Subgroups — C₂×C₉×D₅ #4364

Order 180.

30 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, complemented
2	C₉×D₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₉	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅	C₂×C₃	1	1	yes	characteristic
7	C₃×D₅	C₂×C₃	1	2	yes	—
8	C₂×D₅	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉	—	5	2	no	—
10	C₂×C₉	D₅	1	1	yes	characteristic, direct product factor
11	C₃×C₅	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃	—	5	1	no	—
13	C₂×C₅	C₂×C₉	1	1	yes	characteristic, complemented
14	D₅	C₂×C₉	1	2	yes	direct product factor
15	C₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃	—	5	2	no	—
17	C₂×C₃	C₃×D₅	1	1	yes	characteristic
18	C₅	C₂²×C₉	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	5	1	no	Sylow
20	C₃	C₂×C₃×D₅	1	1	yes	characteristic
21	C₂	—	5	2	no	—
22	C₂	C₉×D₅	1	1	yes	characteristic, direct product factor

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.