Subgroups — #49185657

Order 38125.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₆₁⋊C₅	C₅	1	1	yes	maximal, characteristic
2	C₆₁⋊C₁₂₅	C₅	1	4	yes	maximal, complemented
3	C₆₁×C₁₂₅	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×C₆₁⋊C₅	C₂₅	1	1	yes	characteristic
5	C₂₅×C₆₁	C₅²	1	1	yes	characteristic
6	C₆₁⋊C₂₅	C₂₅	1	4	yes	—
7	C₁₂₅⋊C₅	—	61	1	no	maximal, Sylow
8	C₅×C₆₁	C₅×C₂₅	1	1	yes	characteristic
9	C₆₁⋊C₅	—	5	1	no	—
10	C₅×C₂₅	—	61	1	no	—
11	C₁₂₅	—	61	4	no	—
12	C₁₂₅	C₆₁⋊C₅	1	1	yes	characteristic, complemented
13	C₆₁	C₁₂₅⋊C₅	1	1	yes	characteristic, complemented, Sylow
14	C₅²	—	61	1	no	—
15	C₂₅	—	61	4	no	—
16	C₂₅	C₅×C₆₁⋊C₅	1	1	yes	characteristic
17	C₅	—	305	1	no	—
18	C₅	C₂₅×C₆₁⋊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.