Subgroups — C₂₅² #10597825

Order 625.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₅	C₅	1	6	yes	maximal
2	C₅²	C₅²	1	1	yes	characteristic
3	C₂₅	C₂₅	1	30	yes	direct product factor
4	C₅	C₅×C₂₅	1	6	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, socle, prime radical, cosocle	C₅²	C₅²
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₅² ▷ C₁

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

N	H ≅ G/N	type
3. C₂₅	C₂₅	direct (N × H)

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

subgroup	index
C₅×C₂₅	5