Subgroups — ΓL(1,𝔽₈)×C₅⋊D₃₅ #20301281

Order 7350.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)×D₃₅	—	5	6	no	maximal
4	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅⋊D₃₅	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×C₅⋊D₅	—	7	1	no	maximal
7	C₅×C₇×ΓL(1,𝔽₈)	D₅	1	6	yes	complemented
8	C₃×C₅²×C₇	—	7	1	no	—
9	C₅²×ΓL(1,𝔽₈)	D₇	1	1	yes	characteristic, complemented
10	C₇×D₃₅	—	5	6	no	—
11	C₅⋊D₃₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
12	C₇×C₅⋊D₅	—	7	1	no	—
13	D₇×ΓL(1,𝔽₈)	—	25	1	no	Hall
14	C₅×C₇²	C₃×D₅	1	6	yes	complemented
15	C₃×D₃₅	—	35	6	no	—
16	D₅×ΓL(1,𝔽₈)	—	35	6	no	—
17	C₅²×C₇	—	6	1	no	—
18	C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
20	C₃×C₅⋊D₅	—	49	1	no	Hall
21	C₇×ΓL(1,𝔽₈)	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅×C₇	—	7	6	no	—
23	C₅×ΓL(1,𝔽₈)	D₃₅	1	6	yes	complemented
24	C₇×D₇	—	25	1	no	Hall
25	C₃×C₅²	—	7	1	no	Hall
26	D₃₅	—	5	6	no	—
27	C₇×D₅	—	35	6	no	—
28	C₅⋊D₅	—	7	1	no	Hall
29	C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
30	C₃×D₇	—	175	1	no	—
31	C₂×ΓL(1,𝔽₈)	—	175	1	no	—
32	C₅×C₇	—	6	6	no	—
33	C₅×C₇	D₅×ΓL(1,𝔽₈)	1	6	yes	complemented
34	C₅×C₇	C₃×D₃₅	1	6	yes	complemented
35	C₃×D₅	—	245	6	no	—
36	C₅²	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
37	C₃×C₇	—	7	1	no	—
38	ΓL(1,𝔽₈)	C₅⋊D₃₅	1	1	yes	characteristic, direct product factor
39	C₃×C₅	—	7	6	no	—
40	C₂×C₇	—	175	1	no	—
41	D₇	—	25	1	no	—
42	D₅	—	35	6	no	—
43	C₇	—	6	1	no	—
44	C₇	ΓL(1,𝔽₈)×C₅⋊D₅	1	1	yes	characteristic, complemented
45	C₇	C₃×C₅⋊D₃₅	1	1	yes	characteristic, complemented
46	C₂×C₃	—	1225	1	no	Hall
47	C₅	ΓL(1,𝔽₈)×D₃₅	1	6	yes	complemented
48	C₃	—	7	1	no	Sylow
49	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×ΓL(1,𝔽₈)	C₂	semidirect
2. C₇×C₅⋊D₃₅	C₃	semidirect
4. C₅²×C₇²	C₂×C₃	semidirect
7. C₅×C₇×ΓL(1,𝔽₈)	D₅	semidirect
9. C₅²×ΓL(1,𝔽₈)	D₇	semidirect
11. C₅⋊D₃₅	ΓL(1,𝔽₈)	direct (N × H)
14. C₅×C₇²	C₃×D₅	semidirect
18. C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
19. C₅²×C₇	C₃×D₇	semidirect
21. C₇×ΓL(1,𝔽₈)	C₅⋊D₅	semidirect
23. C₅×ΓL(1,𝔽₈)	D₃₅	semidirect
29. C₇²	C₃×C₅⋊D₅	semidirect
33. C₅×C₇	D₅×ΓL(1,𝔽₈)	semidirect
34. C₅×C₇	C₃×D₃₅	semidirect
36. C₅²	D₇×ΓL(1,𝔽₈)	semidirect
38. ΓL(1,𝔽₈)	C₅⋊D₃₅	direct (N × H)
44. C₇	ΓL(1,𝔽₈)×C₅⋊D₅	semidirect
45. C₇	C₃×C₅⋊D₃₅	semidirect
47. C₅	ΓL(1,𝔽₈)×D₃₅	semidirect

Subgroups — ΓL(1,𝔽8)×C5⋊D35 #20301281

Conjugacy classes of subgroups

Complements

Subgroups — ΓL(1,𝔽₈)×C₅⋊D₃₅ #20301281