Subgroups — C₅×#21439345 #49185684

Order 38125.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₆₁⋊C₅	C₅	1	1	yes	maximal, characteristic
2	#21439345	C₅	1	25	yes	maximal, direct product factor
3	C₅×C₆₁⋊C₂₅	C₅	1	4	yes	maximal, complemented
4	C₅×C₂₅×C₆₁	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅²×C₆₁	C₅²	1	1	yes	characteristic
6	C₅×C₆₁⋊C₅	—	5	5	no	—
7	C₅×C₆₁⋊C₅	C₅²	1	5	yes	—
8	C₂₅×C₆₁	C₅²	1	5	yes	complemented
9	C₆₁⋊C₂₅	C₅²	1	20	yes	complemented
10	C₅×5₋¹⁺²	—	61	1	no	maximal, Sylow
11	C₅×C₆₁	5₋¹⁺²	1	5	yes	complemented
12	C₅×C₆₁	C₅³	1	1	yes	characteristic
13	C₆₁⋊C₅	—	5	5	no	—
14	C₅³	—	61	1	no	—
15	5₋¹⁺²	—	61	25	no	—
16	C₅×C₂₅	—	61	4	no	—
17	C₅×C₂₅	C₆₁⋊C₅	1	1	yes	characteristic, complemented
18	C₆₁	C₅×5₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
19	C₅²	—	305	5	no	—
20	C₅²	—	61	5	no	—
21	C₅²	C₅×C₆₁⋊C₅	1	1	yes	characteristic
22	C₂₅	—	61	20	no	—
23	C₂₅	C₅×C₆₁⋊C₅	1	5	yes	complemented
24	C₅	—	305	5	no	—
25	C₅	#21439345	1	5	yes	direct product factor
26	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.