Subgroups — C₅²×Dic₅ #92551

Order 500.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅³	C₂	1	1	yes	maximal, characteristic
2	C₅³	C₄	1	1	yes	characteristic, complemented, Sylow
3	C₄×C₅²	—	5	1	no	maximal
4	C₅×Dic₅	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²	—	2	12	no	—
6	C₂×C₅²	D₅	1	1	yes	characteristic
7	C₂×C₅²	C₂×C₅	1	6	yes	—
8	C₅²	—	2	12	no	—
9	C₅²	Dic₅	1	1	yes	characteristic, direct product factor
10	C₅²	C₄×C₅	1	6	yes	complemented
11	C₄×C₅	—	5	6	no	—
12	Dic₅	C₅²	1	1	yes	characteristic, direct product factor
13	C₂×C₅	—	2	12	no	—
14	C₂×C₅	C₅×D₅	1	6	yes	—
15	C₂×C₅	C₂×C₅²	1	1	yes	characteristic
16	C₅	—	2	12	no	—
17	C₅	C₅×Dic₅	1	6	yes	direct product factor
18	C₅	C₄×C₅²	1	1	yes	characteristic, complemented
19	C₄	—	5	1	no	Sylow
20	C₂	C₅²×D₅	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.