Subgroups — #49185652

Order 38125.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₆₁⋊C₂₅	C₅	1	5	yes	maximal
2	C₅×C₂₅×C₆₁	C₅	1	1	yes	maximal, characteristic
3	C₅²×C₆₁	C₅²	1	1	yes	characteristic
4	C₂₅×C₆₁	C₂₅	1	5	yes	complemented
5	C₆₁⋊C₂₅	—	5	5	no	—
6	C₂₅⋊C₂₅	—	61	1	no	maximal, Sylow
7	C₅×C₆₁	C₅×C₂₅	1	1	yes	characteristic
8	C₅×C₆₁	5₋¹⁺²	1	5	yes	—
9	C₅×C₂₅	—	61	5	no	—
10	C₅×C₂₅	C₆₁⋊C₅	1	1	yes	characteristic
11	C₆₁	C₂₅⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
12	C₅²	C₅×C₆₁⋊C₅	1	1	yes	characteristic
13	C₂₅	—	305	5	no	—
14	C₂₅	C₆₁⋊C₂₅	1	5	yes	complemented
15	C₅	C₅×C₆₁⋊C₂₅	1	1	yes	characteristic
16	C₅	#21439344	1	5	yes	—

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.