Subgroups — C₁₁×#4023 #13183090

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×Dic₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₂²⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#683	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₁×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₁₁	C₂²	1	2	yes	—
8	C₂×C₁₁×Dic₅	C₄	1	4	yes	complemented
9	C₂×C₁₁×Dic₅	C₂²	1	2	yes	—
10	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
12	C₁₁×#117	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	—	2	2	no	—
14	C₂²×C₅×C₁₁	C₂×C₄	1	2	yes	—
15	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
16	C₄×C₅×C₁₁	—	2	2	no	—
17	C₁₁×Dic₅	—	2	2	no	—
18	C₁₁×Dic₅	C₂×C₄	1	2	yes	—
19	C₁₁×Dic₅	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₁₁	—	5	1	no	—
21	C₁₁×C₄⋊C₄	—	5	2	no	—
22	C₁₁×C₂²⋊C₄	—	5	1	no	—
23	C₁₁×C₂²⋊C₄	D₅	1	1	yes	characteristic
24	C₄²×C₁₁	—	5	2	no	—
25	#4023	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₁₁	—	2	2	no	—
27	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₅×C₁₁	#41	1	2	yes	—
29	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
30	C₂×C₄×C₁₁	—	5	4	no	—
31	C₂×C₄×C₁₁	—	5	1	no	—
32	C₂×C₄×C₁₁	—	5	1	no	—
33	C₂×C₄×C₁₁	—	5	2	no	—
34	C₂×C₄×C₁₁	C₂×D₅	1	2	yes	—
35	C₂²×Dic₅	C₂×C₁₁	1	1	yes	characteristic
36	C₅×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic
37	C₂²⋊Dic₅	C₂×C₁₁	1	1	yes	characteristic
38	#683	C₂×C₁₁	1	2	yes	complemented
39	C₄×Dic₅	C₂×C₁₁	1	2	yes	complemented
40	C₅×C₁₁	#117	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	2	no	—
42	C₂²×C₁₁	C₄×D₅	1	2	yes	—
43	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	C₄×C₁₁	—	2	2	no	—
45	C₄×C₁₁	—	5	2	no	—
46	C₄×C₁₁	—	5	2	no	—
47	C₄×C₁₁	—	10	2	no	—
48	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
49	C₂×C₄×C₅	C₂²×C₁₁	1	2	yes	—
50	C₂×Dic₅	C₄×C₁₁	1	4	yes	complemented
51	C₂×Dic₅	C₂²×C₁₁	1	2	yes	—
52	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
53	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
54	#117	—	5	1	no	Sylow
55	C₂×C₁₁	—	2	2	no	—
56	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
57	C₂×C₁₁	#711	1	2	yes	—
58	C₂²×C₅	—	2	2	no	—
59	C₂²×C₅	C₂×C₄×C₁₁	1	2	yes	—
60	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
61	C₄×C₅	—	2	2	no	—
62	Dic₅	—	2	2	no	—
63	Dic₅	C₂×C₄×C₁₁	1	2	yes	—
64	Dic₅	C₂×C₄×C₁₁	1	2	yes	—
65	C₂²×C₄	—	5	1	no	—
66	C₄⋊C₄	—	5	2	no	—
67	C₂²⋊C₄	—	5	1	no	—
68	C₂²⋊C₄	D₅×C₁₁	1	1	yes	characteristic
69	C₄²	—	5	2	no	—
70	C₁₁	#4023	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₅	—	2	2	no	—
72	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
73	C₂×C₅	C₁₁×#41	1	2	yes	—
74	C₂³	C₂×D₅×C₁₁	1	1	yes	characteristic
75	C₂×C₄	—	5	4	no	—
76	C₂×C₄	—	5	1	no	—
77	C₂×C₄	—	5	1	no	—
78	C₂×C₄	—	5	2	no	—
79	C₂×C₄	C₂×D₅×C₁₁	1	2	yes	—
80	C₅	C₁₁×#117	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	2	2	no	—
82	C₂²	C₄×D₅×C₁₁	1	2	yes	—
83	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	5	2	no	—
86	C₄	—	5	2	no	—
87	C₄	—	10	2	no	—
88	C₂	—	2	2	no	—
89	C₂	C₂×C₄×D₅×C₁₁	1	1	yes	characteristic
90	C₂	C₁₁×#711	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₁₁×#683	C₂	semidirect
5. C₄×C₁₁×Dic₅	C₂	semidirect
8. C₂×C₁₁×Dic₅	C₄	semidirect
25. #4023	C₁₁	direct (N × H)
38. #683	C₂×C₁₁	semidirect
39. C₄×Dic₅	C₂×C₁₁	semidirect
40. C₅×C₁₁	#117	semidirect
50. C₂×Dic₅	C₄×C₁₁	semidirect
70. C₁₁	#4023	direct (N × H)
80. 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×C₁₁×Dic₅	2
C₅×C₁₁×C₂²⋊C₄	2
C₁₁×C₂²⋊Dic₅	2
C₁₁×#683	2
C₄×C₁₁×Dic₅	2
C₁₁×#117	5
#4023	11

Subgroups — C11×#4023 #13183090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#4023 #13183090