Subgroups — C₅×#20262474 #44535913

Order 31375.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₅₁⋊C₅	C₅	1	1	yes	maximal, characteristic
2	#20262474	C₅	1	5	yes	maximal, direct product factor
3	C₅×C₂₅₁	C₂₅	1	1	yes	characteristic, complemented
4	C₂₅₁⋊C₅	C₂₅	1	4	yes	complemented
5	C₂₅₁⋊C₅	C₅²	1	1	yes	characteristic
6	C₂₅₁	C₅×C₂₅	1	1	yes	characteristic, complemented, Sylow
7	C₅×C₂₅	—	251	1	no	maximal, Sylow
8	C₅²	—	251	1	no	—
9	C₂₅	—	251	5	no	—
10	C₅	—	251	1	no	—
11	C₅	—	251	4	no	—
12	C₅	#20262474	1	1	yes	characteristic, direct product factor

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.