Subgroups — C₇×#19127086 #49150708

Order 37100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₂₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×#11761508	—	5	1	no	maximal
4	C₇×#11761506	—	5	1	no	maximal
5	#19127086	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×D₂₆₅	D₅	1	1	yes	characteristic
7	C₅×C₇×D₅₃	—	5	1	no	—
8	C₅×D₂₆₅	C₂×C₇	1	1	yes	characteristic
9	C₅×C₇×C₅₃	—	4	1	no	—
10	C₅×C₇×C₅₃	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₅₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₇×#6157	—	25	1	no	Hall
13	C₅²×C₅₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	#11761508	—	5	1	no	—
15	#11761506	—	5	1	no	—
16	C₇×D₅₃	—	5	1	no	—
17	C₇×#1042	—	53	1	no	maximal, Hall
18	D₂₆₅	C₇×D₅	1	1	yes	characteristic
19	C₅×D₅₃	—	5	1	no	—
20	C₇×C₅₃	#1042	1	1	yes	characteristic, complemented, Hall
21	C₅×C₇×D₅	—	53	1	no	—
22	C₅×C₅₃	—	4	1	no	—
23	C₅×C₅₃	C₇×Dic₅	1	1	yes	characteristic, complemented
24	C₅×C₅₃	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	#6157	—	25	1	no	Hall
26	C₅²×C₇	#6157	1	1	yes	characteristic, complemented, Hall
27	C₇×AGL(1,𝔽₅)	—	265	1	no	—
28	C₇×Dic₅	—	265	1	no	—
29	D₅₃	—	5	1	no	—
30	#1042	—	53	1	no	Hall
31	C₂×C₅×C₇	—	265	1	no	—
32	C₇×D₅	—	53	1	no	—
33	C₅₃	C₇×#1042	1	1	yes	characteristic, complemented, Sylow
34	C₅×D₅	—	53	1	no	—
35	C₅×C₇	—	4	1	no	—
36	C₅×C₇	#11761506	1	1	yes	characteristic, complemented
37	C₅×C₇	#11761508	1	1	yes	characteristic, complemented
38	C₄×C₇	—	1325	1	no	Hall
39	C₅²	C₇×#6157	1	1	yes	characteristic, complemented, Sylow
40	AGL(1,𝔽₅)	—	265	1	no	—
41	Dic₅	—	265	1	no	—
42	C₂×C₇	—	265	1	no	—
43	C₂×C₅	—	265	1	no	—
44	D₅	—	53	1	no	—
45	C₇	#19127086	1	1	yes	characteristic, direct product factor, Sylow
46	C₅	—	4	1	no	—
47	C₅	C₇×#11761506	1	1	yes	characteristic, complemented
48	C₅	C₇×#11761508	1	1	yes	characteristic, complemented
49	C₄	—	1325	1	no	Sylow
50	C₂	—	265	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#19127086
commutator, hypocenter	C₅²×C₅₃	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₅₃	C₄
prime radical	C₅×C₇×D₂₆₅	C₂
cosocle	C₅×D₂₆₅	C₂×C₇
LCS	G ▷ C₅²×C₅₃
UCS	C₁ ◁ C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅²×C₇×C₅₃	C₄	semidirect
5. #19127086	C₇	direct (N × H)
10. C₅×C₇×C₅₃	Dic₅	semidirect
11. C₅×C₇×C₅₃	AGL(1,𝔽₅)	semidirect
13. C₅²×C₅₃	C₄×C₇	semidirect
20. C₇×C₅₃	#1042	semidirect
23. C₅×C₅₃	C₇×Dic₅	semidirect
24. C₅×C₅₃	C₇×AGL(1,𝔽₅)	semidirect
26. C₅²×C₇	#6157	semidirect
33. C₅₃	C₇×#1042	semidirect
36. C₅×C₇	#11761506	semidirect
37. C₅×C₇	#11761508	semidirect
39. C₅²	C₇×#6157	semidirect
45. C₇	#19127086	direct (N × H)
47. C₅	C₇×#11761506	semidirect
48. C₅	C₇×#11761508	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₂₆₅	2
C₇×#11761508	5
C₇×#11761506	5
#19127086	7
C₇×#1042	53

Subgroups — C7×#19127086 #49150708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19127086 #49150708