Subgroups — C₃⋊D₃×D₃₀₅ #24926835

Order 10980.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₉₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₃₀₅	—	3	4	no	maximal
5	C₃²×C₅×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₆₁	—	5	1	no	maximal, Hall
7	D₉₁₅	—	3	4	no	—
8	C₅×D₃×C₆₁	—	3	4	no	—
9	C₃×D₃₀₅	D₃	1	4	yes	complemented
10	C₂×D₃₀₅	—	9	1	no	Hall
11	C₃⋊D₁₈₃	—	5	1	no	—
12	C₃⋊D₃×C₆₁	D₅	1	1	yes	characteristic, complemented
13	C₃²×D₆₁	—	5	1	no	—
14	C₃×C₅×C₆₁	C₂×D₃	1	4	yes	complemented
15	D₃×D₆₁	—	15	4	no	—
16	C₂×C₅×C₆₁	—	9	1	no	—
17	D₃₀₅	—	9	1	no	—
18	D₃₀₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₁₈₃	—	15	4	no	—
21	C₃×D₆₁	—	5	4	no	—
22	D₃×C₆₁	—	3	4	no	—
23	C₅×C₆₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₆₁	—	45	1	no	Hall
25	C₃×C₆₁	D₃×D₅	1	4	yes	complemented
26	D₅×C₃⋊D₃	—	61	1	no	maximal, Hall
27	C₂×C₆₁	—	9	1	no	—
28	D₆₁	—	5	1	no	—
29	D₆₁	—	45	1	no	—
30	C₃⋊D₁₅	—	61	1	no	—
31	C₅×C₃⋊D₃	D₆₁	1	1	yes	characteristic, complemented
32	C₃²×D₅	—	61	1	no	—
33	C₆₁	D₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
34	D₃×D₅	—	183	4	no	—
35	C₃²×C₅	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃⋊D₃	—	305	1	no	Hall
37	D₁₅	—	183	4	no	—
38	C₃×D₅	—	61	4	no	—
39	C₅×D₃	—	3	4	no	—
40	C₂×D₅	—	549	1	no	Hall
41	C₂×C₃²	—	305	1	no	—
42	C₃⋊D₃	—	305	1	no	—
43	C₃⋊D₃	D₃₀₅	1	1	yes	characteristic, direct product factor
44	C₃×C₅	D₃×D₆₁	1	4	yes	complemented
45	C₂×D₃	—	915	4	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	549	1	no	—
48	D₅	—	61	1	no	—
49	C₃²	C₂×D₃₀₅	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	305	4	no	—
51	D₃	—	3	4	no	—
52	D₃	—	915	4	no	—
53	C₅	C₃⋊D₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	2745	1	no	Sylow
55	C₃	D₃×D₃₀₅	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	305	1	no	—
58	C₂	—	2745	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₆₁	C₂²
LCS	G ▷ C₃²×C₅×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₉₁₅	C₂	semidirect
2. C₅×C₃⋊D₃×C₆₁	C₂	semidirect
3. C₃²×D₃₀₅	C₂	semidirect
5. C₃²×C₅×C₆₁	C₂²	semidirect
9. C₃×D₃₀₅	D₃	semidirect
12. C₃⋊D₃×C₆₁	D₅	semidirect
14. C₃×C₅×C₆₁	C₂×D₃	semidirect
18. D₃₀₅	C₃⋊D₃	direct (N × H)
19. C₃²×C₆₁	C₂×D₅	semidirect
23. C₅×C₆₁	C₂×C₃⋊D₃	semidirect
25. C₃×C₆₁	D₃×D₅	semidirect
31. C₅×C₃⋊D₃	D₆₁	semidirect
33. C₆₁	D₅×C₃⋊D₃	semidirect
35. C₃²×C₅	C₂×D₆₁	semidirect
43. C₃⋊D₃	D₃₀₅	direct (N × H)
44. C₃×C₅	D₃×D₆₁	semidirect
49. C₃²	C₂×D₃₀₅	semidirect
53. C₅	C₃⋊D₃×D₆₁	semidirect
55. C₃	D₃×D₃₀₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃⋊D₉₁₅	2
C₅×C₃⋊D₃×C₆₁	2
C₃²×D₃₀₅	2
D₃×D₃₀₅	3
C₃⋊D₃×D₆₁	5
D₅×C₃⋊D₃	61

Subgroups — C3⋊D3×D305 #24926835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×D₃₀₅ #24926835