Subgroups — C₅²⋊(C₂₅₁⋊C₅) #44535905

Order 31375.

30 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	5	yes	maximal, complemented
3	C₅×C₂₅₁	—	5	1	no	—
4	C₅×C₂₅₁	C₅²	1	1	yes	characteristic
5	C₂₅₁⋊C₅	—	5	5	no	—
6	C₂₅₁	H(3,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
7	H(3,𝔽₅)	—	251	1	no	maximal, Sylow
8	C₅²	—	251	5	no	—
9	C₅²	C₂₅₁⋊C₅	1	1	yes	characteristic, complemented
10	C₅	—	5	1	no	—
11	C₅	—	1255	5	no	—
12	C₅	C₅×C₂₅₁⋊C₅	1	1	yes	characteristic

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.