Subgroups — C₂×C₇×C₂₅×C₃₁ #24925738

Order 10850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₅×C₃₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₇×C₃₁	C₅	1	1	yes	maximal, characteristic
3	C₂×C₂₅×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₂₅×C₃₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇×C₃₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₇×C₂₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₃₁	C₅×C₇	1	1	yes	characteristic
9	C₇×C₃₁	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₂₅	C₂×C₃₁	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₃₁	C₂×C₅×C₇	1	1	yes	characteristic
12	C₂×C₅×C₇	C₅×C₃₁	1	1	yes	characteristic
13	C₂×C₃₁	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₂₅	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₇	C₂×C₅×C₃₁	1	1	yes	characteristic
16	C₃₁	C₂×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₅	C₂×C₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₇	C₂₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅	C₅×C₇×C₃₁	1	1	yes	characteristic
20	C₇	C₂×C₂₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₂×C₅×C₇×C₃₁	1	1	yes	characteristic
22	C₂	C₇×C₂₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₇×C₃₁
socle, prime radical	C₂×C₅×C₇×C₃₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₅×C₃₁	C₂	direct (N × H)
3. C₂×C₂₅×C₃₁	C₇	direct (N × H)
5. C₂₅×C₃₁	C₂×C₇	direct (N × H)
6. C₂×C₇×C₃₁	C₂₅	direct (N × H)
7. C₂×C₇×C₂₅	C₃₁	direct (N × H)
9. C₇×C₃₁	C₂×C₂₅	direct (N × H)
10. C₇×C₂₅	C₂×C₃₁	direct (N × H)
13. C₂×C₃₁	C₇×C₂₅	direct (N × H)
14. C₂×C₂₅	C₇×C₃₁	direct (N × H)
16. C₃₁	C₂×C₇×C₂₅	direct (N × H)
17. C₂₅	C₂×C₇×C₃₁	direct (N × H)
18. C₂×C₇	C₂₅×C₃₁	direct (N × H)
20. C₇	C₂×C₂₅×C₃₁	direct (N × H)
22. C₂	C₇×C₂₅×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
C₇×C₂₅×C₃₁	2
C₂×C₅×C₇×C₃₁	5
C₂×C₂₅×C₃₁	7
C₂×C₇×C₂₅	31

Subgroups — C2×C7×C25×C31 #24925738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₅×C₃₁ #24925738