Subgroups — C₅×C₇×D₅×C₃₁ #24925766

Order 10850.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₅×C₇×C₃₁	—	5	1	no	maximal
4	C₅×D₅×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×C₃₁	—	2	2	no	—
6	C₅×C₇×C₃₁	D₅	1	1	yes	characteristic, direct product factor
7	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₃₁	—	5	1	no	Hall
10	C₅×C₇×D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₃₁	—	5	1	no	—
12	D₅×C₃₁	C₅×C₇	1	1	yes	characteristic, direct product factor
13	C₇×C₃₁	C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₅²×C₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
15	C₅×C₃₁	—	2	2	no	—
16	C₅×C₃₁	C₇×D₅	1	1	yes	characteristic, direct product factor
17	C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
18	C₂×C₅×C₇	—	5	1	no	—
19	C₇×D₅	C₅×C₃₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃₁	—	5	1	no	Hall
21	C₅×D₅	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₇	—	2	2	no	—
23	C₅×C₇	D₅×C₃₁	1	1	yes	characteristic, direct product factor
24	C₅×C₇	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
25	C₃₁	C₅×C₇×D₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₅²	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₇	—	5	1	no	Hall
28	C₂×C₅	—	5	1	no	—
29	D₅	C₅×C₇×C₃₁	1	1	yes	characteristic, direct product factor
30	C₇	C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₅	—	2	2	no	—
32	C₅	C₂×C₅×C₇×C₃₁	1	1	yes	characteristic, complemented
33	C₅	C₇×D₅×C₃₁	1	1	yes	characteristic, direct product factor
34	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₃₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₅×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₅×C₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×C₃₁	C₂	semidirect
2. C₇×D₅×C₃₁	C₅	direct (N × H)
4. C₅×D₅×C₃₁	C₇	direct (N × H)
6. C₅×C₇×C₃₁	D₅	direct (N × H)
7. C₅×C₇×C₃₁	C₂×C₅	semidirect
8. C₅²×C₃₁	C₂×C₇	semidirect
10. C₅×C₇×D₅	C₃₁	direct (N × H)
12. D₅×C₃₁	C₅×C₇	direct (N × H)
13. C₇×C₃₁	C₅×D₅	direct (N × H)
14. C₅²×C₇	C₂×C₃₁	semidirect
16. C₅×C₃₁	C₇×D₅	direct (N × H)
17. C₅×C₃₁	C₂×C₅×C₇	semidirect
19. C₇×D₅	C₅×C₃₁	direct (N × H)
21. C₅×D₅	C₇×C₃₁	direct (N × H)
23. C₅×C₇	D₅×C₃₁	direct (N × H)
24. C₅×C₇	C₂×C₅×C₃₁	semidirect
25. C₃₁	C₅×C₇×D₅	direct (N × H)
26. C₅²	C₂×C₇×C₃₁	semidirect
29. D₅	C₅×C₇×C₃₁	direct (N × H)
30. C₇	C₅×D₅×C₃₁	direct (N × H)
32. C₅	C₂×C₅×C₇×C₃₁	semidirect
33. C₅	C₇×D₅×C₃₁	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×C₃₁	2
C₇×D₅×C₃₁	5
C₂×C₅×C₇×C₃₁	5
C₅×D₅×C₃₁	7
C₅×C₇×D₅	31

Subgroups — C5×C7×D5×C31 #24925766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₅×C₃₁ #24925766