Subgroups — C₅²×D₅ #6957

Order 250.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂×C₅²	—	5	1	no	maximal
3	C₅×D₅	C₅	1	6	yes	maximal, direct product factor
4	C₅²	—	2	12	no	—
5	C₅²	D₅	1	1	yes	characteristic, direct product factor
6	C₅²	C₂×C₅	1	6	yes	complemented
7	C₂×C₅	—	5	6	no	—
8	D₅	C₅²	1	1	yes	characteristic, direct product factor
9	C₅	—	2	12	no	—
10	C₅	C₅×D₅	1	6	yes	direct product factor
11	C₅	C₂×C₅²	1	1	yes	characteristic, complemented
12	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅³	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₅²

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.