Subgroups — C₃²×C₅×C₄₁⋊C₅ #22604337

Order 9225.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₄₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₅×C₄₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₄₁	C₃×C₅	1	4	yes	complemented
6	C₃×C₄₁⋊C₅	C₃×C₅	1	20	yes	direct product factor
7	C₃²×C₄₁	C₅²	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅²	—	41	1	no	maximal, Hall
9	C₅×C₄₁	C₃²×C₅	1	1	yes	characteristic, complemented
10	C₄₁⋊C₅	C₃²×C₅	1	5	yes	direct product factor
11	C₃×C₄₁	C₃×C₅²	1	4	yes	complemented
12	C₃×C₅²	—	41	4	no	—
13	C₃²×C₅	—	41	5	no	—
14	C₃²×C₅	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor
15	C₄₁	C₃²×C₅²	1	1	yes	characteristic, complemented, Sylow
16	C₅²	—	41	1	no	Sylow
17	C₃×C₅	—	41	20	no	—
18	C₃×C₅	C₃×C₄₁⋊C₅	1	4	yes	direct product factor
19	C₃²	C₅×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	—	41	5	no	—
21	C₅	C₃²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor
22	C₃	C₃×C₅×C₄₁⋊C₅	1	4	yes	direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.