Subgroups — D₂₅ #253

Order 50.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₅	—	5	1	no	maximal
3	C₅	D₅	1	1	yes	characteristic
4	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅	C₂
Frattini, socle	C₅	D₅
LCS	G ▷ C₂₅
UCS	C₁

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

N	H ≅ G/N	type
1. C₂₅	C₂	semidirect

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

subgroup	index
C₂₅	2
D₅	5