Subgroups — C₅×ΓL(1,𝔽₈)×D₃₅ #20301270

Order 7350.

88 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	C₅×C₇×D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)×D₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₇×ΓL(1,𝔽₈)	—	5	1	no	maximal
5	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₃₅	—	7	1	no	maximal
7	C₅×D₅×ΓL(1,𝔽₈)	—	7	1	no	maximal
8	C₅×C₇×ΓL(1,𝔽₈)	—	2	2	no	—
9	C₅×C₇×ΓL(1,𝔽₈)	D₅	1	1	yes	characteristic, complemented
10	C₅×C₇×ΓL(1,𝔽₈)	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₇	—	7	1	no	—
12	C₅²×ΓL(1,𝔽₈)	D₇	1	1	yes	characteristic, complemented
13	C₇×D₃₅	C₃×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×D₇	—	5	1	no	—
15	C₅×D₃₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
16	C₅×C₇×D₅	—	7	1	no	—
17	D₇×ΓL(1,𝔽₈)	—	5	1	no	Hall
18	C₅×C₇²	—	2	2	no	—
19	C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
20	C₅×C₇²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₃×D₃₅	—	7	1	no	—
22	C₃×C₅×D₇	—	35	1	no	—
23	C₂×C₅×ΓL(1,𝔽₈)	—	35	1	no	—
24	D₅×ΓL(1,𝔽₈)	—	7	1	no	—
25	C₅²×C₇	—	6	1	no	—
26	C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
27	C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
28	C₃×C₅×D₅	—	49	1	no	Hall
29	C₇×ΓL(1,𝔽₈)	C₅×D₅	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₇	—	7	1	no	—
31	C₃×C₅×C₇	—	7	1	no	—
32	C₃×C₅×C₇	—	14	2	no	—
33	C₅×ΓL(1,𝔽₈)	—	2	2	no	—
34	C₅×ΓL(1,𝔽₈)	C₅×D₇	1	1	yes	characteristic, complemented
35	C₅×ΓL(1,𝔽₈)	D₃₅	1	1	yes	characteristic, direct product factor
36	C₇×D₇	—	5	1	no	Hall
37	C₃×C₅²	—	7	1	no	Hall
38	C₂×C₅×C₇	—	35	1	no	—
39	D₃₅	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
40	C₅×D₇	—	5	1	no	—
41	C₇×D₅	—	7	1	no	—
42	C₅×D₅	—	7	1	no	Hall
43	C₇²	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
44	C₃×D₇	—	35	1	no	—
45	C₂×ΓL(1,𝔽₈)	—	35	1	no	—
46	C₅×C₇	—	2	2	no	—
47	C₅×C₇	—	2	2	no	—
48	C₅×C₇	—	6	4	no	—
49	C₅×C₇	—	6	1	no	—
50	C₅×C₇	—	6	1	no	—
51	C₅×C₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
52	C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
53	C₅×C₇	C₃×C₅×D₇	1	1	yes	characteristic, complemented
54	C₅×C₇	C₃×D₃₅	1	1	yes	characteristic, complemented
55	C₂×C₃×C₅	—	245	1	no	—
56	C₃×D₅	—	49	1	no	—
57	C₅²	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₇	—	7	1	no	—
59	ΓL(1,𝔽₈)	C₅×D₃₅	1	1	yes	characteristic, direct product factor
60	C₃×C₅	—	7	1	no	—
61	C₃×C₅	—	7	1	no	—
62	C₃×C₅	—	14	2	no	—
63	C₂×C₇	—	35	1	no	—
64	D₇	—	5	1	no	—
65	C₂×C₅	—	35	1	no	—
66	D₅	—	7	1	no	—
67	C₇	—	6	1	no	—
68	C₇	C₅×D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
69	C₇	C₃×C₅×D₃₅	1	1	yes	characteristic, complemented
70	C₂×C₃	—	245	1	no	Hall
71	C₅	—	2	2	no	—
72	C₅	C₅×D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
73	C₅	ΓL(1,𝔽₈)×D₃₅	1	1	yes	characteristic, direct product factor
74	C₃	—	7	1	no	Sylow
75	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	ΓL(1,𝔽₈)×D₃₅
commutator, hypocenter	C₅×C₇²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₅

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. C₅×C₇×D₃₅	C₃	semidirect
3. ΓL(1,𝔽₈)×D₃₅	C₅	direct (N × H)
5. C₅²×C₇²	C₂×C₃	semidirect
9. C₅×C₇×ΓL(1,𝔽₈)	D₅	semidirect
10. C₅×C₇×ΓL(1,𝔽₈)	C₂×C₅	semidirect
12. C₅²×ΓL(1,𝔽₈)	D₇	semidirect
13. C₇×D₃₅	C₃×C₅	semidirect
15. C₅×D₃₅	ΓL(1,𝔽₈)	direct (N × H)
19. C₅×C₇²	C₃×D₅	semidirect
20. C₅×C₇²	C₂×C₃×C₅	semidirect
26. C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
27. C₅²×C₇	C₃×D₇	semidirect
29. C₇×ΓL(1,𝔽₈)	C₅×D₅	semidirect
34. C₅×ΓL(1,𝔽₈)	C₅×D₇	semidirect
35. C₅×ΓL(1,𝔽₈)	D₃₅	direct (N × H)
39. D₃₅	C₅×ΓL(1,𝔽₈)	direct (N × H)
43. C₇²	C₃×C₅×D₅	semidirect
51. C₅×C₇	D₅×ΓL(1,𝔽₈)	semidirect
52. C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	semidirect
53. C₅×C₇	C₃×C₅×D₇	semidirect
54. C₅×C₇	C₃×D₃₅	semidirect
57. C₅²	D₇×ΓL(1,𝔽₈)	semidirect
59. ΓL(1,𝔽₈)	C₅×D₃₅	direct (N × H)
68. C₇	C₅×D₅×ΓL(1,𝔽₈)	semidirect
69. C₇	C₃×C₅×D₃₅	semidirect
72. C₅	C₅×D₇×ΓL(1,𝔽₈)	semidirect
73. C₅	ΓL(1,𝔽₈)×D₃₅	direct (N × H)

Subgroups — C5×ΓL(1,𝔽8)×D35 #20301270

Conjugacy classes of subgroups

Complements

Subgroups — C₅×ΓL(1,𝔽₈)×D₃₅ #20301270