Subgroups — C₃³×C₉×C₅₃ #27166249

Order 12879.

792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₅₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉×C₅₃	C₃	1	39	yes	maximal, direct product factor
3	C₃³×C₅₃	C₉	1	27	yes	direct product factor
4	C₃³×C₅₃	C₃²	1	13	yes	—
5	C₃×C₉×C₅₃	C₃²	1	117	yes	direct product factor
6	C₃²×C₅₃	C₃×C₉	1	117	yes	direct product factor
7	C₃²×C₅₃	C₃³	1	13	yes	—
8	C₉×C₅₃	C₃³	1	27	yes	direct product factor
9	C₃³×C₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃×C₅₃	C₃²×C₉	1	39	yes	direct product factor
11	C₃×C₅₃	C₃⁴	1	1	yes	characteristic
12	C₃⁴	C₃×C₅₃	1	1	yes	characteristic
13	C₃²×C₉	C₃×C₅₃	1	39	yes	direct product factor
14	C₅₃	C₃³×C₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃³	C₉×C₅₃	1	27	yes	direct product factor
16	C₃³	C₃²×C₅₃	1	13	yes	—
17	C₃×C₉	C₃²×C₅₃	1	117	yes	direct product factor
18	C₃²	C₃×C₉×C₅₃	1	117	yes	direct product factor
19	C₃²	C₃³×C₅₃	1	13	yes	—
20	C₉	C₃³×C₅₃	1	27	yes	direct product factor
21	C₃	C₃²×C₉×C₅₃	1	39	yes	direct product factor
22	C₃	C₃⁴×C₅₃	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.