Subgroups — C₂×C₁₁×#689 #13183158

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#689	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#168	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈×C₁₁	—	2	1	no	—
6	C₅×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₅×C₁₁	—	2	1	no	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×Dic₅	—	2	1	no	—
10	C₁₁×Dic₁₀	—	2	1	no	—
11	C₁₁×Dic₁₀	C₂²	1	2	yes	—
12	C₁₁×#168	C₂²	1	2	yes	—
13	C₂×C₁₁×Q₁₆	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₄×C₅×C₁₁	—	2	2	no	—
16	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
17	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
18	C₁₁×Dic₅	—	2	2	no	—
19	C₂×Q₈×C₁₁	—	5	1	no	—
20	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic
21	C₁₁×Q₁₆	—	5	4	no	—
22	C₂×C₈×C₁₁	—	5	1	no	—
23	C₂×#689	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×C₁₁	Q₁₆	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
26	Q₈×C₁₁	—	2	1	no	—
27	Q₈×C₁₁	—	5	2	no	—
28	Q₈×C₁₁	—	10	1	no	—
29	Q₈×C₁₁	C₂×D₅	1	2	yes	—
30	C₂×C₄×C₁₁	—	2	1	no	—
31	C₂×C₄×C₁₁	—	10	1	no	—
32	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
33	C₈×C₁₁	—	5	2	no	—
34	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic
35	C₂×Dic₁₀	C₂×C₁₁	1	1	yes	characteristic
36	#689	C₂×C₁₁	1	4	yes	direct product factor
37	C₂×#168	C₂×C₁₁	1	1	yes	characteristic
38	C₅×C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
40	C₄×C₁₁	—	2	2	no	—
41	C₄×C₁₁	—	10	2	no	—
42	C₄×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
43	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
44	C₅×Q₈	—	2	1	no	—
45	C₅×Q₈	C₂²×C₁₁	1	2	yes	—
46	C₂×C₄×C₅	—	2	1	no	—
47	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
48	C₂×Dic₅	—	2	1	no	—
49	Dic₁₀	—	2	1	no	—
50	Dic₁₀	C₂²×C₁₁	1	2	yes	—
51	#168	C₂²×C₁₁	1	2	yes	—
52	C₂×Q₁₆	—	5	1	no	Sylow
53	C₂×C₁₁	#689	1	2	yes	direct product factor
54	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
55	C₂²×C₅	D₄×C₁₁	1	1	yes	characteristic
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	D₄×C₁₁	1	1	yes	characteristic
58	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
59	Dic₅	—	2	2	no	—
60	C₂×Q₈	—	5	1	no	—
61	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic
62	Q₁₆	—	5	4	no	—
63	C₂×C₈	—	5	1	no	—
64	C₁₁	C₂×#689	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₅	C₁₁×Q₁₆	1	2	yes	complemented
66	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
67	Q₈	—	2	1	no	—
68	Q₈	—	5	2	no	—
69	Q₈	—	10	1	no	—
70	Q₈	C₂×D₅×C₁₁	1	2	yes	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	10	1	no	—
73	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
74	C₈	—	5	2	no	—
75	C₅	C₂×C₁₁×Q₁₆	1	1	yes	characteristic, complemented, Sylow
76	C₂²	C₁₁×C₂²⋊D₅	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	10	2	no	—
79	C₄	C₁₁×C₂²⋊D₅	1	1	yes	characteristic
80	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
81	C₂	C₁₁×#689	1	2	yes	direct product factor
82	C₂	C₂×C₁₁×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₁₁×#689	C₂	direct (N × H)
23. C₂×#689	C₁₁	direct (N × H)
24. C₂×C₅×C₁₁	Q₁₆	semidirect
36. #689	C₂×C₁₁	direct (N × H)
38. C₅×C₁₁	C₂×Q₁₆	semidirect
53. C₂×C₁₁	#689	direct (N × H)
64. C₁₁	C₂×#689	direct (N × H)
65. C₂×C₅	C₁₁×Q₁₆	semidirect
75. C₅	C₂×C₁₁×Q₁₆	semidirect
81. C₂	C₁₁×#689	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×C₅×Q₈×C₁₁	2
C₂×C₁₁×Dic₁₀	2
C₁₁×#689	2
C₂×C₁₁×#168	2
C₂×C₁₁×Q₁₆	5
C₂×#689	11

Subgroups — C2×C11×#689 #13183158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#689 #13183158