Subgroups — C₃×C₉×C₁₃×C₄₁ #72192533

Order 14391.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₄₁	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₃×C₄₁	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₃×C₄₁	C₉	1	3	yes	direct product factor
4	C₃×C₁₃×C₄₁	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₄₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₃×C₄₁	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₄₁	C₃×C₁₃	1	1	yes	characteristic
8	C₉×C₄₁	C₃×C₁₃	1	3	yes	direct product factor
9	C₃×C₉×C₁₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₄₁	C₉×C₁₃	1	3	yes	direct product factor
11	C₃×C₄₁	C₃²×C₁₃	1	1	yes	characteristic
12	C₃²×C₁₃	C₃×C₄₁	1	1	yes	characteristic
13	C₉×C₁₃	C₃×C₄₁	1	3	yes	direct product factor
14	C₄₁	C₃×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₃	C₉×C₄₁	1	3	yes	direct product factor
16	C₃×C₁₃	C₃²×C₄₁	1	1	yes	characteristic
17	C₃×C₉	C₁₃×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₃	C₃×C₉×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₃×C₁₃×C₄₁	1	1	yes	characteristic
20	C₉	C₃×C₁₃×C₄₁	1	3	yes	direct product factor
21	C₃	C₉×C₁₃×C₄₁	1	3	yes	direct product factor
22	C₃	C₃²×C₁₃×C₄₁	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.