Subgroups — C₂×C₁₁×#676 #13183113

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#676	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₅×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×Dic₅	C₄	1	1	yes	characteristic
8	C₄×D₅×C₁₁	C₄	1	2	yes	—
9	C₄×D₅×C₁₁	C₂²	1	2	yes	—
10	C₅×C₈×C₁₁	C₂²	1	2	yes	complemented
11	C₁₁×#168	C₂²	1	2	yes	complemented
12	C₂×C₁₁×M₁₆	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅×C₁₁	—	2	2	no	—
15	C₂×D₅×C₁₁	C₂×C₄	1	2	yes	—
16	C₄×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×Dic₅	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₁₁	—	5	1	no	—
20	C₁₁×M₁₆	—	5	4	no	—
21	C₂×C₈×C₁₁	—	5	1	no	—
22	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic, complemented
23	C₂×#676	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×C₁₁	M₁₆	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	D₅×C₁₁	—	2	2	no	—
27	C₂³×C₁₁	—	5	1	no	—
28	C₂×C₄×C₁₁	—	5	1	no	—
29	C₂×C₄×C₁₁	—	5	2	no	—
30	C₂×C₄×C₁₁	—	5	2	no	—
31	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
32	C₈×C₁₁	—	5	2	no	—
33	C₈×C₁₁	C₂×D₅	1	2	yes	complemented
34	C₂×C₄×D₅	C₂×C₁₁	1	1	yes	characteristic
35	C₂×C₅×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
36	C₂×#168	C₂×C₁₁	1	1	yes	characteristic, complemented
37	#676	C₂×C₁₁	1	4	yes	direct product factor
38	C₅×C₁₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	—	5	2	no	—
40	C₂²×C₁₁	—	10	2	no	—
41	C₂²×C₁₁	C₄×D₅	1	1	yes	characteristic
42	C₄×C₁₁	—	5	2	no	—
43	C₄×C₁₁	C₄×D₅	1	1	yes	characteristic
44	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
45	C₂²×D₅	C₄×C₁₁	1	1	yes	characteristic
46	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
47	C₂×Dic₅	C₄×C₁₁	1	1	yes	characteristic
48	C₄×D₅	C₄×C₁₁	1	2	yes	—
49	C₄×D₅	C₂²×C₁₁	1	2	yes	—
50	C₅×C₈	C₂²×C₁₁	1	2	yes	complemented
51	#168	C₂²×C₁₁	1	2	yes	complemented
52	C₂×M₁₆	—	5	1	no	Sylow
53	C₂×C₁₁	—	10	2	no	—
54	C₂×C₁₁	#676	1	2	yes	direct product factor
55	C₂×C₁₁	C₂×C₄×D₅	1	1	yes	characteristic
56	C₂²×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
57	C₂×D₅	—	2	2	no	—
58	C₂×D₅	C₂×C₄×C₁₁	1	2	yes	—
59	C₄×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
60	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
61	Dic₅	C₂×C₄×C₁₁	1	2	yes	—
62	C₂²×C₄	—	5	1	no	—
63	M₁₆	—	5	4	no	—
64	C₂×C₈	—	5	1	no	—
65	C₂×C₈	D₅×C₁₁	1	1	yes	characteristic, complemented
66	C₁₁	C₂×#676	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₅	C₁₁×M₁₆	1	2	yes	complemented
68	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
69	D₅	—	2	2	no	—
70	C₂³	—	5	1	no	—
71	C₂×C₄	—	5	1	no	—
72	C₂×C₄	—	5	2	no	—
73	C₂×C₄	—	5	2	no	—
74	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
75	C₈	—	5	2	no	—
76	C₈	C₂×D₅×C₁₁	1	2	yes	complemented
77	C₅	C₂×C₁₁×M₁₆	1	1	yes	characteristic, complemented, Sylow
78	C₂²	—	5	2	no	—
79	C₂²	—	10	2	no	—
80	C₂²	C₄×D₅×C₁₁	1	1	yes	characteristic
81	C₄	—	5	2	no	—
82	C₄	C₄×D₅×C₁₁	1	1	yes	characteristic
83	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
84	C₂	—	10	2	no	—
85	C₂	C₁₁×#676	1	2	yes	direct product factor
86	C₂	C₂×C₄×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₅
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂×C₄
prime radical	C₂²×D₅×C₁₁	C₄
cosocle	C₄×C₅	C₂³×C₁₁
hypercenter	C₂×C₈×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₈×C₁₁	C₂	semidirect
3. C₂×C₁₁×#168	C₂	semidirect
4. C₁₁×#676	C₂	direct (N × H)
10. C₅×C₈×C₁₁	C₂²	semidirect
11. C₁₁×#168	C₂²	semidirect
22. C₂×C₈×C₁₁	D₅	semidirect
23. C₂×#676	C₁₁	direct (N × H)
24. C₂×C₅×C₁₁	M₁₆	semidirect
33. C₈×C₁₁	C₂×D₅	semidirect
35. C₂×C₅×C₈	C₂×C₁₁	semidirect
36. C₂×#168	C₂×C₁₁	semidirect
37. #676	C₂×C₁₁	direct (N × H)
38. C₅×C₁₁	C₂×M₁₆	semidirect
50. C₅×C₈	C₂²×C₁₁	semidirect
51. #168	C₂²×C₁₁	semidirect
54. C₂×C₁₁	#676	direct (N × H)
65. C₂×C₈	D₅×C₁₁	semidirect
66. C₁₁	C₂×#676	direct (N × H)
67. C₂×C₅	C₁₁×M₁₆	semidirect
76. C₈	C₂×D₅×C₁₁	semidirect
77. C₅	C₂×C₁₁×M₁₆	semidirect
85. C₂	C₁₁×#676	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅×C₁₁	2
C₂×C₅×C₈×C₁₁	2
C₂×C₁₁×#168	2
C₁₁×#676	2
C₂×C₁₁×M₁₆	5
C₂×#676	11

Subgroups — C2×C11×#676 #13183113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#676 #13183113