Subgroups — C₁₁×#4099 #13183166

Order 1760.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×C₂²⋊D₅	C₂	1	3	yes	maximal, complemented
3	C₁₁×C₂²⋊Dic₅	C₂	1	3	yes	maximal, complemented
4	C₂³×C₅×C₁₁	—	2	6	no	—
5	C₂³×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂²×D₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
7	C₁₁×C₂²⋊D₅	—	2	6	no	—
8	C₂×C₁₁×Dic₅	C₂²	1	3	yes	complemented
9	C₁₁×#120	—	5	1	no	maximal, Hall
10	C₂²×C₅×C₁₁	—	2	8	no	—
11	C₂²×C₅×C₁₁	—	2	6	no	—
12	C₂²×C₅×C₁₁	D₄	1	6	yes	complemented
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₂×D₅×C₁₁	—	2	3	no	—
15	C₁₁×Dic₅	—	2	3	no	—
16	C₂⁴×C₁₁	D₅	1	1	yes	characteristic, complemented
17	C₂×D₄×C₁₁	—	5	3	no	—
18	C₁₁×C₂²⋊C₄	—	5	3	no	—
19	#4099	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	—	2	6	no	—
21	C₂×C₅×C₁₁	C₂×D₄	1	3	yes	—
22	D₅×C₁₁	—	4	1	no	—
23	C₂³×C₁₁	—	2	6	no	—
24	C₂³×C₁₁	—	5	1	no	—
25	C₂³×C₁₁	C₂×D₅	1	3	yes	—
26	D₄×C₁₁	—	10	6	no	—
27	C₂×C₄×C₁₁	—	5	3	no	—
28	C₂⁴×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
29	C₂×C₂²⋊D₅	C₂×C₁₁	1	3	yes	complemented
30	C₂²⋊Dic₅	C₂×C₁₁	1	3	yes	complemented
31	C₅×C₁₁	#120	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₁	—	2	8	no	—
33	C₂²×C₁₁	—	2	6	no	—
34	C₂²×C₁₁	—	10	3	no	—
35	C₂²×C₁₁	C₂²⋊D₅	1	6	yes	complemented
36	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
37	C₄×C₁₁	—	10	3	no	—
38	C₂³×C₅	—	2	6	no	—
39	C₂³×C₅	C₂²×C₁₁	1	3	yes	—
40	C₂²×D₅	C₂²×C₁₁	1	1	yes	characteristic, complemented
41	C₂²⋊D₅	—	2	6	no	—
42	C₂×Dic₅	C₂²×C₁₁	1	3	yes	complemented
43	#120	—	5	1	no	Sylow
44	C₂×C₁₁	—	2	6	no	—
45	C₂×C₁₁	—	20	1	no	—
46	C₂×C₁₁	C₂×C₂²⋊D₅	1	3	yes	—
47	C₂²×C₅	—	2	8	no	—
48	C₂²×C₅	—	2	6	no	—
49	C₂²×C₅	D₄×C₁₁	1	6	yes	complemented
50	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
51	C₂×D₅	—	2	3	no	—
52	Dic₅	—	2	3	no	—
53	C₂⁴	D₅×C₁₁	1	1	yes	characteristic, complemented
54	C₂×D₄	—	5	3	no	—
55	C₂²⋊C₄	—	5	3	no	—
56	C₁₁	#4099	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₅	—	2	6	no	—
58	C₂×C₅	C₂×D₄×C₁₁	1	3	yes	—
59	D₅	—	4	1	no	—
60	C₂³	—	2	6	no	—
61	C₂³	—	5	1	no	—
62	C₂³	C₂×D₅×C₁₁	1	3	yes	—
63	D₄	—	10	6	no	—
64	C₂×C₄	—	5	3	no	—
65	C₅	C₁₁×#120	1	1	yes	characteristic, complemented, Sylow
66	C₂²	—	2	8	no	—
67	C₂²	—	2	6	no	—
68	C₂²	—	10	3	no	—
69	C₂²	C₁₁×C₂²⋊D₅	1	6	yes	complemented
70	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
71	C₄	—	10	3	no	—
72	C₂	—	2	6	no	—
73	C₂	—	20	1	no	—
74	C₂	C₂×C₁₁×C₂²⋊D₅	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting	C₂⁴×C₅×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂⁴×C₁₁	D₅
hypocenter	C₅	C₁₁×#120
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂×C₁₁×C₂²⋊D₅	C₂	semidirect
3. C₁₁×C₂²⋊Dic₅	C₂	semidirect
6. C₂²×D₅×C₁₁	C₂²	semidirect
8. C₂×C₁₁×Dic₅	C₂²	semidirect
12. C₂²×C₅×C₁₁	D₄	semidirect
16. C₂⁴×C₁₁	D₅	semidirect
19. #4099	C₁₁	direct (N × H)
28. C₂⁴×C₅	C₂×C₁₁	semidirect
29. C₂×C₂²⋊D₅	C₂×C₁₁	semidirect
30. C₂²⋊Dic₅	C₂×C₁₁	semidirect
31. C₅×C₁₁	#120	semidirect
35. C₂²×C₁₁	C₂²⋊D₅	semidirect
40. C₂²×D₅	C₂²×C₁₁	semidirect
42. C₂×Dic₅	C₂²×C₁₁	semidirect
49. C₂²×C₅	D₄×C₁₁	semidirect
53. C₂⁴	D₅×C₁₁	semidirect
56. C₁₁	#4099	direct (N × H)
65. C₅	C₁₁×#120	semidirect
69. C₂²	C₁₁×C₂²⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂×C₁₁×C₂²⋊D₅	2
C₁₁×C₂²⋊Dic₅	2
C₁₁×#120	5
#4099	11

Subgroups — C11×#4099 #13183166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4099 #13183166