Subgroups — #44535910

Order 31375.

20 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
2	#20262472	C₅	1	5	yes	maximal, complemented
3	C₅×C₂₅₁	—	5	1	no	—
4	C₅×C₂₅₁	C₅²	1	1	yes	characteristic
5	C₂₅₁	5₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
6	5₋¹⁺²	—	251	1	no	maximal, Sylow
7	C₅²	C₂₅₁⋊C₅	1	1	yes	characteristic
8	C₂₅	—	251	5	no	—
9	C₅	—	5	1	no	—
10	C₅	C₅×C₂₅₁⋊C₅	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #20262472	C₅	semidirect
5. C₂₅₁	5₋¹⁺²	semidirect

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