Subgroups — C₅²×C₂₁₁⋊C₅ #40995809

Order 26375.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₁₁	C₅	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂₁₁⋊C₅	C₅	1	30	yes	maximal, direct product factor
3	C₅×C₂₁₁	C₅²	1	6	yes	complemented
4	C₂₁₁⋊C₅	C₅²	1	25	yes	direct product factor
5	C₂₁₁	C₅³	1	1	yes	characteristic, complemented, Sylow
6	C₅³	—	211	1	no	maximal, Sylow
7	C₅²	—	211	30	no	—
8	C₅²	C₂₁₁⋊C₅	1	1	yes	characteristic, direct product factor
9	C₅	—	211	25	no	—
10	C₅	C₅×C₂₁₁⋊C₅	1	6	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₅²	C₂₁₁⋊C₅
commutator, cosocle, hypocenter	C₂₁₁	C₅³
Frattini	C₁	G
Fitting, socle	C₅²×C₂₁₁	C₅
LCS	G ▷ C₂₁₁
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.