Subgroups — #49185666

Order 38125.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21439346	C₅	1	4	yes	maximal, complemented
2	C₅×C₆₁⋊C₂₅	C₅	1	1	yes	maximal, characteristic, complemented
3	C₆₁×H(3,𝔽₅)	C₅	1	1	yes	maximal, characteristic
4	C₅²×C₆₁	—	5	1	no	—
5	C₅²×C₆₁	C₅²	1	1	yes	characteristic
6	C₆₁⋊C₂₅	—	5	1	no	—
7	C₆₁⋊C₂₅	—	5	4	no	—
8	#10597832	—	61	1	no	maximal, Sylow
9	C₅×C₆₁	—	5	1	no	—
10	C₅×C₆₁	—	25	1	no	—
11	C₅×C₆₁	H(3,𝔽₅)	1	1	yes	characteristic
12	5₋¹⁺²	—	61	4	no	—
13	H(3,𝔽₅)	C₆₁⋊C₅	1	1	yes	characteristic
14	C₅×C₂₅	—	61	1	no	—
15	C₆₁	#10597832	1	1	yes	characteristic, complemented, Sylow
16	C₅²	—	5	1	no	—
17	C₅²	C₅×C₆₁⋊C₅	1	1	yes	characteristic
18	C₂₅	—	305	1	no	—
19	C₂₅	—	305	4	no	—
20	C₅	—	5	1	no	—
21	C₅	—	25	1	no	—
22	C₅	C₅²⋊(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.