Subgroups — C₅²×C₂₅₁⋊C₅ #44535911

Order 31375.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₅₁	C₅	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂₅₁⋊C₅	C₅	1	30	yes	maximal, direct product factor
3	C₅×C₂₅₁	C₅²	1	6	yes	complemented
4	C₂₅₁⋊C₅	C₅²	1	25	yes	direct product factor
5	C₂₅₁	C₅³	1	1	yes	characteristic, complemented, Sylow
6	C₅³	—	251	1	no	maximal, Sylow
7	C₅²	—	251	30	no	—
8	C₅²	C₂₅₁⋊C₅	1	1	yes	characteristic, direct product factor
9	C₅	—	251	25	no	—
10	C₅	C₅×C₂₅₁⋊C₅	1	6	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₅²	C₂₅₁⋊C₅
commutator, cosocle, hypocenter	C₂₅₁	C₅³
Frattini	C₁	G
Fitting, socle	C₅²×C₂₅₁	C₅
LCS	G ▷ C₂₅₁
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.