Subgroups — C₂×C₃×C₅×C₉ #63202

Order 270.

40 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, direct product factor, Hall
2	C₂×C₃²×C₅	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₉	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃²×C₅	C₂×C₃	1	1	yes	characteristic
6	C₅×C₉	C₂×C₃	1	3	yes	direct product factor
7	C₂×C₃×C₅	C₉	1	3	yes	direct product factor
8	C₂×C₃×C₅	C₃²	1	1	yes	characteristic
9	C₃×C₉	C₂×C₅	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₃²	C₃×C₅	1	1	yes	characteristic
11	C₂×C₉	C₃×C₅	1	3	yes	direct product factor
12	C₃×C₅	C₂×C₉	1	3	yes	direct product factor
13	C₃×C₅	C₂×C₃²	1	1	yes	characteristic
14	C₂×C₅	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃²	C₂×C₃×C₅	1	1	yes	characteristic
16	C₉	C₂×C₃×C₅	1	3	yes	direct product factor
17	C₂×C₃	C₅×C₉	1	3	yes	direct product factor
18	C₂×C₃	C₃²×C₅	1	1	yes	characteristic
19	C₅	C₂×C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₃	C₂×C₅×C₉	1	3	yes	direct product factor
21	C₃	C₂×C₃²×C₅	1	1	yes	characteristic
22	C₂	C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, 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.