Subgroups — C₇⋊#16814886 #39906005

Order 25900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₇×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇⋊#10625193	—	5	1	no	maximal
4	Dic₁₂₉₅	—	5	1	no	maximal
5	#16814886	—	7	1	no	maximal, Hall
6	C₇×D₅×C₃₇	D₅	1	1	yes	characteristic
7	C₂×C₅×C₇×C₃₇	—	5	1	no	—
8	C₅×D₅×C₃₇	D₇	1	1	yes	characteristic
9	C₅×C₇×C₃₇	—	4	1	no	—
10	C₅×C₇×C₃₇	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	Dic₂₅₉	—	25	1	no	Hall
13	C₅²×C₃₇	Dic₇	1	1	yes	characteristic, complemented, Hall
14	#10625193	—	35	1	no	—
15	Dic₁₈₅	—	35	1	no	—
16	C₇⋊#1042	—	37	1	no	maximal, Hall
17	C₂×C₇×C₃₇	—	5	1	no	—
18	C₂×C₅×C₃₇	—	5	1	no	—
19	D₅×C₃₇	D₃₅	1	1	yes	characteristic
20	C₅×C₇×D₅	D₃₇	1	1	yes	characteristic
21	C₇×C₃₇	#1042	1	1	yes	characteristic, complemented, Hall
22	C₅×C₃₇	—	4	1	no	—
23	C₅×C₃₇	Dic₃₅	1	1	yes	characteristic, complemented
24	C₅×C₃₇	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
25	C₅²×C₇	Dic₃₇	1	1	yes	characteristic, complemented, Hall
26	Dic₃₇	—	175	1	no	Hall
27	C₇⋊AGL(1,𝔽₅)	—	185	1	no	—
28	Dic₃₅	—	185	1	no	—
29	#1042	—	259	1	no	Hall
30	C₂×C₃₇	—	5	1	no	—
31	C₂×C₅×C₇	—	5	1	no	—
32	C₇×D₅	D₁₈₅	1	1	yes	characteristic
33	C₅×D₅	D₂₅₉	1	1	yes	characteristic
34	C₃₇	C₇⋊#1042	1	1	yes	characteristic, complemented, Sylow
35	C₅×C₇	—	4	1	no	—
36	C₅×C₇	Dic₁₈₅	1	1	yes	characteristic, complemented
37	C₅×C₇	#10625193	1	1	yes	characteristic, complemented
38	Dic₇	—	925	1	no	Hall
39	C₅²	Dic₂₅₉	1	1	yes	characteristic, complemented, Sylow
40	AGL(1,𝔽₅)	—	1295	1	no	—
41	Dic₅	—	1295	1	no	—
42	C₂×C₇	—	5	1	no	—
43	C₂×C₅	—	5	1	no	—
44	D₅	D₁₂₉₅	1	1	yes	characteristic
45	C₇	#16814886	1	1	yes	characteristic, complemented, Sylow
46	C₅	—	4	1	no	—
47	C₅	Dic₁₂₉₅	1	1	yes	characteristic, complemented
48	C₅	C₇⋊#10625193	1	1	yes	characteristic, complemented
49	C₄	—	6475	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇×C₃₇	C₄
prime radical, cosocle	C₅×C₇×D₅×C₃₇	C₂
LCS	G ▷ C₅²×C₇×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₇×C₃₇	C₄	semidirect
10. C₅×C₇×C₃₇	Dic₅	semidirect
11. C₅×C₇×C₃₇	AGL(1,𝔽₅)	semidirect
13. C₅²×C₃₇	Dic₇	semidirect
21. C₇×C₃₇	#1042	semidirect
23. C₅×C₃₇	Dic₃₅	semidirect
24. C₅×C₃₇	C₇⋊AGL(1,𝔽₅)	semidirect
25. C₅²×C₇	Dic₃₇	semidirect
34. C₃₇	C₇⋊#1042	semidirect
36. C₅×C₇	Dic₁₈₅	semidirect
37. C₅×C₇	#10625193	semidirect
39. C₅²	Dic₂₅₉	semidirect
45. C₇	#16814886	semidirect
47. C₅	Dic₁₂₉₅	semidirect
48. C₅	C₇⋊#10625193	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×D₅×C₃₇	2
C₇⋊#10625193	5
Dic₁₂₉₅	5
#16814886	7
C₇⋊#1042	37

Subgroups — C7⋊#16814886 #39906005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊#16814886 #39906005