Subgroups — Dic₄₅ #4358

Order 180.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₅	—	3	1	no	maximal
3	C₅×C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅	D₃	1	1	yes	characteristic
6	Dic₅	—	9	1	no	Hall
7	C₂×C₉	D₅	1	1	yes	characteristic
8	C₃×C₅	Dic₃	1	1	yes	characteristic
9	Dic₃	—	15	1	no	—
10	C₂×C₅	D₉	1	1	yes	characteristic
11	C₉	Dic₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃	D₁₅	1	1	yes	characteristic
13	C₅	Dic₉	1	1	yes	characteristic, complemented, Sylow
14	C₄	—	45	1	no	Sylow
15	C₃	Dic₁₅	1	1	yes	characteristic
16	C₂	D₄₅	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.