Subgroups — C₄⋊Dic₅ #684

Order 80.

26 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	—	2	2	no	—
6	C₄⋊C₄	—	5	1	no	maximal, Sylow
7	C₂×C₅	C₂×C₄	1	1	yes	characteristic
8	C₂×C₅	D₄	1	1	yes	characteristic
9	C₂×C₅	Q₈	1	1	yes	characteristic
10	C₂×C₄	—	5	2	no	—
11	C₂×C₄	D₅	1	1	yes	characteristic
12	C₅	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂²	C₂×D₅	1	1	yes	characteristic
14	C₄	—	10	2	no	—
15	C₄	Dic₅	1	2	yes	complemented
16	C₂	Dic₁₀	1	1	yes	characteristic
17	C₂	D₂₀	1	1	yes	characteristic
18	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.