Subgroups — C₂₅×D₂₅ #11929366

Order 1250.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₅×C₂₅	—	5	1	no	maximal
3	C₅×D₂₅	C₅	1	1	yes	maximal, characteristic
4	C₅×C₂₅	—	2	2	no	—
5	C₅×C₂₅	D₅	1	1	yes	characteristic
6	C₅×C₂₅	C₂×C₅	1	1	yes	characteristic
7	C₅×D₅	—	5	1	no	—
8	C₂×C₂₅	—	25	1	no	—
9	D₂₅	C₂₅	1	1	yes	characteristic, direct product factor
10	C₅²	C₅×D₅	1	1	yes	characteristic
11	C₂₅	—	2	10	no	—
12	C₂₅	—	2	2	no	—
13	C₂₅	—	2	2	no	—
14	C₂₅	D₂₅	1	1	yes	characteristic, direct product factor
15	C₂₅	C₂×C₂₅	1	1	yes	characteristic, complemented
16	C₂×C₅	—	25	1	no	—
17	D₅	—	5	1	no	—
18	C₅	—	2	2	no	—
19	C₅	C₅×D₂₅	1	1	yes	characteristic
20	C₅	D₅×C₂₅	1	1	yes	characteristic
21	C₂	—	25	1	no	Sylow

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.