Subgroups — C₁₁×#4022 #13183089

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#685	C₂	1	3	yes	maximal
3	C₁₁×#683	C₂	1	3	yes	maximal, complemented
4	C₂²×D₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂×C₁₁×Dic₅	C₂²	1	3	yes	—
7	C₁₁×#126	—	5	1	no	maximal, Hall
8	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×D₅×C₁₁	—	2	3	no	—
10	C₄×C₅×C₁₁	—	2	3	no	—
11	C₁₁×Dic₅	—	2	3	no	—
12	C₁₁×C₄⋊C₄	—	5	3	no	—
13	C₁₁×C₂²⋊C₄	—	5	3	no	—
14	C₄²×C₁₁	D₅	1	1	yes	characteristic, complemented
15	#4022	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×C₁₁	#41	1	3	yes	—
17	D₅×C₁₁	—	4	1	no	—
18	C₂³×C₁₁	—	5	1	no	—
19	C₂×C₄×C₁₁	—	5	3	no	—
20	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
21	C₄²×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
22	#685	C₂×C₁₁	1	3	yes	—
23	#683	C₂×C₁₁	1	3	yes	complemented
24	C₅×C₁₁	#126	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₁₁	—	10	3	no	—
26	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
27	C₄×C₁₁	—	2	3	no	—
28	C₄×C₁₁	—	10	3	no	—
29	C₂²×D₅	C₂²×C₁₁	1	1	yes	characteristic
30	C₂×C₄×C₅	C₂²×C₁₁	1	3	yes	—
31	C₂×Dic₅	C₂²×C₁₁	1	3	yes	—
32	#126	—	5	1	no	Sylow
33	C₂×C₁₁	—	20	1	no	—
34	C₂×C₁₁	#709	1	3	yes	—
35	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
36	C₂×D₅	—	2	3	no	—
37	C₄×C₅	—	2	3	no	—
38	Dic₅	—	2	3	no	—
39	C₄⋊C₄	—	5	3	no	—
40	C₂²⋊C₄	—	5	3	no	—
41	C₄²	D₅×C₁₁	1	1	yes	characteristic, complemented
42	C₁₁	#4022	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₅	C₁₁×#41	1	3	yes	—
44	D₅	—	4	1	no	—
45	C₂³	—	5	1	no	—
46	C₂×C₄	—	5	3	no	—
47	C₂×C₄	C₂×D₅×C₁₁	1	3	yes	—
48	C₅	C₁₁×#126	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	10	3	no	—
50	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	10	3	no	—
53	C₂	—	20	1	no	—
54	C₂	C₁₁×#709	1	3	yes	—

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting	C₄²×C₅×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂²×D₅×C₁₁	C₂²
hypercenter	C₄²×C₁₁	D₅
hypocenter	C₅	C₁₁×#126
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₄²×C₅×C₁₁	C₂	semidirect
3. C₁₁×#683	C₂	semidirect
14. C₄²×C₁₁	D₅	semidirect
15. #4022	C₁₁	direct (N × H)
21. C₄²×C₅	C₂×C₁₁	semidirect
23. #683	C₂×C₁₁	semidirect
24. C₅×C₁₁	#126	semidirect
41. C₄²	D₅×C₁₁	semidirect
42. C₁₁	#4022	direct (N × H)
48. C₅	C₁₁×#126	semidirect

Maximal subgroups

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

subgroup	index
C₄²×C₅×C₁₁	2
C₁₁×#685	2
C₁₁×#683	2
C₁₁×#126	5
#4022	11

Subgroups — C11×#4022 #13183089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4022 #13183089