Subgroups — C₅×C₃⋊C₃₂ #90925

Order 480.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₂	—	3	1	no	maximal, Hall
3	C₃×C₅×C₈	C₄	1	1	yes	characteristic
4	C₃⋊C₃₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₆	D₃	1	1	yes	characteristic
6	C₃×C₄×C₅	C₈	1	1	yes	characteristic
7	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic
8	C₅×C₈	Dic₃	1	1	yes	characteristic
9	C₃₂	—	3	1	no	Sylow
10	C₂×C₃×C₅	C₁₆	1	1	yes	characteristic
11	C₃×C₈	C₄×C₅	1	1	yes	characteristic
12	C₄×C₅	C₃⋊C₈	1	1	yes	characteristic
13	C₁₆	C₅×D₃	1	1	yes	characteristic
14	C₃×C₅	C₃₂	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄	C₅×C₈	1	1	yes	characteristic
16	C₂×C₅	C₃⋊C₁₆	1	1	yes	characteristic
17	C₈	C₅×Dic₃	1	1	yes	characteristic
18	C₂×C₃	C₅×C₁₆	1	1	yes	characteristic
19	C₅	C₃⋊C₃₂	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	C₅×C₃⋊C₈	1	1	yes	characteristic
21	C₃	C₅×C₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂	C₅×C₃⋊C₁₆	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.