Subgroups — C₈₈₁⋊C₂₅ #36347472

Order 22025.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈₈₁	C₅	1	1	yes	maximal, characteristic
2	C₈₈₁	C₂₅	1	1	yes	characteristic, complemented, Sylow
3	C₂₅	—	881	1	no	maximal, Sylow
4	C₅	C₈₈₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₈₈₁⋊C₅
commutator, hypocenter	C₈₈₁	C₂₅
Fitting, socle, prime radical, cosocle	C₅×C₈₈₁	C₅
LCS	G ▷ C₈₈₁
UCS	C₁ ◁ C₅

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

N	H ≅ G/N	type
2. C₈₈₁	C₂₅	semidirect

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

subgroup	index
C₅×C₈₈₁	5
C₂₅	881