Subgroups — D₆₅×#3862 #34062165

Order 19110.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₃×#3862	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	ΓL(1,𝔽₈)×D₆₅	—	7	2	no	maximal
6	C₁₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
7	D₅×#3862	—	13	1	no	maximal, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
9	C₇²×D₁₃	—	5	1	no	Hall
10	C₇×D₆₅	—	3	2	no	—
11	C₇×D₆₅	ΓL(1,𝔽₈)	1	2	yes	complemented
12	C₅×#3862	D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
14	ΓL(1,𝔽₈)×D₁₃	—	35	2	no	—
15	C₇²×D₅	—	13	1	no	Hall
16	C₅×C₇×C₁₃	—	3	2	no	—
17	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
18	C₃×D₆₅	—	49	1	no	Hall
19	C₂×#3862	—	65	1	no	Hall
20	C₁₃×ΓL(1,𝔽₈)	—	7	2	no	—
21	C₅×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
22	D₅×ΓL(1,𝔽₈)	—	91	2	no	—
23	C₃×C₅×C₁₃	—	49	1	no	Hall
24	C₇×D₁₃	—	5	2	no	—
25	C₇×D₁₃	—	15	2	no	—
26	#3862	D₆₅	1	1	yes	characteristic, direct product factor, Hall
27	D₆₅	#3862	1	1	yes	characteristic, direct product factor, Hall
28	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
29	C₂×C₇²	—	65	1	no	Hall
30	C₇×C₁₃	—	3	2	no	—
31	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	2	yes	complemented
32	C₃×D₁₃	—	245	1	no	Hall
33	C₇×D₅	—	13	2	no	—
34	C₇×D₅	—	39	2	no	—
35	C₅×C₁₃	C₂×#3862	1	1	yes	characteristic, complemented, Hall
36	C₇²	C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
37	C₂×ΓL(1,𝔽₈)	—	455	2	no	—
38	C₃×C₁₃	—	49	1	no	Hall
39	C₅×C₇	—	3	2	no	—
40	C₅×C₇	ΓL(1,𝔽₈)×D₁₃	1	2	yes	complemented
41	C₃×D₅	—	637	1	no	Hall
42	D₁₃	—	5	1	no	Hall
43	ΓL(1,𝔽₈)	—	7	2	no	—
44	C₃×C₅	—	49	1	no	Hall
45	C₂×C₇	—	65	2	no	—
46	C₂×C₇	—	195	2	no	—
47	C₁₃	D₅×#3862	1	1	yes	characteristic, complemented, Sylow
48	D₅	—	13	1	no	Hall
49	C₇	—	3	2	no	—
50	C₇	ΓL(1,𝔽₈)×D₆₅	1	2	yes	complemented
51	C₂×C₃	—	3185	1	no	Hall
52	C₅	D₁₃×#3862	1	1	yes	characteristic, complemented, Sylow
53	C₃	—	49	1	no	Sylow
54	C₂	—	65	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×#3862	C₂	semidirect
2. C₇²×D₆₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃×#3862	D₅	semidirect
11. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
12. C₅×#3862	D₁₃	semidirect
13. C₇²×C₁₃	C₃×D₅	semidirect
17. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
21. C₅×C₇²	C₃×D₁₃	semidirect
26. #3862	D₆₅	direct (N × H)
27. D₆₅	#3862	direct (N × H)
31. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
35. C₅×C₁₃	C₂×#3862	semidirect
36. C₇²	C₃×D₆₅	semidirect
40. C₅×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
47. C₁₃	D₅×#3862	semidirect
50. C₇	ΓL(1,𝔽₈)×D₆₅	semidirect
52. C₅	D₁₃×#3862	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×#3862	2
C₇²×D₆₅	3
D₁₃×#3862	5
ΓL(1,𝔽₈)×D₆₅	7
D₅×#3862	13

Subgroups — D65×#3862 #34062165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₅×#3862 #34062165