Subgroups — C₅⋊D₅ #256

Order 50.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₅	—	5	6	no	maximal
3	C₅	D₅	1	6	yes	complemented
4	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁

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

N	H ≅ G/N	type
1. C₅²	C₂	semidirect
3. C₅	D₅	semidirect

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

subgroup	index
C₅²	2
D₅	5