Subgroups — C₂×C₅×C₁₆ #3984

Order 160.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₅	C₄	1	1	yes	characteristic
4	C₅×C₈	C₄	1	1	yes	characteristic
5	C₅×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₅	C₈	1	1	yes	characteristic
8	C₄×C₅	C₈	1	1	yes	characteristic
9	C₄×C₅	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈	C₂×C₅	1	1	yes	characteristic
11	C₁₆	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₅	C₁₆	1	2	yes	direct product factor
13	C₂×C₅	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄	C₄×C₅	1	1	yes	characteristic
15	C₈	C₄×C₅	1	1	yes	characteristic
16	C₈	C₂²×C₅	1	1	yes	characteristic
17	C₅	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
18	C₂²	C₅×C₈	1	1	yes	characteristic
19	C₄	C₅×C₈	1	1	yes	characteristic
20	C₄	C₂×C₄×C₅	1	1	yes	characteristic
21	C₂	C₅×C₁₆	1	2	yes	direct product factor
22	C₂	C₂×C₅×C₈	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.