Subgroups — C₅²×C₂₅⋊C₂₅ #30626897

Order 15625.

4232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₂₅	C₅	1	5	yes	maximal
2	C₅³×C₂₅	C₅	1	1	yes	maximal, characteristic
3	C₅×C₂₅⋊C₂₅	C₅	1	150	yes	maximal, direct product factor
4	C₅⁴	C₅²	1	1	yes	characteristic
5	C₅²×C₂₅	—	5	125	no	—
6	C₅²×C₂₅	C₂₅	1	125	yes	complemented
7	C₅²×C₂₅	C₅²	1	150	yes	—
8	C₅²×C₂₅	C₅²	1	30	yes	—
9	C₂₅⋊C₂₅	C₅²	1	625	yes	direct product factor
10	C₅³	C₅×C₂₅	1	25	yes	—
11	C₅³	5₋¹⁺²	1	125	yes	—
12	C₅³	C₅³	1	6	yes	—
13	C₅×C₂₅	—	5	750	no	—
14	C₅×C₂₅	C₅×C₂₅	1	750	yes	complemented
15	C₅×C₂₅	C₅³	1	125	yes	—
16	C₅×C₂₅	C₅³	1	25	yes	—
17	C₅²	C₂₅⋊C₂₅	1	625	yes	direct product factor
18	C₅²	C₅²×C₂₅	1	30	yes	—
19	C₅²	C₅×5₋¹⁺²	1	150	yes	—
20	C₅²	C₅⁴	1	1	yes	characteristic
21	C₂₅	—	5	125	no	—
22	C₂₅	C₅²×C₂₅	1	125	yes	complemented
23	C₅	C₅×C₂₅⋊C₂₅	1	150	yes	direct product factor
24	C₅	C₅³×C₂₅	1	1	yes	characteristic
25	C₅	C₅²×5₋¹⁺²	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.

subgroup	index
C₅³×C₂₅	5
C₅×C₂₅⋊C₂₅	5