Subgroups — C₂²×Dic₁₀ #4138

Order 160.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅	C₂	1	2	yes	maximal
3	C₂×Dic₁₀	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅	C₂²	1	6	yes	—
6	C₂×Dic₅	C₂²	1	12	yes	—
7	Dic₁₀	C₂²	1	16	yes	direct product factor
8	C₂²×Q₈	—	5	1	no	maximal, Sylow
9	C₂²×C₅	Q₈	1	4	yes	complemented
10	C₂²×C₅	C₂³	1	3	yes	—
11	C₄×C₅	C₂³	1	4	yes	—
12	Dic₅	C₂³	1	8	yes	—
13	C₂×Q₈	—	5	12	no	—
14	C₂²×C₄	—	5	2	no	—
15	C₂²×C₄	D₅	1	1	yes	characteristic
16	C₂×C₅	C₂×Q₈	1	6	yes	complemented
17	C₂×C₅	C₂⁴	1	1	yes	characteristic
18	C₂³	C₂×D₅	1	1	yes	characteristic
19	Q₈	—	5	16	no	—
20	C₂×C₄	—	5	12	no	—
21	C₂×C₄	C₂×D₅	1	6	yes	—
22	C₅	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
23	C₂²	Dic₁₀	1	4	yes	direct product factor
24	C₂²	C₂²×D₅	1	3	yes	—
25	C₄	—	5	8	no	—
26	C₄	C₂²×D₅	1	4	yes	—
27	C₂	C₂×Dic₁₀	1	6	yes	direct product factor
28	C₂	C₂³×D₅	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.