Subgroups — C₃×C₉×C₁₇×C₅₃ #72201627

Order 24327.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₅₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₁₇×C₅₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₇×C₅₃	C₉	1	3	yes	direct product factor
4	C₃×C₁₇×C₅₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₅₃	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅₃	C₃×C₁₇	1	1	yes	characteristic
8	C₉×C₅₃	C₃×C₁₇	1	3	yes	direct product factor
9	C₃×C₉×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅₃	C₉×C₁₇	1	3	yes	direct product factor
11	C₃×C₅₃	C₃²×C₁₇	1	1	yes	characteristic
12	C₃²×C₁₇	C₃×C₅₃	1	1	yes	characteristic
13	C₉×C₁₇	C₃×C₅₃	1	3	yes	direct product factor
14	C₅₃	C₃×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	C₉×C₅₃	1	3	yes	direct product factor
16	C₃×C₁₇	C₃²×C₅₃	1	1	yes	characteristic
17	C₃×C₉	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₁₇	C₃×C₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₃²	C₃×C₁₇×C₅₃	1	1	yes	characteristic
20	C₉	C₃×C₁₇×C₅₃	1	3	yes	direct product factor
21	C₃	C₉×C₁₇×C₅₃	1	3	yes	direct product factor
22	C₃	C₃²×C₁₇×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.