Subgroups — C₁₁×#4065 #13183132

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#713	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#688	C₂	1	2	yes	maximal, complemented
4	C₁₁×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₁₁×D₂₀	—	2	2	no	—
8	C₁₁×D₂₀	C₂²	1	2	yes	—
9	C₄×D₅×C₁₁	—	2	2	no	—
10	C₄×D₅×C₁₁	C₂²	1	1	yes	characteristic
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#168	C₂²	1	1	yes	characteristic
13	C₁₁×#135	—	5	1	no	maximal, Hall
14	C₂×D₅×C₁₁	—	2	2	no	—
15	C₂×D₅×C₁₁	D₄	1	1	yes	characteristic
16	C₄×C₅×C₁₁	—	2	2	no	—
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×Dic₅	D₄	1	1	yes	characteristic
19	C₁₁×#41	—	5	2	no	—
20	C₁₁×Q₁₆	D₅	1	1	yes	characteristic, complemented
21	C₁₁×SD₁₆	—	5	2	no	—
22	C₁₁×D₈	—	5	1	no	—
23	C₂×C₈×C₁₁	—	5	1	no	—
24	#4065	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	D₅×C₁₁	—	2	1	no	—
27	D₅×C₁₁	—	4	2	no	—
28	Q₈×C₁₁	C₂×D₅	1	2	yes	—
29	D₄×C₁₁	—	5	2	no	—
30	D₄×C₁₁	—	10	2	no	—
31	C₂×C₄×C₁₁	—	5	1	no	—
32	C₂×C₄×C₁₁	—	10	2	no	—
33	C₈×C₁₁	—	5	1	no	—
34	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic
35	#713	C₂×C₁₁	1	2	yes	complemented
36	C₅×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
37	#688	C₂×C₁₁	1	2	yes	complemented
38	D₄₀	C₂×C₁₁	1	1	yes	characteristic, complemented
39	C₈×D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
40	C₅×C₁₁	#135	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	5	1	no	—
42	C₂²×C₁₁	—	10	2	no	—
43	C₄×C₁₁	—	2	2	no	—
44	C₄×C₁₁	—	5	1	no	—
45	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
46	C₅×Q₈	C₂²×C₁₁	1	2	yes	—
47	D₂₀	—	2	2	no	—
48	D₂₀	C₂²×C₁₁	1	2	yes	—
49	C₄×D₅	—	2	2	no	—
50	C₄×D₅	C₂²×C₁₁	1	1	yes	characteristic
51	C₅×C₈	C₂²×C₁₁	1	1	yes	characteristic
52	#168	C₂²×C₁₁	1	1	yes	characteristic
53	#135	—	5	1	no	Sylow
54	C₂×C₁₁	—	10	1	no	—
55	C₂×C₁₁	—	20	2	no	—
56	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
57	C₂×D₅	—	2	2	no	—
58	C₂×D₅	D₄×C₁₁	1	1	yes	characteristic
59	C₄×C₅	—	2	2	no	—
60	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
61	Dic₅	D₄×C₁₁	1	1	yes	characteristic
62	#41	—	5	2	no	—
63	Q₁₆	D₅×C₁₁	1	1	yes	characteristic, complemented
64	SD₁₆	—	5	2	no	—
65	D₈	—	5	1	no	—
66	C₂×C₈	—	5	1	no	—
67	C₁₁	#4065	1	1	yes	characteristic, direct product factor, Sylow
68	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
69	D₅	—	2	1	no	—
70	D₅	—	4	2	no	—
71	Q₈	C₂×D₅×C₁₁	1	2	yes	—
72	D₄	—	5	2	no	—
73	D₄	—	10	2	no	—
74	C₂×C₄	—	5	1	no	—
75	C₂×C₄	—	10	2	no	—
76	C₈	—	5	1	no	—
77	C₈	C₂×D₅×C₁₁	1	1	yes	characteristic
78	C₅	C₁₁×#135	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	5	1	no	—
80	C₂²	—	10	2	no	—
81	C₄	—	2	2	no	—
82	C₄	—	5	1	no	—
83	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
84	C₂	—	10	1	no	—
85	C₂	—	20	2	no	—
86	C₂	D₄×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×Q₁₆	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₁₁×Q₁₆	D₅
hypocenter	C₅	C₁₁×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₁₁×#713	C₂	semidirect
2. C₅×C₁₁×Q₁₆	C₂	semidirect
3. C₁₁×#688	C₂	semidirect
4. C₁₁×D₄₀	C₂	semidirect
5. C₈×D₅×C₁₁	C₂	semidirect
20. C₁₁×Q₁₆	D₅	semidirect
24. #4065	C₁₁	direct (N × H)
35. #713	C₂×C₁₁	semidirect
36. C₅×Q₁₆	C₂×C₁₁	semidirect
37. #688	C₂×C₁₁	semidirect
38. D₄₀	C₂×C₁₁	semidirect
39. C₈×D₅	C₂×C₁₁	semidirect
40. C₅×C₁₁	#135	semidirect
63. Q₁₆	D₅×C₁₁	semidirect
67. C₁₁	#4065	direct (N × H)
78. C₅	C₁₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#713	2
C₅×C₁₁×Q₁₆	2
C₁₁×#688	2
C₁₁×D₄₀	2
C₈×D₅×C₁₁	2
C₁₁×#135	5
#4065	11

Subgroups — C11×#4065 #13183132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4065 #13183132