Subgroups — C₃×C₁₁×C₁₁⋊#1043 #49137735

Order 36300.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₁⋊#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁×C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₁₁²×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₁²	—	5	6	no	—
7	C₃×C₁₁⋊#1043	C₁₁	1	1	yes	maximal, characteristic, direct product factor
8	C₃×C₁₁×#1043	—	11	1	no	maximal
9	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	—
11	C₃×C₅×C₁₁²	AGL(1,𝔽₅)	1	6	yes	complemented
12	C₃×C₁₁×C₅⋊D₅	—	2	5	no	—
13	C₃×C₁₁×C₅⋊D₅	D₁₁	1	1	yes	characteristic
14	C₃×C₁₁×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
15	C₃×C₁₁×Dic₁₁	—	25	1	no	Hall
16	D₅×C₁₁²	—	5	6	no	—
17	C₁₁⋊#1043	C₃×C₁₁	1	1	yes	characteristic, direct product factor
18	C₁₁×#1043	—	11	1	no	—
19	C₃×C₅²×C₁₁	—	2	5	no	—
20	C₃×C₅²×C₁₁	Dic₁₁	1	1	yes	characteristic, complemented
21	C₃×C₅²×C₁₁	C₄×C₁₁	1	1	yes	characteristic, complemented
22	C₂×C₃×C₁₁²	—	25	1	no	—
23	C₃×C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	—
24	C₃×C₁₁×AGL(1,𝔽₅)	—	55	6	no	—
25	C₅×C₁₁²	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
26	C₁₁×C₅⋊D₅	—	2	5	no	—
27	C₁₁×C₅⋊D₅	C₃×D₁₁	1	1	yes	characteristic
28	C₁₁×C₅⋊D₅	C₂×C₃×C₁₁	1	1	yes	characteristic
29	C₁₁×Dic₁₁	—	25	1	no	Hall
30	C₃×C₁₁²	#1043	1	1	yes	characteristic, complemented, Hall
31	C₃×D₅×C₁₁	—	5	6	no	—
32	C₃×D₅×C₁₁	—	5	6	no	—
33	C₃×D₅×C₁₁	—	10	30	no	—
34	C₃×#1043	—	11	1	no	Hall
35	C₅²×C₁₁	—	2	5	no	—
36	C₅²×C₁₁	C₃×Dic₁₁	1	1	yes	characteristic, complemented
37	C₅²×C₁₁	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented
38	C₂×C₁₁²	—	25	1	no	—
39	C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	—
40	C₁₁×AGL(1,𝔽₅)	—	55	6	no	—
41	C₃×C₅×C₁₁	—	2	30	no	—
42	C₃×C₅×C₁₁	C₁₁×AGL(1,𝔽₅)	1	6	yes	complemented
43	C₃×C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
44	C₃×C₅⋊D₅	C₁₁×D₁₁	1	1	yes	characteristic
45	C₃×C₄×C₁₁	—	275	1	no	—
46	C₃×Dic₁₁	—	25	1	no	—
47	C₁₁²	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
48	D₅×C₁₁	—	5	6	no	—
49	D₅×C₁₁	—	5	6	no	—
50	D₅×C₁₁	—	10	30	no	—
51	#1043	—	11	1	no	Hall
52	C₃×C₅²	C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×C₁₁	—	25	1	no	—
54	C₂×C₃×C₁₁	—	25	1	no	—
55	C₂×C₃×C₁₁	—	50	5	no	—
56	C₃×AGL(1,𝔽₅)	—	55	6	no	—
57	C₅×C₁₁	—	2	30	no	—
58	C₅×C₁₁	C₃×C₁₁×AGL(1,𝔽₅)	1	6	yes	complemented
59	C₅×C₁₁	C₃×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
60	C₅⋊D₅	C₃×C₁₁×D₁₁	1	1	yes	characteristic
61	C₄×C₁₁	—	275	1	no	—
62	Dic₁₁	—	25	1	no	—
63	C₃×C₁₁	—	2	5	no	—
64	C₃×C₁₁	C₁₁×#1043	1	1	yes	characteristic, complemented
65	C₃×C₁₁	C₁₁⋊#1043	1	1	yes	characteristic, direct product factor
66	C₃×D₅	—	5	6	no	—
67	C₅²	C₃×C₁₁×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₁₁	—	25	1	no	—
69	C₂×C₁₁	—	25	1	no	—
70	C₂×C₁₁	—	50	5	no	—
71	AGL(1,𝔽₅)	—	55	6	no	—
72	C₃×C₅	C₁₁×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
73	C₃×C₄	—	275	1	no	Hall
74	C₁₁	—	2	5	no	—
75	C₁₁	C₃×C₁₁×#1043	1	1	yes	characteristic, complemented
76	C₁₁	C₃×C₁₁⋊#1043	1	1	yes	characteristic, direct product factor
77	D₅	—	5	6	no	—
78	C₂×C₃	—	25	1	no	—
79	C₅	C₃×C₁₁×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
80	C₄	—	275	1	no	Sylow
81	C₃	C₁₁×C₁₁⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	C₁₁⋊#1043
commutator, hypocenter	C₅²×C₁₁	C₃×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₁₁²×C₅⋊D₅	C₂
cosocle	C₁₁×C₅⋊D₅	C₂×C₃×C₁₁
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₁⋊#1043	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
7. C₃×C₁₁⋊#1043	C₁₁	direct (N × H)
9. C₅²×C₁₁²	C₃×C₄	semidirect
11. C₃×C₅×C₁₁²	AGL(1,𝔽₅)	semidirect
17. C₁₁⋊#1043	C₃×C₁₁	direct (N × H)
20. C₃×C₅²×C₁₁	Dic₁₁	semidirect
21. C₃×C₅²×C₁₁	C₄×C₁₁	semidirect
25. C₅×C₁₁²	C₃×AGL(1,𝔽₅)	semidirect
30. C₃×C₁₁²	#1043	semidirect
36. C₅²×C₁₁	C₃×Dic₁₁	semidirect
37. C₅²×C₁₁	C₃×C₄×C₁₁	semidirect
42. C₃×C₅×C₁₁	C₁₁×AGL(1,𝔽₅)	semidirect
43. C₃×C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	semidirect
47. C₁₁²	C₃×#1043	semidirect
52. C₃×C₅²	C₁₁×Dic₁₁	semidirect
58. C₅×C₁₁	C₃×C₁₁×AGL(1,𝔽₅)	semidirect
59. C₅×C₁₁	C₃×C₁₁⋊AGL(1,𝔽₅)	semidirect
64. C₃×C₁₁	C₁₁×#1043	semidirect
65. C₃×C₁₁	C₁₁⋊#1043	direct (N × H)
67. C₅²	C₃×C₁₁×Dic₁₁	semidirect
72. C₃×C₅	C₁₁×C₁₁⋊AGL(1,𝔽₅)	semidirect
75. C₁₁	C₃×C₁₁×#1043	semidirect
76. C₁₁	C₃×C₁₁⋊#1043	direct (N × H)
79. C₅	C₃×C₁₁×C₁₁⋊AGL(1,𝔽₅)	semidirect
81. C₃	C₁₁×C₁₁⋊#1043	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×C₁₁²×C₅⋊D₅	2
C₁₁×C₁₁⋊#1043	3
C₃×C₁₁×C₁₁⋊AGL(1,𝔽₅)	5
C₃×C₁₁⋊#1043	11
C₃×C₁₁×#1043	11

Subgroups — C3×C11×C11⋊#1043 #49137735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₁₁⋊#1043 #49137735