Subgroups — C₅×Dic₂₅ #92520

Order 500.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₅	C₄	1	1	yes	characteristic, complemented, Sylow
3	C₅×Dic₅	—	5	1	no	maximal
4	Dic₂₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₅²	D₅	1	1	yes	characteristic
6	C₂×C₂₅	—	2	2	no	—
7	C₂×C₂₅	C₂×C₅	1	1	yes	characteristic
8	C₅²	Dic₅	1	1	yes	characteristic
9	C₂₅	—	2	2	no	—
10	C₂₅	C₄×C₅	1	1	yes	characteristic, complemented
11	C₄×C₅	—	25	1	no	—
12	Dic₅	—	5	1	no	—
13	C₂×C₅	—	2	2	no	—
14	C₂×C₅	D₂₅	1	1	yes	characteristic
15	C₂×C₅	C₅×D₅	1	1	yes	characteristic
16	C₅	—	2	2	no	—
17	C₅	Dic₂₅	1	1	yes	characteristic, direct product factor
18	C₅	C₅×Dic₅	1	1	yes	characteristic
19	C₄	—	25	1	no	Sylow
20	C₂	C₅×D₂₅	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.