Subgroups — C₁₁×#4015 #13183082

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Dic₁₀	C₂	1	2	yes	maximal
2	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₄⋊Dic₅	C₂	1	4	yes	maximal
4	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
6	C₂×C₁₁×Dic₅	C₂²	1	4	yes	—
7	C₁₁×Dic₁₀	—	2	4	no	—
8	C₁₁×C₄⋊Q₈	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
10	C₄×C₅×C₁₁	D₄	1	2	yes	—
11	C₄×C₅×C₁₁	Q₈	1	4	yes	complemented
12	C₁₁×Dic₅	—	2	4	no	—
13	C₂×Q₈×C₁₁	—	5	2	no	—
14	C₁₁×C₄⋊C₄	—	5	4	no	—
15	C₄²×C₁₁	D₅	1	1	yes	characteristic
16	#4015	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₅×C₁₁	C₂×Q₈	1	2	yes	—
19	Q₈×C₁₁	—	10	4	no	—
20	C₂×C₄×C₁₁	—	5	4	no	—
21	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
22	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
23	C₂×Dic₁₀	C₂×C₁₁	1	2	yes	—
24	C₄²×C₅	C₂×C₁₁	1	1	yes	characteristic
25	C₄⋊Dic₅	C₂×C₁₁	1	4	yes	—
26	C₅×C₁₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
28	C₄×C₁₁	—	10	4	no	—
29	C₄×C₁₁	Dic₁₀	1	4	yes	complemented
30	C₄×C₁₁	D₂₀	1	2	yes	—
31	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
32	C₂×C₄×C₅	C₂²×C₁₁	1	2	yes	—
33	C₂×Dic₅	C₂²×C₁₁	1	4	yes	—
34	Dic₁₀	—	2	4	no	—
35	C₄⋊Q₈	—	5	1	no	Sylow
36	C₂×C₁₁	C₂×Dic₁₀	1	2	yes	—
37	C₂×C₁₁	C₂×D₂₀	1	1	yes	characteristic
38	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
39	C₄×C₅	D₄×C₁₁	1	2	yes	—
40	C₄×C₅	Q₈×C₁₁	1	4	yes	complemented
41	Dic₅	—	2	4	no	—
42	C₂×Q₈	—	5	2	no	—
43	C₄⋊C₄	—	5	4	no	—
44	C₄²	D₅×C₁₁	1	1	yes	characteristic
45	C₁₁	#4015	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
47	C₂×C₅	C₂×Q₈×C₁₁	1	2	yes	—
48	Q₈	—	10	4	no	—
49	C₂×C₄	—	5	4	no	—
50	C₂×C₄	C₂×D₅×C₁₁	1	2	yes	—
51	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
52	C₅	C₁₁×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
54	C₄	—	10	4	no	—
55	C₄	C₁₁×Dic₁₀	1	4	yes	complemented
56	C₄	C₁₁×D₂₀	1	2	yes	—
57	C₂	C₂×C₁₁×Dic₁₀	1	2	yes	—
58	C₂	C₂×C₁₁×D₂₀	1	1	yes	characteristic

	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, prime radical	C₂²×C₅×C₁₁	C₂³
hypercenter	C₄²×C₁₁	D₅
hypocenter	C₅	C₁₁×C₄⋊Q₈
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
11. C₄×C₅×C₁₁	Q₈	semidirect
16. #4015	C₁₁	direct (N × H)
26. C₅×C₁₁	C₄⋊Q₈	semidirect
29. C₄×C₁₁	Dic₁₀	semidirect
40. C₄×C₅	Q₈×C₁₁	semidirect
45. C₁₁	#4015	direct (N × H)
52. C₅	C₁₁×C₄⋊Q₈	semidirect
55. C₄	C₁₁×Dic₁₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×Dic₁₀	2
C₄²×C₅×C₁₁	2
C₁₁×C₄⋊Dic₅	2
C₁₁×C₄⋊Q₈	5
#4015	11

Subgroups — C11×#4015 #13183082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4015 #13183082