Subgroups — C₅×C₇×D₃₁⋊C₅ #24925751

Order 10850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₇×D₃₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₇×ΓL(1,𝔽₃₂)	C₂×C₅	1	5	yes	complemented
7	C₅×ΓL(1,𝔽₃₂)	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₃₁	C₅²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅²×C₇	—	31	1	no	maximal, Hall
10	C₅×D₃₁	C₅×C₇	1	1	yes	characteristic, complemented
11	D₃₁⋊C₅	C₅×C₇	1	5	yes	direct product factor
12	C₇×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅²×C₇	—	31	1	no	Hall
14	C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
15	ΓL(1,𝔽₃₂)	C₂×C₅×C₇	1	5	yes	complemented
16	C₂×C₅×C₇	—	31	5	no	—
17	C₂×C₅×C₇	—	31	1	no	—
18	D₃₁	C₅²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅²	—	31	1	no	Hall
20	C₅×C₇	—	31	5	no	—
21	C₅×C₇	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
22	C₃₁	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Sylow
23	C₅²	—	31	1	no	Sylow
24	C₂×C₇	—	31	1	no	Hall
25	C₂×C₅	—	31	5	no	—
26	C₂×C₅	—	31	1	no	—
27	C₇	C₅×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
28	C₅	—	31	5	no	—
29	C₅	C₇×D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
30	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃₁⋊C₅
commutator, cosocle, hypocenter	C₃₁	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₁	C₂×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₇×D₃₁⋊C₅	C₅	direct (N × H)
3. C₅×C₇×D₃₁	C₅	semidirect
4. C₅×D₃₁⋊C₅	C₇	direct (N × H)
5. C₅×C₇×C₃₁	C₂×C₅	semidirect
6. C₇×ΓL(1,𝔽₃₂)	C₂×C₅	semidirect
7. C₅×ΓL(1,𝔽₃₂)	C₂×C₇	semidirect
8. C₇×D₃₁	C₅²	semidirect
10. C₅×D₃₁	C₅×C₇	semidirect
11. D₃₁⋊C₅	C₅×C₇	direct (N × H)
12. C₇×C₃₁	C₂×C₅²	semidirect
14. C₅×C₃₁	C₂×C₅×C₇	semidirect
15. ΓL(1,𝔽₃₂)	C₂×C₅×C₇	semidirect
18. D₃₁	C₅²×C₇	semidirect
21. C₅×C₇	D₃₁⋊C₅	direct (N × H)
22. C₃₁	C₂×C₅²×C₇	semidirect
27. C₇	C₅×D₃₁⋊C₅	direct (N × H)
29. C₅	C₇×D₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×ΓL(1,𝔽₃₂)	2
C₇×D₃₁⋊C₅	5
C₅×C₇×D₃₁	5
C₅×D₃₁⋊C₅	7
C₂×C₅²×C₇	31

Subgroups — C5×C7×D31⋊C5 #24925751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₃₁⋊C₅ #24925751