Subgroups — C₁₁×#4133 #13183339

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#713	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#700	C₂	1	3	yes	maximal, complemented
3	C₁₁×D₅⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈×C₁₁	C₄	1	1	yes	characteristic
5	C₁₁×D₂₀	C₄	1	3	yes	—
6	C₄×D₅×C₁₁	C₂²	1	3	yes	—
7	C₁₁×#170	C₂²	1	1	yes	characteristic
8	C₁₁×#170	C₂²	1	3	yes	—
9	C₁₁×#131	—	5	1	no	maximal, Hall
10	C₂×D₅×C₁₁	C₂×C₄	1	3	yes	—
11	C₄×C₅×C₁₁	C₂×C₄	1	3	yes	—
12	C₁₁×Dic₅	C₂³	1	1	yes	characteristic
13	C₁₁×#41	—	5	1	no	—
14	C₁₁×M₁₆	—	5	3	no	—
15	C₂×C₈×C₁₁	—	5	3	no	—
16	#4133	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
18	D₅×C₁₁	—	2	3	no	—
19	Q₈×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic
20	D₄×C₁₁	—	5	3	no	—
21	C₂×C₄×C₁₁	—	5	3	no	—
22	C₈×C₁₁	—	5	1	no	—
23	C₈×C₁₁	—	5	3	no	—
24	#713	C₂×C₁₁	1	1	yes	characteristic
25	#700	C₂×C₁₁	1	3	yes	complemented
26	D₅⋊C₈	C₂×C₁₁	1	3	yes	complemented
27	C₅×C₁₁	#131	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	—	5	3	no	—
29	C₄×C₁₁	—	5	1	no	—
30	C₄×C₁₁	C₂×AGL(1,𝔽₅)	1	3	yes	—
31	C₅×Q₈	C₄×C₁₁	1	1	yes	characteristic
32	D₂₀	C₄×C₁₁	1	3	yes	—
33	C₄×D₅	C₂²×C₁₁	1	3	yes	—
34	#170	C₂²×C₁₁	1	1	yes	characteristic
35	#170	C₂²×C₁₁	1	3	yes	—
36	#131	—	5	1	no	Sylow
37	C₂×C₁₁	—	10	3	no	—
38	C₂×C₁₁	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₂×D₅	C₂×C₄×C₁₁	1	3	yes	—
40	C₄×C₅	C₂×C₄×C₁₁	1	3	yes	—
41	Dic₅	C₂³×C₁₁	1	1	yes	characteristic
42	#41	—	5	1	no	—
43	M₁₆	—	5	3	no	—
44	C₂×C₈	—	5	3	no	—
45	C₁₁	#4133	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
47	D₅	—	2	3	no	—
48	Q₈	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
49	D₄	—	5	3	no	—
50	C₂×C₄	—	5	3	no	—
51	C₈	—	5	1	no	—
52	C₈	—	5	3	no	—
53	C₅	C₁₁×#131	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	5	3	no	—
55	C₄	—	5	1	no	—
56	C₄	C₂×C₁₁×AGL(1,𝔽₅)	1	3	yes	—
57	C₂	—	10	3	no	—
58	C₂	C₂²×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₂	C₂²×C₁₁×AGL(1,𝔽₅)
Fitting	C₅×Q₈×C₁₁	C₄
socle	C₂×C₅×C₁₁	C₂²×C₄
prime radical	C₁₁×#713	C₂
cosocle	Dic₅	C₂³×C₁₁
hypercenter	Q₈×C₁₁	AGL(1,𝔽₅)
hypocenter	C₅	C₁₁×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×#700	C₂	semidirect
3. C₁₁×D₅⋊C₈	C₂	semidirect
16. #4133	C₁₁	direct (N × H)
25. #700	C₂×C₁₁	semidirect
26. D₅⋊C₈	C₂×C₁₁	semidirect
27. C₅×C₁₁	#131	semidirect
45. C₁₁	#4133	direct (N × H)
53. C₅	C₁₁×#131	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#713	2
C₁₁×#700	2
C₁₁×D₅⋊C₈	2
C₁₁×#131	5
#4133	11

Subgroups — C11×#4133 #13183339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4133 #13183339