Subgroups — C₅×D₃×C₉ #63191

Order 270.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉	—	3	1	no	maximal
4	D₃×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃²×C₅	C₂×C₃	1	1	yes	characteristic
6	C₅×C₉	—	2	1	no	—
7	C₅×C₉	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₃×C₅	—	3	1	no	—
9	C₅×D₃	C₉	1	1	yes	characteristic, direct product factor
10	C₃×C₉	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
11	C₃×D₃	C₃×C₅	1	1	yes	characteristic
12	C₂×C₉	—	3	1	no	—
13	C₃×C₅	—	2	1	no	—
14	C₃×C₅	C₂×C₉	1	1	yes	characteristic, complemented
15	C₃×C₅	C₃×D₃	1	1	yes	characteristic
16	C₂×C₅	—	3	1	no	Hall
17	C₃²	C₂×C₃×C₅	1	1	yes	characteristic
18	C₉	—	2	1	no	—
19	C₉	C₅×D₃	1	1	yes	characteristic, direct product factor
20	C₂×C₃	—	3	1	no	—
21	D₃	C₅×C₉	1	1	yes	characteristic, direct product factor
22	C₅	D₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₃	—	2	1	no	—
24	C₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented
25	C₃	C₃×C₅×D₃	1	1	yes	characteristic
26	C₂	—	3	1	no	Sylow

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.