Subgroups — C₅×C₈₈₁⋊C₅ #36347474

Order 22025.

16 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, complemented
2	C₈₈₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
3	C₈₈₁	C₅²	1	1	yes	characteristic, complemented, Sylow
4	C₅²	—	881	1	no	maximal, Sylow
5	C₅	—	881	5	no	—
6	C₅	C₈₈₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₅	C₈₈₁⋊C₅
commutator, cosocle, hypocenter	C₈₈₁	C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₈₈₁	C₅
LCS	G ▷ C₈₈₁
UCS	C₁ ◁ C₅

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

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