Subgroups — C₁₁×#4020 #13183087

Order 1760.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₂₀	C₂	1	6	yes	maximal, complemented
2	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₅×C₁₁	C₂²	1	4	yes	—
4	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
5	C₁₁×D₂₀	—	2	12	no	—
6	C₁₁×#127	—	5	1	no	maximal, Hall
7	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
8	C₂×D₅×C₁₁	—	2	12	no	—
9	C₄×C₅×C₁₁	D₄	1	6	yes	complemented
10	C₂×D₄×C₁₁	—	5	6	no	—
11	C₄²×C₁₁	D₅	1	1	yes	characteristic, complemented
12	#4020	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁	C₂×D₄	1	3	yes	—
14	D₅×C₁₁	—	4	4	no	—
15	C₂³×C₁₁	—	5	4	no	—
16	D₄×C₁₁	—	10	12	no	—
17	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
18	C₂×D₂₀	C₂×C₁₁	1	6	yes	complemented
19	C₄²×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₅×C₁₁	#127	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	—	10	12	no	—
22	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
23	C₄×C₁₁	D₂₀	1	6	yes	complemented
24	C₂²×D₅	C₂²×C₁₁	1	4	yes	—
25	C₂×C₄×C₅	C₂²×C₁₁	1	3	yes	—
26	D₂₀	—	2	12	no	—
27	#127	—	5	1	no	Sylow
28	C₂×C₁₁	—	20	4	no	—
29	C₂×C₁₁	C₂×D₂₀	1	3	yes	—
30	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
31	C₂×D₅	—	2	12	no	—
32	C₄×C₅	D₄×C₁₁	1	6	yes	complemented
33	C₂×D₄	—	5	6	no	—
34	C₄²	D₅×C₁₁	1	1	yes	characteristic, complemented
35	C₁₁	#4020	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₅	C₂×D₄×C₁₁	1	3	yes	—
37	D₅	—	4	4	no	—
38	C₂³	—	5	4	no	—
39	D₄	—	10	12	no	—
40	C₂×C₄	C₂×D₅×C₁₁	1	3	yes	—
41	C₅	C₁₁×#127	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	10	12	no	—
43	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
44	C₄	C₁₁×D₂₀	1	6	yes	complemented
45	C₂	—	20	4	no	—
46	C₂	C₂×C₁₁×D₂₀	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
hypercenter	C₄²×C₁₁	D₅
hypocenter	C₅	C₁₁×#127
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. C₂×C₁₁×D₂₀	C₂	semidirect
2. C₄²×C₅×C₁₁	C₂	semidirect
9. C₄×C₅×C₁₁	D₄	semidirect
11. C₄²×C₁₁	D₅	semidirect
12. #4020	C₁₁	direct (N × H)
18. C₂×D₂₀	C₂×C₁₁	semidirect
19. C₄²×C₅	C₂×C₁₁	semidirect
20. C₅×C₁₁	#127	semidirect
23. C₄×C₁₁	D₂₀	semidirect
32. C₄×C₅	D₄×C₁₁	semidirect
34. C₄²	D₅×C₁₁	semidirect
35. C₁₁	#4020	direct (N × H)
41. C₅	C₁₁×#127	semidirect
44. C₄	C₁₁×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×D₂₀	2
C₄²×C₅×C₁₁	2
C₁₁×#127	5
#4020	11

Subgroups — C11×#4020 #13183087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4020 #13183087