Subgroups — C₂×Dic₂₀ #4051

Order 160.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀	C₂	1	2	yes	maximal
2	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂×Dic₅	—	2	2	no	—
6	Dic₁₀	—	2	2	no	—
7	Dic₁₀	C₂²	1	4	yes	—
8	C₅×C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆	—	5	1	no	maximal, Sylow
10	C₂²×C₅	D₄	1	1	yes	characteristic
11	C₄×C₅	D₄	1	1	yes	characteristic
12	C₄×C₅	C₂³	1	1	yes	characteristic
13	Dic₅	—	2	4	no	—
14	C₂×Q₈	—	5	2	no	—
15	Q₁₆	—	5	4	no	—
16	C₂×C₈	D₅	1	1	yes	characteristic
17	C₂×C₅	Q₁₆	1	2	yes	complemented
18	C₂×C₅	C₂×D₄	1	1	yes	characteristic
19	Q₈	—	5	4	no	—
20	Q₈	—	10	2	no	—
21	C₂×C₄	—	10	2	no	—
22	C₂×C₄	C₂×D₅	1	1	yes	characteristic
23	C₈	C₂×D₅	1	2	yes	—
24	C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂²	D₂₀	1	1	yes	characteristic
26	C₄	—	10	4	no	—
27	C₄	D₂₀	1	1	yes	characteristic
28	C₄	C₂²×D₅	1	1	yes	characteristic
29	C₂	Dic₂₀	1	2	yes	direct product factor
30	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.