Subgroups — D₈₀ #3931

Order 160.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₀	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₀	—	2	2	no	—
4	C₅×C₈	C₂²	1	1	yes	characteristic
5	D₁₆	—	5	1	no	maximal, Sylow
6	C₂×D₅	—	4	2	no	—
7	C₄×C₅	D₄	1	1	yes	characteristic
8	D₈	—	5	2	no	—
9	C₁₆	D₅	1	1	yes	characteristic, complemented
10	C₂×C₅	D₈	1	1	yes	characteristic
11	D₅	—	8	2	no	—
12	D₄	—	10	2	no	—
13	C₈	C₂×D₅	1	1	yes	characteristic
14	C₅	D₁₆	1	1	yes	characteristic, complemented, Sylow
15	C₂²	—	20	2	no	—
16	C₄	D₂₀	1	1	yes	characteristic
17	C₂	—	40	2	no	—
18	C₂	D₄₀	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.