Subgroups — C₃³×C₅²×C₄₁ #72204752

Order 27675.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₅×C₄₁	C₅	1	6	yes	maximal, direct product factor
2	C₃²×C₅²×C₄₁	C₃	1	13	yes	maximal, direct product factor
3	C₃×C₅²×C₄₁	C₃²	1	13	yes	direct product factor
4	C₃²×C₅×C₄₁	C₃×C₅	1	78	yes	direct product factor
5	C₃³×C₄₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅²×C₄₁	C₃³	1	1	yes	characteristic, direct product factor, Hall
7	C₃³×C₅²	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₄₁	C₃²×C₅	1	78	yes	direct product factor
9	C₃²×C₄₁	C₃×C₅²	1	13	yes	direct product factor
10	C₃²×C₅²	C₃×C₄₁	1	13	yes	direct product factor
11	C₅×C₄₁	C₃³×C₅	1	6	yes	direct product factor
12	C₃³×C₅	C₅×C₄₁	1	6	yes	direct product factor
13	C₃×C₄₁	C₃²×C₅²	1	13	yes	direct product factor
14	C₃×C₅²	C₃²×C₄₁	1	13	yes	direct product factor
15	C₃²×C₅	C₃×C₅×C₄₁	1	78	yes	direct product factor
16	C₄₁	C₃³×C₅²	1	1	yes	characteristic, direct product factor, Sylow
17	C₃³	C₅²×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₅²	C₃³×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₅	C₃²×C₅×C₄₁	1	78	yes	direct product factor
20	C₃²	C₃×C₅²×C₄₁	1	13	yes	direct product factor
21	C₅	C₃³×C₅×C₄₁	1	6	yes	direct product factor
22	C₃	C₃²×C₅²×C₄₁	1	13	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.