Subgroups — (C₃⋊D₃)⋊D₂₀₅ #20301648

Order 7380.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₆₁₅	C₂	1	2	yes	maximal, complemented
3	D₃×D₂₀₅	—	3	2	no	maximal
4	C₃²×C₅×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	(C₃⋊D₃)⋊D₄₁	—	5	1	no	maximal, Hall
6	D₆₁₅	D₃	1	2	yes	complemented
7	C₅×D₃×C₄₁	—	3	2	no	—
8	C₅×D₃×C₄₁	—	6	1	no	—
9	C₃×D₂₀₅	—	3	2	no	—
10	C₂×D₂₀₅	—	9	1	no	Hall
11	C₃⋊D₃×C₄₁	D₅	1	1	yes	characteristic, complemented
12	C₃×D₁₂₃	—	5	2	no	—
13	C₃×C₅×C₄₁	—	2	1	no	—
14	C₃×C₅×C₄₁	C₂×D₃	1	2	yes	complemented
15	D₃×D₄₁	—	15	2	no	—
16	C₂×C₅×C₄₁	—	9	1	no	—
17	D₂₀₅	—	3	2	no	—
18	C₃²×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	D₁₂₃	—	5	2	no	—
20	C₃×D₄₁	—	15	2	no	—
21	D₃×C₄₁	—	3	2	no	—
22	D₃×C₄₁	—	6	1	no	—
23	C₅×C₄₁	D₃²	1	1	yes	characteristic, complemented, Hall
24	(C₃⋊D₃)⋊D₅	—	41	1	no	maximal, Hall
25	C₂×D₄₁	—	45	1	no	Hall
26	C₃×C₄₁	—	2	1	no	—
27	C₃×C₄₁	D₃×D₅	1	2	yes	complemented
28	C₅×C₃⋊D₃	D₄₁	1	1	yes	characteristic, complemented
29	C₃×D₁₅	—	41	2	no	—
30	C₂×C₄₁	—	9	1	no	—
31	D₄₁	—	15	2	no	—
32	D₃×D₅	—	123	2	no	—
33	C₃²×C₅	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
34	C₄₁	(C₃⋊D₃)⋊D₅	1	1	yes	characteristic, complemented, Sylow
35	D₃²	—	205	1	no	Hall
36	D₁₅	—	41	2	no	—
37	C₃×D₅	—	123	2	no	—
38	C₅×D₃	—	3	2	no	—
39	C₅×D₃	—	6	1	no	—
40	C₂×D₅	—	369	1	no	Hall
41	C₃⋊D₃	D₂₀₅	1	1	yes	characteristic, complemented
42	C₃×D₃	—	205	2	no	—
43	C₃×C₅	—	2	1	no	—
44	C₃×C₅	D₃×D₄₁	1	2	yes	complemented
45	C₂×D₃	—	615	2	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	123	2	no	—
48	C₃²	C₂×D₂₀₅	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃	—	615	2	no	—
50	D₃	—	3	2	no	—
51	D₃	—	6	1	no	—
52	D₃	—	205	2	no	—
53	C₅	(C₃⋊D₃)⋊D₄₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	1845	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₂₀₅	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	615	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₄₁	C₂²
LCS	G ▷ C₃²×C₅×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₃×C₄₁	C₂	semidirect
2. C₃×D₆₁₅	C₂	semidirect
4. C₃²×C₅×C₄₁	C₂²	semidirect
6. D₆₁₅	D₃	semidirect
11. C₃⋊D₃×C₄₁	D₅	semidirect
14. C₃×C₅×C₄₁	C₂×D₃	semidirect
18. C₃²×C₄₁	C₂×D₅	semidirect
23. C₅×C₄₁	D₃²	semidirect
27. C₃×C₄₁	D₃×D₅	semidirect
28. C₅×C₃⋊D₃	D₄₁	semidirect
33. C₃²×C₅	C₂×D₄₁	semidirect
34. C₄₁	(C₃⋊D₃)⋊D₅	semidirect
41. C₃⋊D₃	D₂₀₅	semidirect
44. C₃×C₅	D₃×D₄₁	semidirect
48. C₃²	C₂×D₂₀₅	semidirect
53. C₅	(C₃⋊D₃)⋊D₄₁	semidirect
56. C₃	D₃×D₂₀₅	semidirect

Subgroups — (C3⋊D3)⋊D205 #20301648

Conjugacy classes of subgroups

Complements

Subgroups — (C₃⋊D₃)⋊D₂₀₅ #20301648