Subgroups — C₅×Dic₅ #1038

Order 100.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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