Subgroups — Dic₄₀ #3933

Order 160.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀	C₂	1	2	yes	maximal
2	C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀	—	2	2	no	—
4	C₅×C₈	C₂²	1	1	yes	characteristic
5	Q₃₂	—	5	1	no	maximal, Sylow
6	C₄×C₅	D₄	1	1	yes	characteristic
7	Dic₅	—	4	2	no	—
8	Q₁₆	—	5	2	no	—
9	C₁₆	D₅	1	1	yes	characteristic
10	C₂×C₅	D₈	1	1	yes	characteristic
11	Q₈	—	10	2	no	—
12	C₈	C₂×D₅	1	1	yes	characteristic
13	C₅	Q₃₂	1	1	yes	characteristic, complemented, Sylow
14	C₄	—	20	2	no	—
15	C₄	D₂₀	1	1	yes	characteristic
16	C₂	D₄₀	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₅	Q₃₂	semidirect

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