Subgroups — C₁₁×#4053 #13183120

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#709	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#676	C₂	1	2	yes	maximal, complemented
5	C₈×D₅×C₁₁	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₁₁×C₂²⋊D₅	C₄	1	2	yes	—
8	C₁₁×D₂₀	C₄	1	1	yes	characteristic
9	C₄×D₅×C₁₁	C₂²	1	2	yes	—
10	C₁₁×Dic₁₀	C₄	1	1	yes	characteristic
11	C₅×C₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#168	C₂²	1	1	yes	characteristic
13	C₁₁×#168	C₂²	1	1	yes	characteristic
14	C₁₁×#131	—	5	1	no	maximal, Hall
15	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₅×C₁₁	C₂×C₄	1	2	yes	—
17	C₄×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	C₁₁×Dic₅	C₂×C₄	1	2	yes	—
20	C₁₁×#41	—	5	1	no	—
21	C₁₁×M₁₆	—	5	2	no	—
22	C₁₁×M₁₆	D₅	1	1	yes	characteristic, complemented
23	C₂×C₈×C₁₁	—	5	2	no	—
24	C₂×C₈×C₁₁	—	5	1	no	—
25	#4053	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₁₁	—	2	1	no	—
27	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	D₅×C₁₁	—	2	2	no	—
29	Q₈×C₁₁	—	5	1	no	—
30	D₄×C₁₁	—	5	2	no	—
31	D₄×C₁₁	—	5	1	no	—
32	C₂×C₄×C₁₁	—	5	2	no	—
33	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
34	C₈×C₁₁	—	5	1	no	—
35	C₈×C₁₁	—	5	1	no	—
36	C₈×C₁₁	C₂×D₅	1	2	yes	—
37	#709	C₂×C₁₁	1	1	yes	characteristic
38	C₅×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
39	C₂×#168	C₂×C₁₁	1	1	yes	characteristic, complemented
40	#676	C₂×C₁₁	1	2	yes	complemented
41	C₈×D₅	C₂×C₁₁	1	2	yes	complemented
42	C₅×C₁₁	#131	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₁	—	5	2	no	—
44	C₂²×C₁₁	C₄×D₅	1	1	yes	characteristic
45	C₄×C₁₁	—	5	2	no	—
46	C₄×C₁₁	C₄×D₅	1	1	yes	characteristic
47	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
48	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
49	C₂²⋊D₅	C₄×C₁₁	1	2	yes	—
50	D₂₀	C₄×C₁₁	1	1	yes	characteristic
51	C₄×D₅	C₂²×C₁₁	1	2	yes	—
52	Dic₁₀	C₄×C₁₁	1	1	yes	characteristic
53	C₅×C₈	C₂²×C₁₁	1	2	yes	—
54	#168	C₂²×C₁₁	1	1	yes	characteristic
55	#168	C₂²×C₁₁	1	1	yes	characteristic
56	#131	—	5	1	no	Sylow
57	C₂×C₁₁	—	2	1	no	—
58	C₂×C₁₁	—	10	2	no	—
59	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
60	C₂²×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
61	C₂×D₅	C₂×C₄×C₁₁	1	2	yes	—
62	C₄×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
63	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
64	Dic₅	C₂×C₄×C₁₁	1	2	yes	—
65	#41	—	5	1	no	—
66	M₁₆	—	5	2	no	—
67	M₁₆	D₅×C₁₁	1	1	yes	characteristic, complemented
68	C₂×C₈	—	5	1	no	—
69	C₂×C₈	—	5	2	no	—
70	C₁₁	#4053	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₅	—	2	1	no	—
72	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
73	D₅	—	2	2	no	—
74	Q₈	—	5	1	no	—
75	D₄	—	5	2	no	—
76	D₄	—	5	1	no	—
77	C₂×C₄	—	5	2	no	—
78	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
79	C₈	—	5	1	no	—
80	C₈	—	5	1	no	—
81	C₈	C₂×D₅×C₁₁	1	2	yes	—
82	C₅	C₁₁×#131	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	5	2	no	—
84	C₂²	C₄×D₅×C₁₁	1	1	yes	characteristic
85	C₄	—	5	2	no	—
86	C₄	C₄×D₅×C₁₁	1	1	yes	characteristic
87	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	10	2	no	—
90	C₂	C₂×C₄×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	C₂²×D₅
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×M₁₆	C₂
socle	C₂×C₅×C₁₁	C₂²×C₄
prime radical	C₁₁×#709	C₂
cosocle	C₄×C₅	C₂³×C₁₁
hypercenter	C₁₁×M₁₆	D₅
hypocenter	C₅	C₁₁×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄×C₁₁ ◁ C₁₁×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₁×M₁₆	C₂	semidirect
3. C₂×C₁₁×#168	C₂	semidirect
4. C₁₁×#676	C₂	semidirect
5. C₈×D₅×C₁₁	C₂	semidirect
22. C₁₁×M₁₆	D₅	semidirect
25. #4053	C₁₁	direct (N × H)
38. C₅×M₁₆	C₂×C₁₁	semidirect
39. C₂×#168	C₂×C₁₁	semidirect
40. #676	C₂×C₁₁	semidirect
41. C₈×D₅	C₂×C₁₁	semidirect
42. C₅×C₁₁	#131	semidirect
67. M₁₆	D₅×C₁₁	semidirect
70. C₁₁	#4053	direct (N × H)
82. C₅	C₁₁×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#709	2
C₅×C₁₁×M₁₆	2
C₂×C₁₁×#168	2
C₁₁×#676	2
C₈×D₅×C₁₁	2
C₁₁×#131	5
#4053	11

Subgroups — C11×#4053 #13183120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4053 #13183120