Subgroups — C₃×C₉×C₂₉×C₃₁ #72201552

Order 24273.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic
2	C₉×C₂₉×C₃₁	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂₉×C₃₁	C₉	1	3	yes	direct product factor
4	C₃×C₂₉×C₃₁	C₃²	1	1	yes	characteristic
5	C₂₉×C₃₁	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₉×C₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₉×C₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃²×C₃₁	C₃×C₂₉	1	1	yes	characteristic
9	C₉×C₃₁	C₃×C₂₉	1	3	yes	direct product factor
10	C₃²×C₂₉	C₃×C₃₁	1	1	yes	characteristic
11	C₉×C₂₉	C₃×C₃₁	1	3	yes	direct product factor
12	C₃×C₃₁	C₉×C₂₉	1	3	yes	direct product factor
13	C₃×C₃₁	C₃²×C₂₉	1	1	yes	characteristic
14	C₃×C₂₉	C₉×C₃₁	1	3	yes	direct product factor
15	C₃×C₂₉	C₃²×C₃₁	1	1	yes	characteristic
16	C₃₁	C₃×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₂₉	C₃×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₃×C₉	C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₃×C₂₉×C₃₁	1	1	yes	characteristic
20	C₉	C₃×C₂₉×C₃₁	1	3	yes	direct product factor
21	C₃	C₉×C₂₉×C₃₁	1	3	yes	direct product factor
22	C₃	C₃²×C₂₉×C₃₁	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.