Subgroups — C₁₁×#4072 #13183139

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂²⋊Dic₅	C₂	1	2	yes	maximal
3	C₁₁×C₄⋊Dic₅	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₁×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₁₁	C₄	1	4	yes	complemented
7	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×Dic₅	C₂²	1	4	yes	—
10	C₁₁×#117	—	5	1	no	maximal, Hall
11	C₂²×C₅×C₁₁	—	2	2	no	—
12	C₂²×C₅×C₁₁	C₂×C₄	1	2	yes	—
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	—
15	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	—
16	C₁₁×Dic₅	—	2	4	no	—
17	C₂²×C₄×C₁₁	D₅	1	1	yes	characteristic
18	C₁₁×C₄⋊C₄	—	5	2	no	—
19	C₁₁×C₂²⋊C₄	—	5	2	no	—
20	C₄²×C₁₁	—	5	2	no	—
21	#4072	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₁₁	—	2	2	no	—
23	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₅×C₁₁	#41	1	2	yes	—
25	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
26	C₂×C₄×C₁₁	—	5	4	no	—
27	C₂×C₄×C₁₁	Dic₅	1	4	yes	complemented
28	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
30	C₂²×C₄×C₅	C₂×C₁₁	1	1	yes	characteristic
31	C₂²⋊Dic₅	C₂×C₁₁	1	2	yes	—
32	C₄⋊Dic₅	C₂×C₁₁	1	2	yes	complemented
33	C₄×Dic₅	C₂×C₁₁	1	2	yes	complemented
34	C₅×C₁₁	#117	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₁₁	—	2	2	no	—
36	C₂²×C₁₁	C₂×Dic₅	1	2	yes	—
37	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
38	C₄×C₁₁	—	10	4	no	—
39	C₄×C₁₁	C₂×Dic₅	1	2	yes	—
40	C₄×C₁₁	C₂×Dic₅	1	2	yes	—
41	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
42	C₂×C₄×C₅	C₄×C₁₁	1	4	yes	complemented
43	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
45	C₂×Dic₅	C₂²×C₁₁	1	4	yes	—
46	#117	—	5	1	no	Sylow
47	C₂×C₁₁	—	2	2	no	—
48	C₂×C₁₁	#709	1	2	yes	—
49	C₂×C₁₁	C₂²×Dic₅	1	1	yes	characteristic
50	C₂²×C₅	—	2	2	no	—
51	C₂²×C₅	C₂×C₄×C₁₁	1	2	yes	—
52	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
53	C₄×C₅	C₂×C₄×C₁₁	1	2	yes	—
54	C₄×C₅	C₂×C₄×C₁₁	1	2	yes	—
55	Dic₅	—	2	4	no	—
56	C₂²×C₄	D₅×C₁₁	1	1	yes	characteristic
57	C₄⋊C₄	—	5	2	no	—
58	C₂²⋊C₄	—	5	2	no	—
59	C₄²	—	5	2	no	—
60	C₁₁	#4072	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
63	C₂×C₅	C₁₁×#41	1	2	yes	—
64	C₂³	C₂×D₅×C₁₁	1	1	yes	characteristic
65	C₂×C₄	—	5	4	no	—
66	C₂×C₄	C₁₁×Dic₅	1	4	yes	complemented
67	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
68	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
69	C₅	C₁₁×#117	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	2	2	no	—
71	C₂²	C₂×C₁₁×Dic₅	1	2	yes	—
72	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
73	C₄	—	10	4	no	—
74	C₄	C₂×C₁₁×Dic₅	1	2	yes	—
75	C₄	C₂×C₁₁×Dic₅	1	2	yes	—
76	C₂	—	2	2	no	—
77	C₂	C₁₁×#709	1	2	yes	—
78	C₂	C₂²×C₁₁×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₅
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting	C₂²×C₄×C₅×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
prime radical	C₂³×C₅×C₁₁	C₂²
cosocle	C₂²×C₅	C₂³×C₁₁
hypercenter	C₂²×C₄×C₁₁	D₅
hypocenter	C₅	C₁₁×#117
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₁₁×C₄⋊Dic₅	C₂	semidirect
4. C₄×C₁₁×Dic₅	C₂	semidirect
6. C₂×C₄×C₅×C₁₁	C₄	semidirect
21. #4072	C₁₁	direct (N × H)
27. C₂×C₄×C₁₁	Dic₅	semidirect
32. C₄⋊Dic₅	C₂×C₁₁	semidirect
33. C₄×Dic₅	C₂×C₁₁	semidirect
34. C₅×C₁₁	#117	semidirect
42. C₂×C₄×C₅	C₄×C₁₁	semidirect
60. C₁₁	#4072	direct (N × H)
66. C₂×C₄	C₁₁×Dic₅	semidirect
69. C₅	C₁₁×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×C₁₁	2
C₁₁×C₂²⋊Dic₅	2
C₁₁×C₄⋊Dic₅	2
C₄×C₁₁×Dic₅	2
C₁₁×#117	5
#4072	11

Subgroups — C11×#4072 #13183139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4072 #13183139