Subgroups — C₅×C₅⋊D₅ #6958

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	C₅⋊D₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×D₅	—	5	6	no	maximal
4	C₅²	—	2	12	no	—
5	C₅²	D₅	1	6	yes	complemented
6	C₅²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₂×C₅	—	25	1	no	—
8	D₅	—	5	6	no	—
9	C₅	—	2	12	no	—
10	C₅	C₅×D₅	1	6	yes	complemented
11	C₅	C₅⋊D₅	1	1	yes	characteristic, direct product factor
12	C₂	—	25	1	no	Sylow

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

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.