Subgroups — Dic₂₀ #679

Order 80.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₀	C₂	1	2	yes	maximal
2	C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅	C₂²	1	1	yes	characteristic
4	Dic₅	—	2	2	no	—
5	Q₁₆	—	5	1	no	maximal, Sylow
6	C₂×C₅	D₄	1	1	yes	characteristic
7	Q₈	—	5	2	no	—
8	C₈	D₅	1	1	yes	characteristic
9	C₅	Q₁₆	1	1	yes	characteristic, complemented, Sylow
10	C₄	—	10	2	no	—
11	C₄	C₂×D₅	1	1	yes	characteristic
12	C₂	D₂₀	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. C₅	Q₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.