Subgroups — C₅×C₃₇×D₃₅ #27188317

Order 12950.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₇×C₃₇	—	5	1	no	maximal
4	C₅×D₅×C₃₇	—	7	1	no	maximal, Hall
5	C₅×C₇×C₃₇	—	2	2	no	—
6	C₅×C₇×C₃₇	D₅	1	1	yes	characteristic, complemented
7	C₅×C₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₃₇	D₇	1	1	yes	characteristic, complemented, Hall
9	D₇×C₃₇	—	5	1	no	Hall
10	C₂×C₅×C₃₇	—	35	1	no	—
11	D₅×C₃₇	—	7	1	no	—
12	C₅×D₃₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇×C₃₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₃₇	—	2	2	no	—
15	C₅×C₃₇	C₅×D₇	1	1	yes	characteristic, complemented
16	C₅×C₃₇	D₃₅	1	1	yes	characteristic, direct product factor
17	C₅²×C₇	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃₇	—	35	1	no	Hall
19	D₃₅	C₅×C₃₇	1	1	yes	characteristic, direct product factor
20	C₅×D₇	—	5	1	no	—
21	C₅×D₅	—	7	1	no	Hall
22	C₃₇	C₅×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₅×C₇	—	2	2	no	—
24	C₅×C₇	D₅×C₃₇	1	1	yes	characteristic, complemented
25	C₅×C₇	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented
26	C₅²	D₇×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	D₇	—	5	1	no	Hall
28	C₂×C₅	—	35	1	no	—
29	D₅	—	7	1	no	—
30	C₇	C₅×D₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₅×D₇×C₃₇	1	1	yes	characteristic, complemented
33	C₅	C₃₇×D₃₅	1	1	yes	characteristic, direct product factor
34	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₇	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×C₃₇	C₂	semidirect
2. C₃₇×D₃₅	C₅	direct (N × H)
6. C₅×C₇×C₃₇	D₅	semidirect
7. C₅×C₇×C₃₇	C₂×C₅	semidirect
8. C₅²×C₃₇	D₇	semidirect
12. C₅×D₃₅	C₃₇	direct (N × H)
13. C₇×C₃₇	C₅×D₅	semidirect
15. C₅×C₃₇	C₅×D₇	semidirect
16. C₅×C₃₇	D₃₅	direct (N × H)
17. C₅²×C₇	C₂×C₃₇	semidirect
19. D₃₅	C₅×C₃₇	direct (N × H)
22. C₃₇	C₅×D₃₅	direct (N × H)
24. C₅×C₇	D₅×C₃₇	semidirect
25. C₅×C₇	C₂×C₅×C₃₇	semidirect
26. C₅²	D₇×C₃₇	semidirect
30. C₇	C₅×D₅×C₃₇	semidirect
32. C₅	C₅×D₇×C₃₇	semidirect
33. C₅	C₃₇×D₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₇×C₃₇	2
C₃₇×D₃₅	5
C₅×D₇×C₃₇	5
C₅×D₅×C₃₇	7
C₅×D₃₅	37

Subgroups — C5×C37×D35 #27188317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃₇×D₃₅ #27188317