Subgroups — C₁₁×#4150 #13183437

Order 1760.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×D₅×C₁₁	C₂	1	2	yes	maximal, complemented
3	C₁₁×#711	C₂	1	6	yes	maximal, complemented
4	C₁₁×#709	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₁×Dic₁₀	C₂	1	3	yes	maximal, complemented
6	C₅×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₅×D₄×C₁₁	C₂²	1	3	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
9	C₁₁×C₂²⋊D₅	C₂²	1	6	yes	—
10	C₂×C₁₁×Dic₅	C₂²	1	6	yes	—
11	C₁₁×D₂₀	C₂²	1	1	yes	characteristic
12	C₄×D₅×C₁₁	C₂²	1	6	yes	—
13	C₁₁×Dic₁₀	C₂²	1	3	yes	—
14	C₁₁×Dic₁₀	C₂²	1	6	yes	—
15	C₁₁×2₋¹⁺⁴	—	5	1	no	maximal, Hall
16	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
17	C₂×D₅×C₁₁	C₂³	1	2	yes	—
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₂³	1	3	yes	—
20	C₁₁×Dic₅	C₂³	1	6	yes	—
21	C₁₁×#41	—	5	6	no	—
22	C₁₁×#41	—	5	3	no	—
23	C₁₁×#41	D₅	1	1	yes	characteristic, complemented
24	C₂×Q₈×C₁₁	—	5	2	no	—
25	C₂×Q₈×C₁₁	—	5	3	no	—
26	#4150	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	—	2	3	no	—
28	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
29	D₅×C₁₁	—	2	2	no	—
30	Q₈×C₁₁	—	5	6	no	—
31	Q₈×C₁₁	—	5	3	no	—
32	Q₈×C₁₁	C₂×D₅	1	1	yes	characteristic
33	D₄×C₁₁	—	5	6	no	—
34	D₄×C₁₁	—	5	1	no	—
35	D₄×C₁₁	C₂×D₅	1	3	yes	—
36	C₂×C₄×C₁₁	—	5	6	no	—
37	C₂×C₄×C₁₁	—	5	6	no	—
38	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
39	C₅×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
40	Q₈×D₅	C₂×C₁₁	1	2	yes	complemented
41	#711	C₂×C₁₁	1	6	yes	complemented
42	#709	C₂×C₁₁	1	3	yes	complemented
43	C₂×Dic₁₀	C₂×C₁₁	1	3	yes	complemented
44	C₅×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₁₁	—	5	2	no	—
46	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
47	C₄×C₁₁	—	5	6	no	—
48	C₄×C₁₁	C₂²×D₅	1	3	yes	—
49	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
50	C₅×Q₈	C₂²×C₁₁	1	1	yes	characteristic
51	C₅×D₄	C₂²×C₁₁	1	3	yes	—
52	C₂×C₄×C₅	C₂²×C₁₁	1	3	yes	—
53	C₂²⋊D₅	C₂²×C₁₁	1	6	yes	—
54	C₂×Dic₅	C₂²×C₁₁	1	6	yes	—
55	D₂₀	C₂²×C₁₁	1	1	yes	characteristic
56	C₄×D₅	C₂²×C₁₁	1	6	yes	—
57	Dic₁₀	C₂²×C₁₁	1	3	yes	—
58	Dic₁₀	C₂²×C₁₁	1	6	yes	—
59	2₋¹⁺⁴	—	5	1	no	Sylow
60	C₂×C₁₁	—	2	3	no	—
61	C₂×C₁₁	—	10	2	no	—
62	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
63	C₂²×C₅	C₂³×C₁₁	1	3	yes	—
64	C₂×D₅	C₂³×C₁₁	1	2	yes	—
65	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
66	C₄×C₅	C₂³×C₁₁	1	3	yes	—
67	Dic₅	C₂³×C₁₁	1	6	yes	—
68	#41	—	5	6	no	—
69	#41	—	5	3	no	—
70	#41	D₅×C₁₁	1	1	yes	characteristic, complemented
71	C₂×Q₈	—	5	2	no	—
72	C₂×Q₈	—	5	3	no	—
73	C₁₁	#4150	1	1	yes	characteristic, direct product factor, Sylow
74	C₂×C₅	—	2	3	no	—
75	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
76	D₅	—	2	2	no	—
77	Q₈	—	5	6	no	—
78	Q₈	—	5	3	no	—
79	Q₈	C₂×D₅×C₁₁	1	1	yes	characteristic
80	D₄	—	5	6	no	—
81	D₄	—	5	1	no	—
82	D₄	C₂×D₅×C₁₁	1	3	yes	—
83	C₂×C₄	—	5	6	no	—
84	C₂×C₄	—	5	6	no	—
85	C₂×C₄	C₂×D₅×C₁₁	1	3	yes	—
86	C₅	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
87	C₂²	—	5	2	no	—
88	C₂²	C₂²×D₅×C₁₁	1	3	yes	—
89	C₄	—	5	6	no	—
90	C₄	C₂²×D₅×C₁₁	1	3	yes	—
91	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	—	10	2	no	—
94	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	C₂³×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂⁴
hypercenter	C₁₁×#41	D₅
hypocenter	C₅	C₁₁×2₋¹⁺⁴
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₁₁×#41

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#41	C₂	semidirect
2. Q₈×D₅×C₁₁	C₂	semidirect
3. C₁₁×#711	C₂	semidirect
4. C₁₁×#709	C₂	semidirect
5. C₂×C₁₁×Dic₁₀	C₂	semidirect
23. C₁₁×#41	D₅	semidirect
26. #4150	C₁₁	direct (N × H)
39. C₅×#41	C₂×C₁₁	semidirect
40. Q₈×D₅	C₂×C₁₁	semidirect
41. #711	C₂×C₁₁	semidirect
42. #709	C₂×C₁₁	semidirect
43. C₂×Dic₁₀	C₂×C₁₁	semidirect
44. C₅×C₁₁	2₋¹⁺⁴	semidirect
70. #41	D₅×C₁₁	semidirect
73. C₁₁	#4150	direct (N × H)
86. C₅	C₁₁×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#41	2
Q₈×D₅×C₁₁	2
C₁₁×#711	2
C₁₁×#709	2
C₂×C₁₁×Dic₁₀	2
C₁₁×2₋¹⁺⁴	5
#4150	11

Subgroups — C11×#4150 #13183437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4150 #13183437