Subgroups — ΓL(1,𝔽₈)×D₅₉₅ #38735964

Order 24990.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)×D₁₁₉	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	ΓL(1,𝔽₈)×D₈₅	—	7	1	no	maximal
6	C₃×D₅₉₅	—	7	1	no	maximal
7	C₇×C₁₇×ΓL(1,𝔽₈)	D₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅×C₇×C₁₇	—	7	1	no	—
9	C₅×C₁₇×ΓL(1,𝔽₈)	D₇	1	1	yes	characteristic, complemented
10	C₇×D₁₁₉	—	5	1	no	Hall
11	ΓL(1,𝔽₈)×D₃₅	—	17	1	no	maximal, Hall
12	D₅₉₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
13	C₇×D₈₅	—	7	1	no	—
14	C₇²×C₁₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×ΓL(1,𝔽₈)	D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃×D₁₁₉	—	35	1	no	—
17	ΓL(1,𝔽₈)×D₁₇	—	35	1	no	—
18	C₅×C₇×C₁₇	—	6	1	no	—
19	C₅×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
20	C₅×C₇×C₁₇	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×D₈₅	—	49	1	no	Hall
22	C₇×D₃₅	—	17	1	no	Hall
23	C₃×C₇×C₁₇	—	7	1	no	—
24	C₁₇×ΓL(1,𝔽₈)	D₃₅	1	1	yes	characteristic, complemented
25	D₇×ΓL(1,𝔽₈)	—	85	1	no	Hall
26	C₃×C₅×C₁₇	—	7	1	no	Hall
27	C₅×C₇²	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
28	D₁₁₉	—	5	1	no	—
29	C₇×D₁₇	—	35	1	no	—
30	C₃×D₃₅	—	119	1	no	—
31	D₅×ΓL(1,𝔽₈)	—	119	1	no	—
32	D₈₅	—	7	1	no	Hall
33	C₇×ΓL(1,𝔽₈)	D₈₅	1	1	yes	characteristic, complemented, Hall
34	C₇×C₁₇	—	6	1	no	—
35	C₇×C₁₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
36	C₇×C₁₇	C₃×D₃₅	1	1	yes	characteristic, complemented
37	C₃×C₅×C₇	—	7	1	no	—
38	C₅×ΓL(1,𝔽₈)	D₁₁₉	1	1	yes	characteristic, complemented
39	C₃×D₁₇	—	245	1	no	Hall
40	C₇×D₇	—	85	1	no	Hall
41	C₅×C₁₇	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
42	D₃₅	—	17	1	no	—
43	C₇×D₅	—	119	1	no	—
44	C₃×C₁₇	—	7	1	no	Hall
45	C₇²	C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
46	C₃×D₇	—	595	1	no	—
47	C₂×ΓL(1,𝔽₈)	—	595	1	no	—
48	C₅×C₇	—	6	1	no	—
49	C₅×C₇	ΓL(1,𝔽₈)×D₁₇	1	1	yes	characteristic, complemented
50	C₅×C₇	C₃×D₁₁₉	1	1	yes	characteristic, complemented
51	D₁₇	—	35	1	no	Hall
52	C₃×D₅	—	833	1	no	Hall
53	C₃×C₇	—	7	1	no	—
54	ΓL(1,𝔽₈)	D₅₉₅	1	1	yes	characteristic, direct product factor
55	C₁₇	ΓL(1,𝔽₈)×D₃₅	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₅	—	7	1	no	Hall
57	C₂×C₇	—	595	1	no	—
58	D₇	—	85	1	no	—
59	D₅	—	119	1	no	Hall
60	C₇	—	6	1	no	—
61	C₇	C₃×D₅₉₅	1	1	yes	characteristic, complemented
62	C₇	ΓL(1,𝔽₈)×D₈₅	1	1	yes	characteristic, complemented
63	C₂×C₃	—	4165	1	no	Hall
64	C₅	ΓL(1,𝔽₈)×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
65	C₃	—	7	1	no	Sylow
66	C₂	—	595	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₇×ΓL(1,𝔽₈)	C₂	semidirect
2. C₇×D₅₉₅	C₃	semidirect
4. C₅×C₇²×C₁₇	C₂×C₃	semidirect
7. C₇×C₁₇×ΓL(1,𝔽₈)	D₅	semidirect
9. C₅×C₁₇×ΓL(1,𝔽₈)	D₇	semidirect
12. D₅₉₅	ΓL(1,𝔽₈)	direct (N × H)
14. C₇²×C₁₇	C₃×D₅	semidirect
15. C₅×C₇×ΓL(1,𝔽₈)	D₁₇	semidirect
19. C₅×C₇×C₁₇	C₂×ΓL(1,𝔽₈)	semidirect
20. C₅×C₇×C₁₇	C₃×D₇	semidirect
24. C₁₇×ΓL(1,𝔽₈)	D₃₅	semidirect
27. C₅×C₇²	C₃×D₁₇	semidirect
33. C₇×ΓL(1,𝔽₈)	D₈₅	semidirect
35. C₇×C₁₇	D₅×ΓL(1,𝔽₈)	semidirect
36. C₇×C₁₇	C₃×D₃₅	semidirect
38. C₅×ΓL(1,𝔽₈)	D₁₁₉	semidirect
41. C₅×C₁₇	D₇×ΓL(1,𝔽₈)	semidirect
45. C₇²	C₃×D₈₅	semidirect
49. C₅×C₇	ΓL(1,𝔽₈)×D₁₇	semidirect
50. C₅×C₇	C₃×D₁₁₉	semidirect
54. ΓL(1,𝔽₈)	D₅₉₅	direct (N × H)
55. C₁₇	ΓL(1,𝔽₈)×D₃₅	semidirect
61. C₇	C₃×D₅₉₅	semidirect
62. C₇	ΓL(1,𝔽₈)×D₈₅	semidirect
64. C₅	ΓL(1,𝔽₈)×D₁₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₇×ΓL(1,𝔽₈)	2
C₇×D₅₉₅	3
ΓL(1,𝔽₈)×D₁₁₉	5
ΓL(1,𝔽₈)×D₈₅	7
C₃×D₅₉₅	7
ΓL(1,𝔽₈)×D₃₅	17

Subgroups — ΓL(1,𝔽8)×D595 #38735964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ΓL(1,𝔽₈)×D₅₉₅ #38735964