Finite Group Databasebeta

← C₄×C₂₅×C₁₀₇ #24924131

Subgroups — C₄×C₂₅×C₁₀₇ #24924131

Order 10700.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂₅×C₁₀₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅×C₁₀₇	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₀₇	C₂×C₅	1	1	yes	characteristic
5	C₅×C₁₀₇	C₄×C₅	1	1	yes	characteristic
6	C₄×C₁₀₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₀₇	C₂×C₂₅	1	1	yes	characteristic
8	C₁₀₇	C₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₄×C₂₅	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₂₅	C₂×C₁₀₇	1	1	yes	characteristic
11	C₂₅	C₄×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₅	C₅×C₁₀₇	1	1	yes	characteristic
13	C₂×C₅	C₂×C₅×C₁₀₇	1	1	yes	characteristic
14	C₅	C₄×C₅×C₁₀₇	1	1	yes	characteristic
15	C₄	C₂₅×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₂₅×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅×C₁₀₇
socle, prime radical	C₂×C₅×C₁₀₇	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₅×C₁₀₇	C₄	direct (N × H)
6. C₄×C₁₀₇	C₂₅	direct (N × H)
8. C₁₀₇	C₄×C₂₅	direct (N × H)
9. C₄×C₂₅	C₁₀₇	direct (N × H)
11. C₂₅	C₄×C₁₀₇	direct (N × H)
15. C₄	C₂₅×C₁₀₇	direct (N × H)