Subgroups — C₅⋊(C₁₁⋊#64423) #30633554

Order 16170.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊#64423	—	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×#3861	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅⋊#64423	—	11	1	no	maximal, Hall
9	C₅×C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₅×C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₅×C₁₁×ΓL(1,𝔽₈)	—	14	3	no	—
12	C₇×D₇₇	—	5	1	no	Hall
13	D₃₈₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₇×D₅₅	—	7	1	no	—
15	C₅×#3861	D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
17	C₇×D₃₅	—	11	1	no	Hall
18	C₁₁⋊AGL(1,𝔽₇)	—	35	1	no	—
19	ΓL(1,𝔽₈)×D₁₁	—	35	1	no	—
20	C₅×C₇×C₁₁	—	2	3	no	—
21	C₅×C₇×C₁₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₃×D₅₅	—	49	1	no	Hall
24	#64423	—	55	1	no	Hall
25	C₅×C₇²	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
26	C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
27	C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
28	C₁₁×ΓL(1,𝔽₈)	—	14	3	no	—
29	C₅⋊AGL(1,𝔽₇)	—	77	1	no	—
30	D₅×ΓL(1,𝔽₈)	—	77	1	no	—
31	C₃×C₅×C₁₁	—	49	1	no	Hall
32	D₇₇	—	5	1	no	—
33	C₇×D₁₁	—	105	1	no	—
34	#3861	D₅₅	1	1	yes	characteristic, complemented, Hall
35	D₅₅	—	7	1	no	Hall
36	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
37	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
38	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
39	C₇×D₇	—	55	1	no	Hall
40	C₇×C₁₁	—	2	3	no	—
41	C₇×C₁₁	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
42	C₇×C₁₁	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
43	D₃₅	—	11	1	no	—
44	C₇×D₅	—	77	1	no	—
45	C₃×D₁₁	—	245	1	no	Hall
46	C₅×C₁₁	#64423	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×ΓL(1,𝔽₈)	—	385	1	no	—
49	AGL(1,𝔽₇)	—	385	1	no	—
50	C₅×C₇	—	2	3	no	—
51	C₅×C₇	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, complemented
52	C₅×C₇	C₁₁⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
53	C₃×C₁₁	—	49	1	no	Hall
54	C₃×D₅	—	539	1	no	Hall
55	D₁₁	—	105	1	no	Hall
56	ΓL(1,𝔽₈)	—	7	1	no	—
57	ΓL(1,𝔽₈)	—	7	1	no	—
58	ΓL(1,𝔽₈)	—	14	3	no	—
59	C₃×C₅	—	49	1	no	Hall
60	C₂×C₇	—	1155	1	no	—
61	D₇	—	55	1	no	—
62	C₁₁	C₅⋊#64423	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	231	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	ΓL(1,𝔽₈)×D₅₅	1	1	yes	characteristic, complemented
66	C₇	C₅⋊(C₁₁⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
67	C₂×C₃	—	2695	1	no	Hall
68	C₅	C₁₁⋊#64423	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	49	1	no	Sylow
70	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×#3861	C₂	semidirect
2. C₇×D₃₈₅	C₃	semidirect
4. C₅×C₇²×C₁₁	C₂×C₃	semidirect
7. C₁₁×#3861	D₅	semidirect
13. D₃₈₅	ΓL(1,𝔽₈)	semidirect
15. C₅×#3861	D₁₁	semidirect
16. C₇²×C₁₁	C₃×D₅	semidirect
21. C₅×C₇×C₁₁	AGL(1,𝔽₇)	semidirect
22. C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	semidirect
25. C₅×C₇²	C₃×D₁₁	semidirect
34. #3861	D₅₅	semidirect
41. C₇×C₁₁	D₅×ΓL(1,𝔽₈)	semidirect
42. C₇×C₁₁	C₅⋊AGL(1,𝔽₇)	semidirect
46. C₅×C₁₁	#64423	semidirect
47. C₇²	C₃×D₅₅	semidirect
51. C₅×C₇	ΓL(1,𝔽₈)×D₁₁	semidirect
52. C₅×C₇	C₁₁⋊AGL(1,𝔽₇)	semidirect
62. C₁₁	C₅⋊#64423	semidirect
65. C₇	ΓL(1,𝔽₈)×D₅₅	semidirect
66. C₇	C₅⋊(C₁₁⋊AGL(1,𝔽₇))	semidirect
68. C₅	C₁₁⋊#64423	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#3861	2
C₇×D₃₈₅	3
C₁₁⋊#64423	5
C₅⋊(C₁₁⋊AGL(1,𝔽₇))	7
ΓL(1,𝔽₈)×D₅₅	7
C₅⋊#64423	11

Subgroups — C5⋊(C11⋊#64423) #30633554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₁₁⋊#64423) #30633554