Subgroups — C₅×C₃⋊(D₄₁⋊C₅) #20259642

Order 6150.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₄₁⋊C₅	—	3	1	no	maximal, Hall
3	C₅×D₁₂₃	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃⋊(D₄₁⋊C₅)	C₅	1	5	yes	maximal, direct product factor
5	C₅×C₄₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×C₄₁⋊C₅	C₂×C₅	1	5	yes	complemented
8	C₅×D₄₁	—	3	1	no	—
9	D₄₁⋊C₅	—	3	5	no	—
10	D₁₂₃	C₅²	1	1	yes	characteristic, complemented, Hall
11	C₅×C₄₁	C₅×D₃	1	1	yes	characteristic, complemented
12	C₄₁⋊C₅	C₅×D₃	1	5	yes	complemented
13	C₅²×D₃	—	41	1	no	maximal, Hall
14	C₃×C₄₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	D₄₁	—	3	1	no	Hall
16	C₃×C₅²	—	41	1	no	Hall
17	C₂×C₅²	—	123	1	no	Hall
18	C₄₁	C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
19	C₅×D₃	—	41	5	no	—
20	C₅×D₃	—	41	1	no	—
21	C₅²	—	41	1	no	Sylow
22	C₃×C₅	—	41	5	no	—
23	C₃×C₅	D₄₁⋊C₅	1	1	yes	characteristic, complemented
24	C₂×C₅	—	123	5	no	—
25	C₂×C₅	—	123	1	no	—
26	D₃	—	41	1	no	Hall
27	C₅	—	41	5	no	—
28	C₅	C₃⋊(D₄₁⋊C₅)	1	1	yes	characteristic, direct product factor
29	C₃	C₅×D₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	123	1	no	Sylow

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