Subgroups — C₂×ΓL(1,𝔽₈)×D₆₅ #19129809

Order 5460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	ΓL(1,𝔽₈)×D₆₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₃×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₃×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×ΓL(1,𝔽₈)×D₁₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₆₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×D₆₅	—	7	1	no	maximal, Hall
9	C₂×C₁₃×ΓL(1,𝔽₈)	D₅	1	1	yes	characteristic, complemented
10	ΓL(1,𝔽₈)×D₁₃	—	5	2	no	—
11	C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×D₅×ΓL(1,𝔽₈)	—	13	1	no	maximal, Hall
13	C₂×C₃×C₅×C₁₃	—	7	1	no	—
14	C₃×D₆₅	—	7	2	no	—
15	C₂×C₇×D₁₃	—	5	1	no	Hall
16	C₁₃×ΓL(1,𝔽₈)	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×D₆₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₅×ΓL(1,𝔽₈)	D₁₃	1	1	yes	characteristic, complemented
19	D₅×ΓL(1,𝔽₈)	—	13	2	no	—
20	C₃×C₅×C₁₃	—	7	1	no	Hall
21	C₂×C₇×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
22	C₇×D₁₃	—	5	2	no	—
23	C₂×C₃×D₁₃	—	35	1	no	Hall
24	C₂×C₇×D₅	—	13	1	no	Hall
25	C₂×C₅×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	D₆₅	C₂×ΓL(1,𝔽₈)	1	2	yes	direct product factor
27	C₅×ΓL(1,𝔽₈)	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₂²×ΓL(1,𝔽₈)	—	65	1	no	Hall
30	C₂×C₃×C₁₃	—	7	1	no	—
31	C₃×D₁₃	—	35	2	no	—
32	C₂×C₅×C₇	C₃×D₁₃	1	1	yes	characteristic, complemented
33	C₇×D₅	—	13	2	no	—
34	C₅×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×D₅	—	91	1	no	Hall
36	C₂×D₁₃	—	5	1	no	Hall
37	C₂×ΓL(1,𝔽₈)	—	65	2	no	—
38	C₂×ΓL(1,𝔽₈)	D₆₅	1	1	yes	characteristic, direct product factor
39	C₃×C₁₃	—	7	1	no	Hall
40	C₅×C₇	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₅	—	7	1	no	—
42	C₃×D₅	—	91	2	no	—
43	C₂²×C₇	—	65	1	no	Hall
44	C₂×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
45	D₁₃	—	5	2	no	—
46	ΓL(1,𝔽₈)	C₂×D₆₅	1	1	yes	characteristic, direct product factor, Hall
47	C₂×D₅	—	13	1	no	Hall
48	C₃×C₅	—	7	1	no	Hall
49	C₂×C₇	—	65	2	no	—
50	C₂×C₇	C₃×D₆₅	1	1	yes	characteristic, complemented
51	C₁₃	C₂×D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	455	1	no	Hall
53	C₂×C₅	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
54	D₅	—	13	2	no	—
55	C₇	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	7	1	no	—
57	C₂×C₃	—	455	2	no	—
58	C₅	C₂×ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	65	1	no	Sylow
60	C₃	—	7	1	no	Sylow
61	C₂	—	65	2	no	—
62	C₂	ΓL(1,𝔽₈)×D₆₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₈)×D₆₅
commutator, hypocenter	C₅×C₇×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. ΓL(1,𝔽₈)×D₆₅	C₂	direct (N × H)
2. C₂×C₅×C₁₃×ΓL(1,𝔽₈)	C₂	semidirect
3. C₂×C₇×D₆₅	C₃	semidirect
4. C₅×C₁₃×ΓL(1,𝔽₈)	C₂²	semidirect
6. C₂×C₅×C₇×C₁₃	C₂×C₃	semidirect
7. C₇×D₆₅	C₂×C₃	semidirect
9. C₂×C₁₃×ΓL(1,𝔽₈)	D₅	semidirect
11. C₅×C₇×C₁₃	C₂²×C₃	semidirect
16. C₁₃×ΓL(1,𝔽₈)	C₂×D₅	semidirect
17. C₂×D₆₅	ΓL(1,𝔽₈)	direct (N × H)
18. C₂×C₅×ΓL(1,𝔽₈)	D₁₃	semidirect
21. C₂×C₇×C₁₃	C₃×D₅	semidirect
25. C₂×C₅×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
26. D₆₅	C₂×ΓL(1,𝔽₈)	direct (N × H)
27. C₅×ΓL(1,𝔽₈)	C₂×D₁₃	semidirect
28. C₇×C₁₃	C₂×C₃×D₅	semidirect
32. C₂×C₅×C₇	C₃×D₁₃	semidirect
34. C₅×C₁₃	C₂²×ΓL(1,𝔽₈)	semidirect
38. C₂×ΓL(1,𝔽₈)	D₆₅	direct (N × H)
40. C₅×C₇	C₂×C₃×D₁₃	semidirect
44. C₂×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
46. ΓL(1,𝔽₈)	C₂×D₆₅	direct (N × H)
50. C₂×C₇	C₃×D₆₅	semidirect
51. C₁₃	C₂×D₅×ΓL(1,𝔽₈)	semidirect
53. C₂×C₅	ΓL(1,𝔽₈)×D₁₃	semidirect
55. C₇	C₂×C₃×D₆₅	semidirect
58. C₅	C₂×ΓL(1,𝔽₈)×D₁₃	semidirect
62. C₂	ΓL(1,𝔽₈)×D₆₅	direct (N × H)

Subgroups — C2×ΓL(1,𝔽8)×D65 #19129809

Conjugacy classes of subgroups

Complements

Subgroups — C₂×ΓL(1,𝔽₈)×D₆₅ #19129809