Subgroups — #13183352

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	#11724975	C₂	1	3	yes	maximal, complemented
3	D₅⋊(C₁₁⋊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	#67001	—	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	#4318	—	5	3	no	—
15	C₂×C₁₁⋊C₈	—	5	3	no	—
16	#4133	—	11	1	no	maximal, 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	C₁₁⋊C₈	—	5	1	no	—
23	C₁₁⋊C₈	—	5	3	no	—
24	#713	D₁₁	1	1	yes	characteristic
25	#700	—	11	3	no	—
26	D₅⋊C₈	—	11	3	no	—
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	Dic₁₁	1	1	yes	characteristic
32	D₂₀	Dic₁₁	1	3	yes	—
33	C₄×D₅	C₂×D₁₁	1	3	yes	—
34	#170	—	11	1	no	—
35	#170	—	11	3	no	—
36	#131	—	55	1	no	Sylow
37	C₂×C₁₁	—	10	3	no	—
38	C₂×C₁₁	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₂×D₅	C₂×Dic₁₁	1	3	yes	—
40	C₄×C₅	C₂×Dic₁₁	1	3	yes	—
41	Dic₅	C₂²×D₁₁	1	1	yes	characteristic
42	#41	—	5	1	no	—
43	M₁₆	—	55	3	no	—
44	C₂×C₈	—	55	3	no	—
45	C₁₁	#4133	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	C₂²×Dic₁₁	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	—	55	1	no	—
52	C₈	—	55	3	no	—
53	C₅	#67001	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, Frattini	C₂	C₂²×C₁₁⋊AGL(1,𝔽₅)
commutator, socle	C₂×C₅×C₁₁	C₂²×C₄
Fitting	C₅×Q₈×C₁₁	C₄
prime radical	C₁₁×#713	C₂
cosocle	C₁₁×Dic₅	C₂³
hypercenter	Q₈	C₁₁⋊AGL(1,𝔽₅)
hypocenter	C₅×C₁₁	#131
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
2. #11724975	C₂	semidirect
3. D₅⋊(C₁₁⋊C₈)	C₂	semidirect
27. C₅×C₁₁	#131	semidirect
45. C₁₁	#4133	semidirect
53. C₅	#67001	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
#11724975	2
D₅⋊(C₁₁⋊C₈)	2
#67001	5
#4133	11