Subgroups — C₇²×C₁₁×D₁₅ #30633576

Order 16170.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₅×C₁₁	—	3	1	no	maximal, Hall
3	D₃×C₇²×C₁₁	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₁₅	C₇	1	8	yes	maximal, direct product factor
6	C₃×C₇²×C₁₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₇²×D₁₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₇×C₁₁	C₂×C₇	1	8	yes	complemented
9	C₂×C₇²×C₁₁	—	15	1	no	Hall
10	C₇×D₅×C₁₁	—	3	8	no	—
11	C₃×C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₁	D₁₅	1	1	yes	characteristic, direct product factor, Hall
13	C₇²×D₅	—	3	1	no	Hall
14	D₃×C₇×C₁₁	—	5	8	no	—
15	C₅×C₇×C₁₁	D₃×C₇	1	8	yes	complemented
16	C₁₁×D₁₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	D₃×C₇²	—	5	1	no	Hall
18	C₅×C₇²	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₁₁	C₇×D₅	1	8	yes	complemented
20	C₇×D₁₅	C₇×C₁₁	1	8	yes	direct product factor
21	C₃×C₅×C₁₁	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇×C₁₁	—	15	8	no	—
23	C₃×C₇²	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₁	—	3	1	no	Hall
25	C₃×C₅×C₇	C₂×C₇×C₁₁	1	8	yes	complemented
26	C₂×C₇²	—	15	1	no	Hall
27	C₇×C₁₁	C₇×D₁₅	1	8	yes	direct product factor
28	C₇×D₅	—	3	8	no	—
29	D₃×C₁₁	—	5	1	no	Hall
30	C₅×C₁₁	D₃×C₇²	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₁₁×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
32	D₃×C₇	—	5	8	no	—
33	C₅×C₇	D₃×C₇×C₁₁	1	8	yes	complemented
34	C₃×C₁₁	C₇²×D₅	1	1	yes	characteristic, complemented, Hall
35	D₁₅	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₁₁	—	15	1	no	Hall
37	C₃×C₇	C₇×D₅×C₁₁	1	8	yes	complemented
38	C₃×C₅	C₂×C₇²×C₁₁	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	—	15	8	no	—
40	C₁₁	C₇²×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	—	3	1	no	Hall
42	C₇	C₇×C₁₁×D₁₅	1	8	yes	direct product factor
43	D₃	—	5	1	no	Hall
44	C₅	D₃×C₇²×C₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₇²×D₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²×C₁₁	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₇²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₁	C₂	semidirect
4. C₅×C₇²×C₁₁	D₃	semidirect
5. C₇×C₁₁×D₁₅	C₇	direct (N × H)
6. C₃×C₇²×C₁₁	D₅	semidirect
7. C₇²×D₁₅	C₁₁	direct (N × H)
8. C₃×C₅×C₇×C₁₁	C₂×C₇	semidirect
11. C₃×C₅×C₇²	C₂×C₁₁	semidirect
12. C₇²×C₁₁	D₁₅	direct (N × H)
15. C₅×C₇×C₁₁	D₃×C₇	semidirect
16. C₁₁×D₁₅	C₇²	direct (N × H)
18. C₅×C₇²	D₃×C₁₁	semidirect
19. C₃×C₇×C₁₁	C₇×D₅	semidirect
20. C₇×D₁₅	C₇×C₁₁	direct (N × H)
21. C₃×C₅×C₁₁	C₂×C₇²	semidirect
23. C₃×C₇²	D₅×C₁₁	semidirect
25. C₃×C₅×C₇	C₂×C₇×C₁₁	semidirect
27. C₇×C₁₁	C₇×D₁₅	direct (N × H)
30. C₅×C₁₁	D₃×C₇²	semidirect
31. C₇²	C₁₁×D₁₅	direct (N × H)
33. C₅×C₇	D₃×C₇×C₁₁	semidirect
34. C₃×C₁₁	C₇²×D₅	semidirect
35. D₁₅	C₇²×C₁₁	direct (N × H)
37. C₃×C₇	C₇×D₅×C₁₁	semidirect
38. C₃×C₅	C₂×C₇²×C₁₁	semidirect
40. C₁₁	C₇²×D₁₅	direct (N × H)
42. C₇	C₇×C₁₁×D₁₅	direct (N × H)
44. C₅	D₃×C₇²×C₁₁	semidirect
45. C₃	C₇²×D₅×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₁	2
C₇²×D₅×C₁₁	3
D₃×C₇²×C₁₁	5
C₇×C₁₁×D₁₅	7
C₇²×D₁₅	11

Subgroups — C72×C11×D15 #30633576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₁₁×D₁₅ #30633576