Subgroups — D₆₅×#3861 #34062161

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₃×#3861	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	ΓL(1,𝔽₈)×D₆₅	—	7	8	no	maximal
6	C₁₃×#3861	D₅	1	1	yes	characteristic, complemented, Hall
7	D₅×#3861	—	13	1	no	maximal, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
9	C₇²×D₁₃	—	5	1	no	Hall
10	C₇×D₆₅	ΓL(1,𝔽₈)	1	8	yes	complemented
11	C₅×#3861	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	ΓL(1,𝔽₈)×D₁₃	—	35	8	no	—
14	C₇²×D₅	—	13	1	no	Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₃×D₆₅	—	49	1	no	Hall
17	C₂×#3861	—	65	1	no	Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	8	no	—
19	C₅×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
20	D₅×ΓL(1,𝔽₈)	—	91	8	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₇×D₁₃	—	5	8	no	—
23	#3861	D₆₅	1	1	yes	characteristic, direct product factor, Hall
24	D₆₅	#3861	1	1	yes	characteristic, direct product factor, Hall
25	C₅×ΓL(1,𝔽₈)	—	7	8	no	—
26	C₂×C₇²	—	65	1	no	Hall
27	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	8	yes	complemented
28	C₃×D₁₃	—	245	1	no	Hall
29	C₇×D₅	—	13	8	no	—
30	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	455	8	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	ΓL(1,𝔽₈)×D₁₃	1	8	yes	complemented
35	C₃×D₅	—	637	1	no	Hall
36	D₁₃	—	5	1	no	Hall
37	ΓL(1,𝔽₈)	—	7	8	no	—
38	C₃×C₅	—	49	1	no	Hall
39	C₂×C₇	—	65	8	no	—
40	C₁₃	D₅×#3861	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	13	1	no	Hall
42	C₇	ΓL(1,𝔽₈)×D₆₅	1	8	yes	complemented
43	C₂×C₃	—	3185	1	no	Hall
44	C₅	D₁₃×#3861	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	49	1	no	Sylow
46	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×#3861	C₂	semidirect
2. C₇²×D₆₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
6. C₁₃×#3861	D₅	semidirect
10. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
11. C₅×#3861	D₁₃	semidirect
12. C₇²×C₁₃	C₃×D₅	semidirect
15. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
19. C₅×C₇²	C₃×D₁₃	semidirect
23. #3861	D₆₅	direct (N × H)
24. D₆₅	#3861	direct (N × H)
27. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
30. C₅×C₁₃	C₂×#3861	semidirect
31. C₇²	C₃×D₆₅	semidirect
34. C₅×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
40. C₁₃	D₅×#3861	semidirect
42. C₇	ΓL(1,𝔽₈)×D₆₅	semidirect
44. C₅	D₁₃×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×#3861	2
C₇²×D₆₅	3
D₁₃×#3861	5
ΓL(1,𝔽₈)×D₆₅	7
D₅×#3861	13

Subgroups — D65×#3861 #34062161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₅×#3861 #34062161