Subgroups — C₃×C₅×D₁₁×C₁₁⋊C₅ #31827630

Order 18150.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₁×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×D₁₁	C₅	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₁×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
5	C₅×C₁₁×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×C₁₁×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
8	C₃×C₅²×D₁₁	—	11	1	no	maximal
9	C₂×C₃×C₅×C₁₁⋊C₅	—	11	1	no	maximal
10	C₅×C₁₁×D₁₁	C₃×C₅	1	1	yes	characteristic, complemented
11	D₁₁×C₁₁⋊C₅	C₃×C₅	1	5	yes	direct product factor
12	C₃×C₅²×C₁₁	—	11	1	no	—
13	C₃×C₅×C₁₁⋊C₅	D₁₁	1	1	yes	characteristic, direct product factor
14	C₃×C₁₁×D₁₁	C₅²	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₁×C₁₁⋊C₅	C₂×C₃×C₅	1	5	yes	complemented
17	C₅²×D₁₁	—	11	1	no	—
18	C₂×C₅×C₁₁⋊C₅	—	11	1	no	—
19	C₃×C₁₁²	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×C₁₁	—	11	1	no	—
21	C₃×C₅×D₁₁	—	11	5	no	—
22	C₃×C₅×D₁₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃×C₁₁⋊C₅	—	11	5	no	—
24	C₅²×C₁₁	—	11	1	no	—
25	C₅×C₁₁⋊C₅	C₃×D₁₁	1	1	yes	characteristic, direct product factor
26	C₁₁×D₁₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
27	C₃×C₅×C₁₁	—	10	1	no	—
28	C₃×C₅×C₁₁	—	11	5	no	—
29	C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
30	C₃×C₅×C₁₁	C₅×D₁₁	1	1	yes	characteristic, complemented
31	C₃×C₁₁⋊C₅	C₅×D₁₁	1	5	yes	direct product factor
32	C₂×C₃×C₅²	—	121	1	no	Hall
33	C₁₁²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅×C₁₁	—	11	1	no	—
35	C₅×D₁₁	—	11	5	no	—
36	C₅×D₁₁	C₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
37	C₂×C₁₁⋊C₅	—	11	5	no	—
38	C₃×C₅²	—	11	1	no	Hall
39	C₂×C₃×C₁₁	—	11	1	no	—
40	C₃×D₁₁	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
41	C₅×C₁₁	—	10	1	no	—
42	C₅×C₁₁	—	11	5	no	—
43	C₅×C₁₁	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
44	C₅×C₁₁	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented
45	C₁₁⋊C₅	C₃×C₅×D₁₁	1	5	yes	direct product factor
46	C₂×C₅²	—	121	1	no	Hall
47	C₃×C₁₁	—	10	1	no	—
48	C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented
49	C₃×C₁₁	C₅²×D₁₁	1	1	yes	characteristic, complemented
50	C₂×C₃×C₅	—	11	1	no	—
51	C₂×C₃×C₅	—	121	5	no	—
52	C₅²	—	11	1	no	Sylow
53	C₂×C₁₁	—	11	1	no	—
54	D₁₁	C₃×C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
55	C₃×C₅	—	11	5	no	—
56	C₃×C₅	D₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
57	C₁₁	—	10	1	no	—
58	C₁₁	C₂×C₃×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented
59	C₁₁	C₃×C₅²×D₁₁	1	1	yes	characteristic, complemented
60	C₂×C₅	—	11	1	no	—
61	C₂×C₅	—	121	5	no	—
62	C₂×C₃	—	11	1	no	Hall
63	C₅	—	11	5	no	—
64	C₅	C₃×D₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
65	C₃	C₅×D₁₁×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₁×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₂×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₁₁⋊C₅	C₂	semidirect
2. C₅×D₁₁×C₁₁⋊C₅	C₃	direct (N × H)
3. C₃×C₅×C₁₁×D₁₁	C₅	semidirect
4. C₃×D₁₁×C₁₁⋊C₅	C₅	direct (N × H)
5. C₅×C₁₁×C₁₁⋊C₅	C₂×C₃	semidirect
6. C₃×C₅×C₁₁²	C₂×C₅	semidirect
7. C₃×C₁₁×C₁₁⋊C₅	C₂×C₅	semidirect
10. C₅×C₁₁×D₁₁	C₃×C₅	semidirect
11. D₁₁×C₁₁⋊C₅	C₃×C₅	direct (N × H)
13. C₃×C₅×C₁₁⋊C₅	D₁₁	direct (N × H)
14. C₃×C₁₁×D₁₁	C₅²	semidirect
15. C₅×C₁₁²	C₂×C₃×C₅	semidirect
16. C₁₁×C₁₁⋊C₅	C₂×C₃×C₅	semidirect
19. C₃×C₁₁²	C₂×C₅²	semidirect
22. C₃×C₅×D₁₁	C₁₁⋊C₅	direct (N × H)
25. C₅×C₁₁⋊C₅	C₃×D₁₁	direct (N × H)
26. C₁₁×D₁₁	C₃×C₅²	semidirect
29. C₃×C₅×C₁₁	C₂×C₁₁⋊C₅	semidirect
30. C₃×C₅×C₁₁	C₅×D₁₁	semidirect
31. C₃×C₁₁⋊C₅	C₅×D₁₁	direct (N × H)
33. C₁₁²	C₂×C₃×C₅²	semidirect
36. C₅×D₁₁	C₃×C₁₁⋊C₅	direct (N × H)
40. C₃×D₁₁	C₅×C₁₁⋊C₅	direct (N × H)
43. C₅×C₁₁	C₂×C₃×C₁₁⋊C₅	semidirect
44. C₅×C₁₁	C₃×C₅×D₁₁	semidirect
45. C₁₁⋊C₅	C₃×C₅×D₁₁	direct (N × H)
48. C₃×C₁₁	C₂×C₅×C₁₁⋊C₅	semidirect
49. C₃×C₁₁	C₅²×D₁₁	semidirect
54. D₁₁	C₃×C₅×C₁₁⋊C₅	direct (N × H)
56. C₃×C₅	D₁₁×C₁₁⋊C₅	direct (N × H)
58. C₁₁	C₂×C₃×C₅×C₁₁⋊C₅	semidirect
59. C₁₁	C₃×C₅²×D₁₁	semidirect
64. C₅	C₃×D₁₁×C₁₁⋊C₅	direct (N × H)
65. C₃	C₅×D₁₁×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
C₃×C₅×C₁₁×C₁₁⋊C₅	2
C₅×D₁₁×C₁₁⋊C₅	3
C₃×C₅×C₁₁×D₁₁	5
C₃×D₁₁×C₁₁⋊C₅	5
C₃×C₅²×D₁₁	11
C₂×C₃×C₅×C₁₁⋊C₅	11

Subgroups — C3×C5×D11×C11⋊C5 #31827630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₁×C₁₁⋊C₅ #31827630