Subgroups — Dic₂₅ #1033

Order 100.

9 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₂₅	C₄	1	1	yes	characteristic, complemented, Sylow
3	Dic₅	—	5	1	no	maximal
4	C₂×C₅	D₅	1	1	yes	characteristic
5	C₅	Dic₅	1	1	yes	characteristic
6	C₄	—	25	1	no	Sylow
7	C₂	D₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₂₅
commutator, hypocenter	C₂₅	C₄
Frattini, socle, prime radical	C₂×C₅	D₅
Fitting, cosocle	C₂×C₂₅	C₂
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂

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

N	H ≅ G/N	type
2. C₂₅	C₄	semidirect

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

subgroup	index
C₂×C₂₅	2
Dic₅	5