Subgroups — C₂×D₄₀ #4049

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₀	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₅	—	2	2	no	—
5	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
6	D₂₀	—	2	2	no	—
7	D₂₀	C₂²	1	4	yes	complemented
8	C₅×C₈	C₂²	1	2	yes	complemented
9	C₂×D₈	—	5	1	no	maximal, Sylow
10	C₂²×C₅	D₄	1	1	yes	characteristic
11	C₂×D₅	—	2	4	no	—
12	C₂×D₅	—	4	4	no	—
13	C₄×C₅	D₄	1	1	yes	characteristic
14	C₄×C₅	C₂³	1	1	yes	characteristic
15	C₂×D₄	—	5	2	no	—
16	D₈	—	5	4	no	—
17	C₂×C₈	D₅	1	1	yes	characteristic, complemented
18	C₂×C₅	D₈	1	2	yes	complemented
19	C₂×C₅	C₂×D₄	1	1	yes	characteristic
20	D₅	—	4	4	no	—
21	C₂³	—	10	2	no	—
22	D₄	—	5	4	no	—
23	D₄	—	10	2	no	—
24	C₂×C₄	C₂×D₅	1	1	yes	characteristic
25	C₈	C₂×D₅	1	2	yes	complemented
26	C₅	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	10	4	no	—
28	C₂²	—	20	4	no	—
29	C₂²	D₂₀	1	1	yes	characteristic
30	C₄	D₂₀	1	1	yes	characteristic
31	C₄	C₂²×D₅	1	1	yes	characteristic
32	C₂	—	20	4	no	—
33	C₂	D₄₀	1	2	yes	direct product factor
34	C₂	C₂×D₂₀	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.