Subgroups — C₂³×Dic₅ #4151

Order 160.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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