Subgroups — #44535902

Order 31375.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₂₅₁	C₅	1	1	yes	maximal, characteristic
2	C₅×C₂₅₁	C₂₅	1	1	yes	characteristic
3	C₂₅₁	C₁₂₅	1	1	yes	characteristic, complemented, Sylow
4	C₁₂₅	—	251	1	no	maximal, Sylow
5	C₂₅	C₂₅₁⋊C₅	1	1	yes	characteristic
6	C₅	#20262472	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂₅	C₂₅₁⋊C₅
commutator, hypocenter	C₂₅₁	C₁₂₅
Fitting, cosocle	C₂₅×C₂₅₁	C₅
socle, prime radical	C₅×C₂₅₁	C₂₅
LCS	G ▷ C₂₅₁
UCS	C₁ ◁ C₂₅

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂₅₁	C₁₂₅	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₅×C₂₅₁	5
C₁₂₅	251