Subgroups — Dic₅×C₂₅ #92521

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	C₅	1	1	yes	maximal, characteristic
4	C₄×C₂₅	—	5	1	no	maximal
5	C₂×C₅²	C₂×C₅	1	1	yes	characteristic
6	C₂×C₂₅	—	2	2	no	—
7	C₂×C₂₅	D₅	1	1	yes	characteristic
8	C₅²	C₄×C₅	1	1	yes	characteristic
9	C₂₅	—	2	2	no	—
10	C₂₅	Dic₅	1	1	yes	characteristic, direct product factor
11	C₄×C₅	—	5	1	no	—
12	Dic₅	C₂₅	1	1	yes	characteristic, direct product factor
13	C₂×C₅	—	2	2	no	—
14	C₂×C₅	C₂×C₂₅	1	1	yes	characteristic
15	C₂×C₅	C₅×D₅	1	1	yes	characteristic
16	C₅	—	2	2	no	—
17	C₅	C₄×C₂₅	1	1	yes	characteristic, complemented
18	C₅	C₅×Dic₅	1	1	yes	characteristic
19	C₄	—	5	1	no	Sylow
20	C₂	D₅×C₂₅	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.