Subgroups — C₂×C₃×D₃×C₁₁⋊C₅ #14520443

Order 1980.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₃×C₁₁⋊C₅	—	3	1	no	maximal
4	C₂×D₃×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃×C₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂×C₃×C₁₁⋊C₅	—	2	1	no	—
8	C₂×C₃×C₁₁⋊C₅	—	3	2	no	—
9	C₂×C₃×C₁₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₁⋊C₅	C₂×C₃	1	2	yes	direct product factor
12	C₂²×C₁₁⋊C₅	—	3	1	no	Hall
13	C₂×C₃²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×D₃×C₁₁	C₂×C₅	1	2	yes	complemented
15	C₂×C₃×C₅×D₃	—	11	1	no	maximal, Hall
16	C₃×C₁₁⋊C₅	—	2	1	no	—
17	C₃×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, direct product factor
18	C₃×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₁₁	—	3	1	no	—
20	C₂×D₃×C₁₁	C₃×C₅	1	1	yes	characteristic, complemented
21	C₂×C₁₁⋊C₅	—	3	2	no	—
22	C₂×C₁₁⋊C₅	C₃×D₃	1	1	yes	characteristic, direct product factor
23	C₃²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₅	—	11	1	no	—
25	C₃×C₅×D₃	—	11	2	no	—
26	C₂×C₃×C₁₁	—	2	1	no	—
27	C₂×C₃×C₁₁	—	3	2	no	—
28	C₂×C₃×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented
29	C₂×C₃×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
30	D₃×C₁₁	C₂×C₃×C₅	1	2	yes	complemented
31	C₂²×C₃×C₅	—	33	1	no	—
32	C₂×C₅×D₃	—	11	1	no	—
33	C₁₁⋊C₅	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
34	C₃²×C₅	—	11	1	no	Hall
35	C₂²×C₁₁	—	3	1	no	Hall
36	C₂×C₃×D₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₁₁	—	2	1	no	—
38	C₃×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
39	C₃×C₁₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅	—	11	1	no	—
41	C₂×C₃×C₅	—	11	1	no	—
42	C₂×C₃×C₅	—	22	1	no	—
43	C₂×C₃×C₅	—	33	2	no	—
44	C₅×D₃	—	11	2	no	—
45	C₂×C₁₁	—	3	2	no	—
46	C₂×C₁₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
47	C₂²×C₅	—	33	1	no	Hall
48	C₂×C₃²	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
49	C₃×D₃	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
50	C₃×C₅	—	11	1	no	—
51	C₃×C₅	—	11	1	no	—
52	C₃×C₅	—	22	1	no	—
53	C₂²×C₃	—	3	1	no	—
54	C₂×D₃	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
55	C₁₁	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	11	1	no	—
57	C₂×C₅	—	33	2	no	—
58	C₃²	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	3	2	no	—
61	C₂×C₃	D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
62	C₂×C₃	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
63	D₃	C₂×C₃×C₁₁⋊C₅	1	2	yes	direct product factor
64	C₅	—	11	1	no	Sylow
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
68	C₃	C₂²×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₁₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₁⋊C₅	C₂	semidirect
2. C₃×D₃×C₁₁⋊C₅	C₂	direct (N × H)
4. C₂×D₃×C₁₁⋊C₅	C₃	direct (N × H)
5. C₃²×C₁₁⋊C₅	C₂²	semidirect
6. C₂×C₃×D₃×C₁₁	C₅	semidirect
9. C₂×C₃×C₁₁⋊C₅	D₃	direct (N × H)
10. C₂×C₃×C₁₁⋊C₅	C₂×C₃	semidirect
11. D₃×C₁₁⋊C₅	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₁₁	C₂×C₅	semidirect
14. C₃×D₃×C₁₁	C₂×C₅	semidirect
17. C₃×C₁₁⋊C₅	C₂×D₃	direct (N × H)
18. C₃×C₁₁⋊C₅	C₂²×C₃	semidirect
20. C₂×D₃×C₁₁	C₃×C₅	semidirect
22. C₂×C₁₁⋊C₅	C₃×D₃	direct (N × H)
23. C₃²×C₁₁	C₂²×C₅	semidirect
28. C₂×C₃×C₁₁	C₅×D₃	semidirect
29. C₂×C₃×C₁₁	C₂×C₃×C₅	semidirect
30. D₃×C₁₁	C₂×C₃×C₅	semidirect
33. C₁₁⋊C₅	C₂×C₃×D₃	direct (N × H)
36. C₂×C₃×D₃	C₁₁⋊C₅	direct (N × H)
38. C₃×C₁₁	C₂×C₅×D₃	semidirect
39. C₃×C₁₁	C₂²×C₃×C₅	semidirect
46. C₂×C₁₁	C₃×C₅×D₃	semidirect
48. C₂×C₃²	C₂×C₁₁⋊C₅	semidirect
49. C₃×D₃	C₂×C₁₁⋊C₅	direct (N × H)
54. C₂×D₃	C₃×C₁₁⋊C₅	direct (N × H)
55. C₁₁	C₂×C₃×C₅×D₃	semidirect
58. C₃²	C₂²×C₁₁⋊C₅	semidirect
61. C₂×C₃	D₃×C₁₁⋊C₅	direct (N × H)
62. C₂×C₃	C₂×C₃×C₁₁⋊C₅	semidirect
63. D₃	C₂×C₃×C₁₁⋊C₅	direct (N × H)
67. C₃	C₂×D₃×C₁₁⋊C₅	direct (N × H)
68. C₃	C₂²×C₃×C₁₁⋊C₅	semidirect
70. C₂	C₃×D₃×C₁₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₁⋊C₅	2
C₃×D₃×C₁₁⋊C₅	2
C₂²×C₃×C₁₁⋊C₅	3
C₂×D₃×C₁₁⋊C₅	3
C₂×C₃×D₃×C₁₁	5
C₂×C₃×C₅×D₃	11

Subgroups — C2×C3×D3×C11⋊C5 #14520443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃×C₁₁⋊C₅ #14520443