Subgroups — C₂×C₃×C₉×C₂₂₉ #72190751

Order 12366.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂₂₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃²×C₂₂₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₂₂₉	C₃	1	3	yes	maximal, direct product factor
4	C₃²×C₂₂₉	C₂×C₃	1	1	yes	characteristic
5	C₉×C₂₂₉	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃×C₂₂₉	C₉	1	3	yes	direct product factor
7	C₂×C₃×C₂₂₉	C₃²	1	1	yes	characteristic
8	C₃×C₂₂₉	C₂×C₉	1	3	yes	direct product factor
9	C₃×C₂₂₉	C₂×C₃²	1	1	yes	characteristic
10	C₂×C₂₂₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂₂₉	C₂×C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃×C₉	C₂₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₉	C₂×C₂₂₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃²	C₃×C₂₂₉	1	1	yes	characteristic
15	C₂×C₉	C₃×C₂₂₉	1	3	yes	direct product factor
16	C₃²	C₂×C₃×C₂₂₉	1	1	yes	characteristic
17	C₉	C₂×C₃×C₂₂₉	1	3	yes	direct product factor
18	C₂×C₃	C₉×C₂₂₉	1	3	yes	direct product factor
19	C₂×C₃	C₃²×C₂₂₉	1	1	yes	characteristic
20	C₃	C₂×C₉×C₂₂₉	1	3	yes	direct product factor
21	C₃	C₂×C₃²×C₂₂₉	1	1	yes	characteristic
22	C₂	C₃×C₉×C₂₂₉	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.