×#679011yescharacteristic
subgroupG/H
centerC4#6790
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC3×C5×#41C22
socleC2×C3×C5C22×D4
hypercenter#41D3×D5
hypocenterC3×C5#575
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #41×D15C2semidirect
2. #92016C2semidirect
3. C5×#950C2semidirect
4. C3×#4096C2semidirect
5. #91524C2semidirect
6. #91522C2semidirect
7. #91512C2semidirect
8. #91506C2semidirect
9. #91500C2semidirect
10. #91498C2semidirect
11. #91488C2semidirect
12. #91482C2semidirect
13. #91311C2semidirect
14. #91303C2semidirect
15. C2×#6651C2semidirect
17. C3×C5×#41C22semidirect
19. Q8×D15C22semidirect
23. D4×D15C22semidirect
25. #6817C22semidirect
28. C5×#235C22semidirect
29. C3×#709C22semidirect
32. #6777C22semidirect
35. D15⋊Q8C22semidirect
38. C5×#216C22semidirect
39. C5×#215C22semidirect
40. C5×#214C22semidirect
41. C5×#213C22semidirect
42. C2×C5×C3⋊C8C22semidirect
43. C3×#689C22semidirect
44. C3×#688C22semidirect
45. C3×#687C22semidirect
46. C3×#686C22semidirect
47. C2×C3×#168C22semidirect
48. #6663C22semidirect
49. #6662C22semidirect
50. #6660C22semidirect
51. #6659C22semidirect
52. #6658C22semidirect
53. #6657C22semidirect
54. #6654C22semidirect
55. #6653C22semidirect
56. #6651C22semidirect
57. #6651C22semidirect
58. #6651C22semidirect
59. #6651C22semidirect
65. #4096D3semidirect
123. #950D5semidirect
135. C5×#41C2×D3semidirect
151. #709C2×D3semidirect
161. #689C2×D3semidirect
163. #688C2×D3semidirect
165. #687C2×D3semidirect
167. #686C2×D3semidirect
168. C2×#168C2×D3semidirect
197. C3×#41C2×D5semidirect
213. #235C2×D5semidirect
223. #216C2×D5semidirect
225. #215C2×D5semidirect
227. #214C2×D5semidirect
229. #213C2×D5semidirect
230. C2×C3⋊C8C2×D5semidirect
377. #41D3×D5semidirect
409. C3×C5#575semidirect
487. C5#5768semidirect
506. C3#66102semidirect

Maximal subgroups

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

subgroupindex
#41×D152
#920162
C5×#9502
C3×#40962
#915242
#915222
#915122
#915062
#915002
#914982
#914882
#914822
#913112
#913032
C2×#66512
#661023
#57685