Subgroups — C₅⋊(C₁₁⋊#64422) #30633556

Order 16170.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊#64422	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(C₁₁⋊AGL(1,𝔽₇))	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×D₅₅	—	7	1	no	maximal
7	C₁₁×#3862	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅⋊#64422	—	11	1	no	maximal, Hall
9	C₅×C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₅×C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₇×D₇₇	—	5	1	no	Hall
12	D₃₈₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₇×D₅₅	—	21	1	no	—
14	C₅×#3862	D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₇²×C₁₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
16	C₇×D₃₅	—	11	1	no	Hall
17	C₁₁⋊AGL(1,𝔽₇)	—	35	1	no	—
18	ΓL(1,𝔽₈)×D₁₁	—	35	1	no	—
19	C₅×C₇×C₁₁	—	6	1	no	—
20	C₅×C₇×C₁₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₃×D₅₅	—	49	1	no	Hall
23	#64422	—	55	1	no	Hall
24	C₅×C₇²	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
27	C₅⋊AGL(1,𝔽₇)	—	77	1	no	—
28	D₅×ΓL(1,𝔽₈)	—	77	1	no	—
29	C₃×C₅×C₁₁	—	49	1	no	Hall
30	D₇₇	—	5	1	no	—
31	C₇×D₁₁	—	35	1	no	—
32	#3862	D₅₅	1	1	yes	characteristic, complemented, Hall
33	D₅₅	—	7	1	no	Hall
34	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
35	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
36	C₇×D₇	—	55	1	no	Hall
37	C₇×C₁₁	—	6	1	no	—
38	C₇×C₁₁	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₇×C₁₁	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
40	D₃₅	—	11	1	no	—
41	C₇×D₅	—	231	1	no	—
42	C₃×D₁₁	—	245	1	no	Hall
43	C₅×C₁₁	#64422	1	1	yes	characteristic, complemented, Hall
44	C₇²	C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×ΓL(1,𝔽₈)	—	385	1	no	—
46	AGL(1,𝔽₇)	—	385	1	no	—
47	C₅×C₇	—	6	1	no	—
48	C₅×C₇	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, complemented
49	C₅×C₇	C₁₁⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
50	C₃×C₁₁	—	49	1	no	Hall
51	C₃×D₅	—	539	1	no	Hall
52	D₁₁	—	105	1	no	Hall
53	ΓL(1,𝔽₈)	—	7	1	no	—
54	ΓL(1,𝔽₈)	—	7	1	no	—
55	C₃×C₅	—	49	1	no	Hall
56	C₂×C₇	—	1155	1	no	—
57	D₇	—	55	1	no	—
58	C₁₁	C₅⋊#64422	1	1	yes	characteristic, complemented, Sylow
59	D₅	—	231	1	no	Hall
60	C₇	—	6	1	no	—
61	C₇	ΓL(1,𝔽₈)×D₅₅	1	1	yes	characteristic, complemented
62	C₇	C₅⋊(C₁₁⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
63	C₂×C₃	—	2695	1	no	Hall
64	C₅	C₁₁⋊#64422	1	1	yes	characteristic, complemented, Sylow
65	C₃	—	49	1	no	Sylow
66	C₂	—	1155	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#3862	C₂	semidirect
2. C₇×D₃₈₅	C₃	semidirect
4. C₅×C₇²×C₁₁	C₂×C₃	semidirect
7. C₁₁×#3862	D₅	semidirect
12. D₃₈₅	ΓL(1,𝔽₈)	semidirect
14. C₅×#3862	D₁₁	semidirect
15. C₇²×C₁₁	C₃×D₅	semidirect
20. C₅×C₇×C₁₁	AGL(1,𝔽₇)	semidirect
21. C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	semidirect
24. C₅×C₇²	C₃×D₁₁	semidirect
32. #3862	D₅₅	semidirect
38. C₇×C₁₁	D₅×ΓL(1,𝔽₈)	semidirect
39. C₇×C₁₁	C₅⋊AGL(1,𝔽₇)	semidirect
43. C₅×C₁₁	#64422	semidirect
44. C₇²	C₃×D₅₅	semidirect
48. C₅×C₇	ΓL(1,𝔽₈)×D₁₁	semidirect
49. C₅×C₇	C₁₁⋊AGL(1,𝔽₇)	semidirect
58. C₁₁	C₅⋊#64422	semidirect
61. C₇	ΓL(1,𝔽₈)×D₅₅	semidirect
62. C₇	C₅⋊(C₁₁⋊AGL(1,𝔽₇))	semidirect
64. C₅	C₁₁⋊#64422	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#3862	2
C₇×D₃₈₅	3
C₁₁⋊#64422	5
C₅⋊(C₁₁⋊AGL(1,𝔽₇))	7
ΓL(1,𝔽₈)×D₅₅	7
C₅⋊#64422	11

Subgroups — C5⋊(C11⋊#64422) #30633556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₁₁⋊#64422) #30633556