Subgroups — C₉²×C₁₃×C₁₇ #72195708

Order 17901.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₃×C₁₇	C₃	1	4	yes	maximal
2	C₃²×C₁₃×C₁₇	C₃²	1	1	yes	characteristic
3	C₉×C₁₃×C₁₇	C₉	1	12	yes	direct product factor
4	C₉²×C₁₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₉²×C₁₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₁₇	C₃×C₉	1	4	yes	—
7	C₃×C₉×C₁₇	C₃×C₁₃	1	4	yes	—
8	C₃×C₉×C₁₃	C₃×C₁₇	1	4	yes	—
9	C₁₃×C₁₇	C₉²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₁₇	C₃²×C₁₃	1	1	yes	characteristic
11	C₉×C₁₇	C₉×C₁₃	1	12	yes	direct product factor
12	C₃²×C₁₃	C₃²×C₁₇	1	1	yes	characteristic
13	C₉×C₁₃	C₉×C₁₇	1	12	yes	direct product factor
14	C₉²	C₁₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₇	C₃×C₉×C₁₃	1	4	yes	—
16	C₃×C₁₃	C₃×C₉×C₁₇	1	4	yes	—
17	C₃×C₉	C₃×C₁₃×C₁₇	1	4	yes	—
18	C₁₇	C₉²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₃	C₉²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₃²	C₃²×C₁₃×C₁₇	1	1	yes	characteristic
21	C₉	C₉×C₁₃×C₁₇	1	12	yes	direct product factor
22	C₃	C₃×C₉×C₁₃×C₁₇	1	4	yes	—

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.