Finite Group Databasebeta

← C₂₁₄₁⋊C₅ #24924172

Subgroups — C₂₁₄₁⋊C₅ #24924172

Order 10705.

4 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₁₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₅	—	2141	1	no	maximal, Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₁₄₁	C₅
LCS	G ▷ C₂₁₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₁₄₁	C₅	semidirect