Subgroups — C₅⋊#16838460 #34062143

Order 19110.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838460	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×D₆₅	—	7	1	no	maximal
7	C₁₃×#3861	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅⋊#64423	—	13	1	no	maximal, Hall
9	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₅×C₁₃×ΓL(1,𝔽₈)	—	14	3	no	—
12	C₇×D₉₁	—	5	1	no	Hall
13	D₄₅₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₇×D₆₅	—	21	1	no	—
15	C₅×#3861	D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
17	ΓL(1,𝔽₈)⋊D₁₃	—	35	1	no	—
18	ΓL(1,𝔽₈)×D₁₃	—	35	1	no	—
19	C₇×D₃₅	—	13	1	no	Hall
20	C₅×C₇×C₁₃	—	2	3	no	—
21	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
23	C₃×D₆₅	—	49	1	no	Hall
24	#64423	—	65	1	no	Hall
25	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
27	C₁₃×ΓL(1,𝔽₈)	—	14	3	no	—
28	C₅×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
30	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
31	C₃×C₅×C₁₃	—	49	1	no	Hall
32	D₉₁	—	5	1	no	—
33	C₇×D₁₃	—	105	1	no	—
34	#3861	D₆₅	1	1	yes	characteristic, complemented, Hall
35	D₆₅	—	21	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	—	65	1	no	Hall
40	C₇×C₁₃	—	2	3	no	—
41	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
42	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
43	C₃×D₁₃	—	245	1	no	Hall
44	D₃₅	—	13	1	no	—
45	C₇×D₅	—	273	1	no	—
46	C₅×C₁₃	#64423	1	1	yes	characteristic, complemented, Hall
47	C₇²	C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
49	AGL(1,𝔽₇)	—	455	1	no	—
50	C₃×C₁₃	—	49	1	no	Hall
51	C₅×C₇	—	2	3	no	—
52	C₅×C₇	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
53	C₅×C₇	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
54	C₃×D₅	—	637	1	no	Hall
55	D₁₃	—	35	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	—	455	1	no	—
61	D₇	—	65	1	no	—
62	C₁₃	C₅⋊#64423	1	1	yes	characteristic, complemented, Sylow
63	D₅	—	91	1	no	Hall
64	C₇	—	2	3	no	—
65	C₇	ΓL(1,𝔽₈)×D₆₅	1	1	yes	characteristic, complemented
66	C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	1	1	yes	characteristic, complemented
67	C₂×C₃	—	3185	1	no	Hall
68	C₅	#16838460	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	49	1	no	Sylow
70	C₂	—	1365	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×#3861	C₂	semidirect
2. C₇×D₄₅₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. C₁₃×#3861	D₅	semidirect
13. D₄₅₅	ΓL(1,𝔽₈)	semidirect
15. C₅×#3861	D₁₃	semidirect
16. C₇²×C₁₃	C₃×D₅	semidirect
21. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
22. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
28. C₅×C₇²	C₃×D₁₃	semidirect
34. #3861	D₆₅	semidirect
41. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
42. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
46. C₅×C₁₃	#64423	semidirect
47. C₇²	C₃×D₆₅	semidirect
52. C₅×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
53. C₅×C₇	ΓL(1,𝔽₈)⋊D₁₃	semidirect
62. C₁₃	C₅⋊#64423	semidirect
65. C₇	ΓL(1,𝔽₈)×D₆₅	semidirect
66. C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	semidirect
68. C₅	#16838460	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×#3861	2
C₇×D₄₅₅	3
#16838460	5
C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	7
ΓL(1,𝔽₈)×D₆₅	7
C₅⋊#64423	13

Subgroups — C5⋊#16838460 #34062143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838460 #34062143