Finite Group Databasebeta

← C₄₃₁⋊C₂₅ #24924678

Subgroups — C₄₃₁⋊C₂₅ #24924678

Order 10775.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₃₁	C₅	1	1	yes	maximal, characteristic
2	C₄₃₁	C₂₅	1	1	yes	characteristic, complemented, Sylow
3	C₂₅	—	431	1	no	maximal, Sylow
4	C₅	C₄₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₄₃₁⋊C₅
commutator, hypocenter	C₄₃₁	C₂₅
Fitting, socle, prime radical, cosocle	C₅×C₄₃₁	C₅
LCS	G ▷ C₄₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
2. C₄₃₁	C₂₅	semidirect