Subgroups — C₃²×C₅³×C₁₇ #72196833

Order 19125.

768 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅³×C₁₇	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅²×C₁₇	C₅	1	31	yes	maximal, direct product factor
3	C₅³×C₁₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅²×C₁₇	C₃×C₅	1	124	yes	direct product factor
5	C₃²×C₅³	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃²×C₅×C₁₇	C₅²	1	31	yes	direct product factor
7	C₅²×C₁₇	C₃²×C₅	1	31	yes	direct product factor
8	C₃×C₅³	C₃×C₁₇	1	4	yes	direct product factor
9	C₃×C₅×C₁₇	C₃×C₅²	1	124	yes	direct product factor
10	C₃²×C₅²	C₅×C₁₇	1	31	yes	direct product factor
11	C₃²×C₁₇	C₅³	1	1	yes	characteristic, direct product factor, Hall
12	C₅³	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₅×C₁₇	C₃²×C₅²	1	31	yes	direct product factor
14	C₃×C₅²	C₃×C₅×C₁₇	1	124	yes	direct product factor
15	C₃×C₁₇	C₃×C₅³	1	4	yes	direct product factor
16	C₃²×C₅	C₅²×C₁₇	1	31	yes	direct product factor
17	C₅²	C₃²×C₅×C₁₇	1	31	yes	direct product factor
18	C₁₇	C₃²×C₅³	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₃×C₅²×C₁₇	1	124	yes	direct product factor
20	C₃²	C₅³×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₃²×C₅²×C₁₇	1	31	yes	direct product factor
22	C₃	C₃×C₅³×C₁₇	1	4	yes	direct product factor

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.