Subgroups — C₅⋊#16838474 #34062158

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274262	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838474	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊#10587717	—	7	3	no	maximal
6	C₅⋊#10587717	—	7	5	no	maximal
7	#14274262	D₅	1	1	yes	characteristic, complemented, Hall
8	D₅×#3861	—	13	1	no	maximal, Hall
9	C₅×#63271	—	7	3	no	—
10	C₅×#63271	—	7	5	no	—
11	C₇²×D₁₃	—	5	1	no	Hall
12	C₇×D₆₅	ΓL(1,𝔽₈)	1	3	yes	complemented
13	C₇×D₆₅	ΓL(1,𝔽₈)	1	5	yes	complemented
14	C₅×#3861	—	13	1	no	Hall
15	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
16	#10587717	—	35	3	no	—
17	#10587717	—	35	5	no	—
18	C₇²×D₅	—	39	1	no	Hall
19	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	3	yes	complemented
20	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	5	yes	complemented
21	C₅⋊(D₁₃⋊C₃)	—	49	1	no	Hall
22	C₂×#3861	—	65	1	no	Hall
23	#63271	—	7	3	no	—
24	#63271	—	7	5	no	—
25	C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	D₅×ΓL(1,𝔽₈)	—	91	3	no	—
27	D₅×ΓL(1,𝔽₈)	—	91	5	no	—
28	C₅×C₁₃⋊C₃	—	49	1	no	Hall
29	C₇×D₁₃	—	5	3	no	—
30	C₇×D₁₃	—	5	5	no	—
31	#3861	—	13	1	no	Hall
32	D₆₅	#3861	1	1	yes	characteristic, complemented, Hall
33	C₅×ΓL(1,𝔽₈)	—	91	3	no	—
34	C₅×ΓL(1,𝔽₈)	—	91	5	no	—
35	C₂×C₇²	—	195	1	no	Hall
36	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	3	yes	complemented
37	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	5	yes	complemented
38	D₁₃⋊C₃	—	245	1	no	Hall
39	C₇×D₅	—	39	3	no	—
40	C₇×D₅	—	39	5	no	—
41	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
42	C₇²	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
43	C₂×ΓL(1,𝔽₈)	—	455	3	no	—
44	C₂×ΓL(1,𝔽₈)	—	455	5	no	—
45	C₁₃⋊C₃	—	49	1	no	Hall
46	C₅×C₇	#10587717	1	3	yes	complemented
47	C₅×C₇	#10587717	1	5	yes	complemented
48	C₃×D₅	—	637	1	no	Hall
49	D₁₃	—	5	1	no	Hall
50	ΓL(1,𝔽₈)	—	91	3	no	—
51	ΓL(1,𝔽₈)	—	91	5	no	—
52	C₃×C₅	—	637	1	no	Hall
53	C₂×C₇	—	65	3	no	—
54	C₂×C₇	—	195	5	no	—
55	C₁₃	D₅×#3861	1	1	yes	characteristic, complemented, Sylow
56	D₅	—	39	1	no	Hall
57	C₇	C₅⋊#10587717	1	3	yes	complemented
58	C₇	C₅⋊#10587717	1	5	yes	complemented
59	C₂×C₃	—	3185	1	no	Hall
60	C₅	#16838474	1	1	yes	characteristic, complemented, Sylow
61	C₃	—	637	1	no	Sylow
62	C₂	—	195	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×#14274262	C₂	semidirect
2. C₇²×D₆₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
7. #14274262	D₅	semidirect
12. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
13. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
15. C₇²×C₁₃	C₃×D₅	semidirect
19. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
20. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
25. C₅×C₇²	D₁₃⋊C₃	semidirect
32. D₆₅	#3861	semidirect
36. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
37. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
41. C₅×C₁₃	C₂×#3861	semidirect
42. C₇²	C₅⋊(D₁₃⋊C₃)	semidirect
46. C₅×C₇	#10587717	semidirect
47. C₅×C₇	#10587717	semidirect
55. C₁₃	D₅×#3861	semidirect
57. C₇	C₅⋊#10587717	semidirect
58. C₇	C₅⋊#10587717	semidirect
60. C₅	#16838474	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14274262	2
C₇²×D₆₅	3
#16838474	5
C₅⋊#10587717	7
D₅×#3861	13

Subgroups — C5⋊#16838474 #34062158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838474 #34062158