Subgroups — C₅⋊(C₅⋊D₅) #6959

Order 250.

128 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	—	5	31	no	maximal
3	C₅²	D₅	1	31	yes	complemented
4	D₅	—	25	31	no	—
5	C₅	C₅⋊D₅	1	31	yes	complemented
6	C₂	—	125	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅³	C₂
LCS	G ▷ C₅³
UCS	C₁

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.

subgroup	index
C₅³	2
C₅⋊D₅	5