Subgroups — C₅⋊#17987958 #37552051

Order 23310.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14556422	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊(D₃₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#17987958	—	5	1	no	maximal, Hall
4	C₅×C₇×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
5	C₅⋊(#66526⋊C₂)	—	7	1	no	maximal, Hall
6	C₇×D₁₈₅	C₉	1	1	yes	characteristic, complemented, Hall
7	#14556422	D₅	1	1	yes	characteristic, complemented, Hall
8	C₅×#66526	—	7	1	no	Hall
9	C₇×D₃₇⋊C₃	—	5	1	no	—
10	C₅×C₇×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅⋊(D₃₇⋊C₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₇×C₃₇⋊C₃	C₃×D₅	1	1	yes	characteristic
13	#66526⋊C₂	—	35	1	no	Hall
14	D₅×C₇⋊C₉	—	37	1	no	maximal, Hall
15	C₅×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₇×D₃₇	—	5	1	no	Hall
17	D₁₈₅	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
18	#66526	—	7	1	no	Hall
19	C₅×C₇⋊C₉	—	37	1	no	Hall
20	C₇×C₃₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
21	D₃₇⋊C₃	—	5	1	no	—
22	C₃×C₇×D₅	—	37	1	no	—
23	C₅×C₃₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇⋊C₉	—	185	1	no	Hall
25	C₃₇⋊C₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₃×C₅×C₇	—	37	1	no	—
27	C₉×D₅	—	259	1	no	Hall
28	D₃₇	—	5	1	no	Hall
29	C₇×D₅	—	333	1	no	Hall
30	C₇⋊C₉	—	37	1	no	Hall
31	C₅×C₉	—	259	1	no	Hall
32	C₂×C₃×C₇	—	185	1	no	—
33	C₃₇	D₅×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
34	C₅×C₇	#66526⋊C₂	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	37	1	no	—
36	C₃×C₇	—	37	1	no	—
37	C₂×C₉	—	1295	1	no	Hall
38	C₃×C₅	—	37	1	no	—
39	C₂×C₇	—	1665	1	no	Hall
40	D₅	—	37	1	no	Hall
41	C₉	—	259	1	no	Sylow
42	C₇	C₅⋊(#66526⋊C₂)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	185	1	no	—
44	C₅	#17987958	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	37	1	no	—
46	C₂	—	1665	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₃₇	C₂×C₉
prime radical	C₇×C₅⋊(D₃₇⋊C₃)	C₃
cosocle	C₅×C₇×C₃₇⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×#14556422	C₂	semidirect
6. C₇×D₁₈₅	C₉	semidirect
7. #14556422	D₅	semidirect
10. C₅×C₇×C₃₇	C₂×C₉	semidirect
17. D₁₈₅	C₇⋊C₉	semidirect
20. C₇×C₃₇	C₉×D₅	semidirect
23. C₅×C₃₇	C₂×C₇⋊C₉	semidirect
33. C₃₇	D₅×C₇⋊C₉	semidirect
34. C₅×C₇	#66526⋊C₂	semidirect
42. C₇	C₅⋊(#66526⋊C₂)	semidirect
44. C₅	#17987958	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14556422	2
C₇×C₅⋊(D₃₇⋊C₃)	3
#17987958	5
C₅⋊(#66526⋊C₂)	7
D₅×C₇⋊C₉	37

Subgroups — C5⋊#17987958 #37552051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#17987958 #37552051