Subgroups — C₅⋊#16838466 #34062149

Order 19110.

68 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	C₇×D₄₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838466	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	—	7	1	no	maximal
6	ΓL(1,𝔽₈)×D₆₅	—	7	1	no	maximal
7	C₁₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅⋊#64422	—	13	1	no	maximal, Hall
9	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₇×D₉₁	—	5	1	no	Hall
12	D₄₅₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₇×D₆₅	—	21	1	no	—
14	C₅×#3862	D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
16	ΓL(1,𝔽₈)⋊D₁₃	—	35	1	no	—
17	ΓL(1,𝔽₈)×D₁₃	—	35	1	no	—
18	C₇×D₃₅	—	13	1	no	Hall
19	C₅×C₇×C₁₃	—	6	1	no	—
20	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
21	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₃×D₆₅	—	49	1	no	Hall
23	#64422	—	65	1	no	Hall
24	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
25	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₅×C₇²	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
27	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
28	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
29	C₃×C₅×C₁₃	—	49	1	no	Hall
30	D₉₁	—	5	1	no	—
31	C₇×D₁₃	—	105	1	no	—
32	#3862	D₆₅	1	1	yes	characteristic, complemented, Hall
33	D₆₅	—	21	1	no	Hall
34	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
35	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
36	C₇×D₇	—	65	1	no	Hall
37	C₇×C₁₃	—	6	1	no	—
38	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
40	C₃×D₁₃	—	245	1	no	Hall
41	D₃₅	—	13	1	no	—
42	C₇×D₅	—	273	1	no	—
43	C₅×C₁₃	#64422	1	1	yes	characteristic, complemented, Hall
44	C₇²	C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
46	AGL(1,𝔽₇)	—	455	1	no	—
47	C₃×C₁₃	—	49	1	no	Hall
48	C₅×C₇	—	6	1	no	—
49	C₅×C₇	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic, complemented
50	C₅×C₇	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic, complemented
51	C₃×D₅	—	637	1	no	Hall
52	D₁₃	—	105	1	no	Hall
53	ΓL(1,𝔽₈)	—	7	1	no	—
54	ΓL(1,𝔽₈)	—	7	1	no	—
55	C₃×C₅	—	49	1	no	Hall
56	C₂×C₇	—	1365	1	no	—
57	D₇	—	65	1	no	—
58	C₁₃	C₅⋊#64422	1	1	yes	characteristic, complemented, Sylow
59	D₅	—	273	1	no	Hall
60	C₇	—	6	1	no	—
61	C₇	ΓL(1,𝔽₈)×D₆₅	1	1	yes	characteristic, complemented
62	C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	1	1	yes	characteristic, complemented
63	C₂×C₃	—	3185	1	no	Hall
64	C₅	#16838466	1	1	yes	characteristic, complemented, Sylow
65	C₃	—	49	1	no	Sylow
66	C₂	—	1365	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. C₇×D₄₅₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. C₁₃×#3862	D₅	semidirect
12. D₄₅₅	ΓL(1,𝔽₈)	semidirect
14. C₅×#3862	D₁₃	semidirect
15. C₇²×C₁₃	C₃×D₅	semidirect
20. C₅×C₇×C₁₃	AGL(1,𝔽₇)	semidirect
21. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
26. C₅×C₇²	C₃×D₁₃	semidirect
32. #3862	D₆₅	semidirect
38. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
39. C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	semidirect
43. C₅×C₁₃	#64422	semidirect
44. C₇²	C₃×D₆₅	semidirect
49. C₅×C₇	ΓL(1,𝔽₈)×D₁₃	semidirect
50. C₅×C₇	ΓL(1,𝔽₈)⋊D₁₃	semidirect
58. C₁₃	C₅⋊#64422	semidirect
61. C₇	ΓL(1,𝔽₈)×D₆₅	semidirect
62. C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	semidirect
64. C₅	#16838466	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
C₇×D₄₅₅	3
#16838466	5
C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	7
ΓL(1,𝔽₈)×D₆₅	7
C₅⋊#64422	13

Subgroups — C5⋊#16838466 #34062149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838466 #34062149