Subgroups — C₃×C₅×C₉×C₁₇₉ #72201445

Order 24165.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₇₉	C₃	1	1	yes	maximal, characteristic
2	C₅×C₉×C₁₇₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₉×C₁₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₇₉	C₉	1	3	yes	direct product factor
5	C₃×C₅×C₁₇₉	C₃²	1	1	yes	characteristic
6	C₃²×C₁₇₉	C₃×C₅	1	1	yes	characteristic
7	C₉×C₁₇₉	C₃×C₅	1	3	yes	direct product factor
8	C₅×C₁₇₉	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₇₉	C₅×C₉	1	3	yes	direct product factor
10	C₃×C₁₇₉	C₃²×C₅	1	1	yes	characteristic
11	C₁₇₉	C₃×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×C₅×C₉	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅	C₃×C₁₇₉	1	1	yes	characteristic
14	C₅×C₉	C₃×C₁₇₉	1	3	yes	direct product factor
15	C₃×C₉	C₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₃×C₅	C₉×C₁₇₉	1	3	yes	direct product factor
17	C₃×C₅	C₃²×C₁₇₉	1	1	yes	characteristic
18	C₃²	C₃×C₅×C₁₇₉	1	1	yes	characteristic
19	C₉	C₃×C₅×C₁₇₉	1	3	yes	direct product factor
20	C₅	C₃×C₉×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₅×C₉×C₁₇₉	1	3	yes	direct product factor
22	C₃	C₃²×C₅×C₁₇₉	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.