Subgroups — C₄×Dic₅ #682

Order 80.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅	C₂	1	2	yes	maximal
3	C₂²×C₅	C₂²	1	1	yes	characteristic
4	C₄×C₅	C₄	1	2	yes	complemented
5	Dic₅	C₄	1	4	yes	direct product factor
6	C₄²	—	5	1	no	maximal, Sylow
7	C₂×C₅	C₂×C₄	1	2	yes	—
8	C₂×C₅	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄	—	5	2	no	—
10	C₂×C₄	D₅	1	1	yes	characteristic
11	C₅	C₄²	1	1	yes	characteristic, complemented, Sylow
12	C₂²	C₂×D₅	1	1	yes	characteristic
13	C₄	—	5	4	no	—
14	C₄	Dic₅	1	2	yes	direct product factor
15	C₂	C₄×D₅	1	2	yes	—
16	C₂	C₂×Dic₅	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.