Subgroups — D₅×C₁₁×D₈ #13183123

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×D₅×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₅×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#686	C₂	1	2	yes	maximal, complemented
4	C₁₁×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅×C₁₁	—	2	2	no	—
7	C₅×D₄×C₁₁	C₂²	1	2	yes	complemented
8	C₁₁×C₂²⋊D₅	—	2	2	no	—
9	C₁₁×D₂₀	C₂²	1	2	yes	complemented
10	C₄×D₅×C₁₁	C₂²	1	1	yes	characteristic
11	C₅×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
12	C₁₁×#168	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₁×D₈	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	—	2	2	no	—
15	C₂×D₅×C₁₁	—	2	2	no	—
16	C₂×D₅×C₁₁	—	4	4	no	—
17	C₂×D₅×C₁₁	D₄	1	1	yes	characteristic
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	C₁₁×Dic₅	D₄	1	1	yes	characteristic
20	C₂×D₄×C₁₁	—	5	2	no	—
21	C₁₁×D₈	—	5	1	no	—
22	C₁₁×D₈	—	5	2	no	—
23	C₁₁×D₈	D₅	1	1	yes	characteristic, direct product factor
24	C₂×C₈×C₁₁	—	5	1	no	—
25	D₅×D₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₁₁	—	4	2	no	—
27	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
28	D₅×C₁₁	—	4	2	no	—
29	D₅×C₁₁	D₈	1	2	yes	direct product factor
30	C₂³×C₁₁	—	10	2	no	—
31	D₄×C₁₁	—	5	2	no	—
32	D₄×C₁₁	—	10	2	no	—
33	D₄×C₁₁	C₂×D₅	1	2	yes	complemented
34	C₂×C₄×C₁₁	—	5	1	no	—
35	C₈×C₁₁	—	5	1	no	—
36	C₈×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
37	D₄×D₅	C₂×C₁₁	1	2	yes	complemented
38	C₅×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
39	#686	C₂×C₁₁	1	2	yes	complemented
40	D₄₀	C₂×C₁₁	1	1	yes	characteristic, complemented
41	C₈×D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
42	C₅×C₁₁	C₂×D₈	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₁	—	2	2	no	—
44	C₂²×C₁₁	—	5	1	no	—
45	C₂²×C₁₁	—	10	2	no	—
46	C₂²×C₁₁	—	20	4	no	—
47	C₄×C₁₁	—	5	1	no	—
48	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
49	C₂²×D₅	—	2	2	no	—
50	C₅×D₄	C₂²×C₁₁	1	2	yes	complemented
51	C₂²⋊D₅	—	2	2	no	—
52	D₂₀	C₂²×C₁₁	1	2	yes	complemented
53	C₄×D₅	C₂²×C₁₁	1	1	yes	characteristic
54	C₅×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
55	#168	C₂²×C₁₁	1	1	yes	characteristic, complemented
56	C₂×D₈	—	5	1	no	Sylow
57	C₂×C₁₁	—	4	2	no	—
58	C₂×C₁₁	—	5	2	no	—
59	C₂×C₁₁	—	20	2	no	—
60	C₂×C₁₁	D₄×D₅	1	1	yes	characteristic
61	C₂²×C₅	—	2	2	no	—
62	C₂×D₅	—	2	2	no	—
63	C₂×D₅	—	4	4	no	—
64	C₂×D₅	D₄×C₁₁	1	1	yes	characteristic
65	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
66	Dic₅	D₄×C₁₁	1	1	yes	characteristic
67	C₂×D₄	—	5	2	no	—
68	D₈	—	5	2	no	—
69	D₈	—	5	1	no	—
70	D₈	D₅×C₁₁	1	1	yes	characteristic, direct product factor
71	C₂×C₈	—	5	1	no	—
72	C₁₁	D₅×D₈	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₅	—	4	2	no	—
74	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
75	D₅	—	4	2	no	—
76	D₅	C₁₁×D₈	1	2	yes	direct product factor
77	C₂³	—	10	2	no	—
78	D₄	—	5	2	no	—
79	D₄	—	10	2	no	—
80	D₄	C₂×D₅×C₁₁	1	2	yes	complemented
81	C₂×C₄	—	5	1	no	—
82	C₈	—	5	1	no	—
83	C₈	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
84	C₅	C₂×C₁₁×D₈	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	2	2	no	—
86	C₂²	—	5	1	no	—
87	C₂²	—	10	2	no	—
88	C₂²	—	20	4	no	—
89	C₄	—	5	1	no	—
90	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	—	5	2	no	—
93	C₂	—	20	2	no	—
94	C₂	D₄×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₅×C₁₁×D₈	C₂
socle	C₂×C₅×C₁₁	C₂×D₄
hypercenter	C₁₁×D₈	D₅
hypocenter	C₅	C₂×C₁₁×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₁₁×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×D₅×C₁₁	C₂	semidirect
2. C₅×C₁₁×D₈	C₂	semidirect
3. C₁₁×#686	C₂	semidirect
4. C₁₁×D₄₀	C₂	semidirect
5. C₈×D₅×C₁₁	C₂	semidirect
7. C₅×D₄×C₁₁	C₂²	semidirect
9. C₁₁×D₂₀	C₂²	semidirect
11. C₅×C₈×C₁₁	C₂²	semidirect
12. C₁₁×#168	C₂²	semidirect
23. C₁₁×D₈	D₅	direct (N × H)
25. D₅×D₈	C₁₁	direct (N × H)
29. D₅×C₁₁	D₈	direct (N × H)
33. D₄×C₁₁	C₂×D₅	semidirect
36. C₈×C₁₁	C₂×D₅	semidirect
37. D₄×D₅	C₂×C₁₁	semidirect
38. C₅×D₈	C₂×C₁₁	semidirect
39. #686	C₂×C₁₁	semidirect
40. D₄₀	C₂×C₁₁	semidirect
41. C₈×D₅	C₂×C₁₁	semidirect
42. C₅×C₁₁	C₂×D₈	semidirect
50. C₅×D₄	C₂²×C₁₁	semidirect
52. D₂₀	C₂²×C₁₁	semidirect
54. C₅×C₈	C₂²×C₁₁	semidirect
55. #168	C₂²×C₁₁	semidirect
70. D₈	D₅×C₁₁	direct (N × H)
72. C₁₁	D₅×D₈	direct (N × H)
76. D₅	C₁₁×D₈	direct (N × H)
80. D₄	C₂×D₅×C₁₁	semidirect
83. C₈	C₂×D₅×C₁₁	semidirect
84. C₅	C₂×C₁₁×D₈	semidirect

Maximal subgroups

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

subgroup	index
D₄×D₅×C₁₁	2
C₅×C₁₁×D₈	2
C₁₁×#686	2
C₁₁×D₄₀	2
C₈×D₅×C₁₁	2
C₂×C₁₁×D₈	5
D₅×D₈	11

Subgroups — D5×C11×D8 #13183123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₁×D₈ #13183123