Subgroups — C₁₁×#4093 #13183160

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#685	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₅×C₁₁	C₂²	1	2	yes	—
6	C₅×Q₈×C₁₁	—	2	2	no	—
7	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
10	C₁₁×D₂₀	—	2	2	no	—
11	C₁₁×#124	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₅×C₁₁	—	2	2	no	—
14	C₂×D₅×C₁₁	—	2	4	no	—
15	C₄×C₅×C₁₁	—	2	2	no	—
16	C₄×C₅×C₁₁	D₄	1	2	yes	—
17	C₁₁×Dic₅	—	2	2	no	—
18	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
19	C₂×D₄×C₁₁	—	5	1	no	—
20	C₁₁×C₂²⋊C₄	—	5	4	no	—
21	C₄²×C₁₁	—	5	1	no	—
22	#4093	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₅×C₁₁	#41	1	2	yes	—
25	D₅×C₁₁	—	4	2	no	—
26	C₂³×C₁₁	—	5	2	no	—
27	Q₈×C₁₁	—	2	2	no	—
28	D₄×C₁₁	—	10	2	no	—
29	C₂×C₄×C₁₁	—	5	2	no	—
30	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
31	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
32	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
33	C₂×D₂₀	C₂×C₁₁	1	1	yes	characteristic
34	#685	C₂×C₁₁	1	4	yes	complemented
35	C₄×Dic₅	C₂×C₁₁	1	1	yes	characteristic, complemented
36	C₅×C₁₁	#124	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₁₁	—	10	4	no	—
38	C₂²×C₁₁	—	10	2	no	—
39	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
40	C₄×C₁₁	—	2	2	no	—
41	C₄×C₁₁	—	10	2	no	—
42	C₄×C₁₁	C₂²⋊D₅	1	2	yes	—
43	C₂²×D₅	C₂²×C₁₁	1	2	yes	—
44	C₅×Q₈	—	2	2	no	—
45	C₂×C₄×C₅	C₂²×C₁₁	1	2	yes	—
46	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
47	C₂×Dic₅	C₂²×C₁₁	1	2	yes	—
48	D₂₀	—	2	2	no	—
49	#124	—	5	1	no	Sylow
50	C₂×C₁₁	—	20	2	no	—
51	C₂×C₁₁	#713	1	2	yes	—
52	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
53	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
54	C₂×D₅	—	2	2	no	—
55	C₂×D₅	—	2	4	no	—
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	D₄×C₁₁	1	2	yes	—
58	Dic₅	—	2	2	no	—
59	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic, complemented
60	C₂×D₄	—	5	1	no	—
61	C₂²⋊C₄	—	5	4	no	—
62	C₄²	—	5	1	no	—
63	C₁₁	#4093	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
65	C₂×C₅	C₁₁×#41	1	2	yes	—
66	D₅	—	4	2	no	—
67	C₂³	—	5	2	no	—
68	Q₈	—	2	2	no	—
69	D₄	—	10	2	no	—
70	C₂×C₄	—	5	2	no	—
71	C₂×C₄	C₂×D₅×C₁₁	1	2	yes	—
72	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
73	C₅	C₁₁×#124	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	10	4	no	—
75	C₂²	—	10	2	no	—
76	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	10	2	no	—
79	C₄	C₁₁×C₂²⋊D₅	1	2	yes	—
80	C₂	—	20	2	no	—
81	C₂	C₁₁×#713	1	2	yes	—
82	C₂	C₂×C₁₁×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂×C₁₁×D₂₀	C₂
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₁₁×#124
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#685	C₂	semidirect
4. C₄×C₁₁×Dic₅	C₂	semidirect
18. C₂×Q₈×C₁₁	D₅	semidirect
22. #4093	C₁₁	direct (N × H)
32. C₂×C₅×Q₈	C₂×C₁₁	semidirect
34. #685	C₂×C₁₁	semidirect
35. C₄×Dic₅	C₂×C₁₁	semidirect
36. C₅×C₁₁	#124	semidirect
59. C₂×Q₈	D₅×C₁₁	semidirect
63. C₁₁	#4093	direct (N × H)
73. C₅	C₁₁×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₈×C₁₁	2
C₂×C₁₁×D₂₀	2
C₁₁×#685	2
C₄×C₁₁×Dic₅	2
C₁₁×#124	5
#4093	11

Subgroups — C11×#4093 #13183160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4093 #13183160