Subgroups — C₅⋊#16838473 #34062157

Order 19110.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274263	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838473	—	5	1	no	maximal, Hall
4	C₅×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊#10587716	—	7	1	no	maximal
6	C₅⋊#10587716	—	7	1	no	maximal
7	C₅⋊#10587716	—	7	6	no	maximal
8	#14274263	D₅	1	1	yes	characteristic, complemented, Hall
9	D₅×#3861	—	13	1	no	maximal, Hall
10	C₅×#63270	—	7	1	no	—
11	C₅×#63270	—	7	1	no	—
12	C₅×#63270	—	7	6	no	—
13	C₇²×D₁₃	—	5	1	no	Hall
14	C₇×D₆₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
15	C₇×D₆₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	C₇×D₆₅	ΓL(1,𝔽₈)	1	6	yes	complemented
17	C₅×#3861	—	13	1	no	Hall
18	C₇²×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
19	#10587716	—	35	1	no	—
20	#10587716	—	35	1	no	—
21	#10587716	—	35	6	no	—
22	C₇²×D₅	—	39	1	no	Hall
23	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
25	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	6	yes	complemented
26	C₅⋊(D₁₃⋊C₃)	—	49	1	no	Hall
27	C₂×#3861	—	65	1	no	Hall
28	#63270	—	7	1	no	—
29	#63270	—	7	1	no	—
30	#63270	—	7	6	no	—
31	C₅×C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
32	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
33	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
34	D₅×ΓL(1,𝔽₈)	—	91	6	no	—
35	C₅×C₁₃⋊C₃	—	49	1	no	Hall
36	C₇×D₁₃	—	5	1	no	—
37	C₇×D₁₃	—	5	1	no	—
38	C₇×D₁₃	—	5	6	no	—
39	#3861	—	13	1	no	Hall
40	D₆₅	#3861	1	1	yes	characteristic, complemented, Hall
41	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
42	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
43	C₅×ΓL(1,𝔽₈)	—	91	6	no	—
44	C₂×C₇²	—	195	1	no	Hall
45	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
46	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
47	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	6	yes	complemented
48	D₁₃⋊C₃	—	245	1	no	Hall
49	C₇×D₅	—	13	1	no	—
50	C₇×D₅	—	39	1	no	—
51	C₇×D₅	—	39	6	no	—
52	C₅×C₁₃	C₂×#3861	1	1	yes	characteristic, complemented, Hall
53	C₇²	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
54	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
55	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
56	C₂×ΓL(1,𝔽₈)	—	455	6	no	—
57	C₁₃⋊C₃	—	49	1	no	Hall
58	C₅×C₇	#10587716	1	1	yes	characteristic, complemented
59	C₅×C₇	#10587716	1	1	yes	characteristic, complemented
60	C₅×C₇	#10587716	1	6	yes	complemented
61	C₃×D₅	—	637	1	no	Hall
62	D₁₃	—	5	1	no	Hall
63	ΓL(1,𝔽₈)	—	91	1	no	—
64	ΓL(1,𝔽₈)	—	91	1	no	—
65	ΓL(1,𝔽₈)	—	91	6	no	—
66	C₃×C₅	—	637	1	no	Hall
67	C₂×C₇	—	65	1	no	—
68	C₂×C₇	—	195	1	no	—
69	C₂×C₇	—	195	6	no	—
70	C₁₃	D₅×#3861	1	1	yes	characteristic, complemented, Sylow
71	D₅	—	39	1	no	Hall
72	C₇	C₅⋊#10587716	1	1	yes	characteristic, complemented
73	C₇	C₅⋊#10587716	1	1	yes	characteristic, complemented
74	C₇	C₅⋊#10587716	1	6	yes	complemented
75	C₂×C₃	—	3185	1	no	Hall
76	C₅	#16838473	1	1	yes	characteristic, complemented, Sylow
77	C₃	—	637	1	no	Sylow
78	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×#14274263	C₂	semidirect
2. C₇²×D₆₅	C₃	semidirect
4. C₅×C₇²×C₁₃	C₂×C₃	semidirect
8. #14274263	D₅	semidirect
14. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
15. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
16. C₇×D₆₅	ΓL(1,𝔽₈)	semidirect
18. C₇²×C₁₃	C₃×D₅	semidirect
23. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
24. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
25. C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	semidirect
31. C₅×C₇²	D₁₃⋊C₃	semidirect
40. D₆₅	#3861	semidirect
45. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
46. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
47. C₇×C₁₃	D₅×ΓL(1,𝔽₈)	semidirect
52. C₅×C₁₃	C₂×#3861	semidirect
53. C₇²	C₅⋊(D₁₃⋊C₃)	semidirect
58. C₅×C₇	#10587716	semidirect
59. C₅×C₇	#10587716	semidirect
60. C₅×C₇	#10587716	semidirect
70. C₁₃	D₅×#3861	semidirect
72. C₇	C₅⋊#10587716	semidirect
73. C₇	C₅⋊#10587716	semidirect
74. C₇	C₅⋊#10587716	semidirect
76. C₅	#16838473	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14274263	2
C₇²×D₆₅	3
#16838473	5
C₅⋊#10587716	7
D₅×#3861	13

Subgroups — C5⋊#16838473 #34062157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838473 #34062157