Subgroups — C₂²×C₄×C₅×D₁₁ #13183411

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×D₁₁	C₂	1	12	yes	maximal, direct product factor
5	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₅×D₁₁	C₄	1	8	yes	direct product factor
7	C₂²×C₅×D₁₁	C₂²	1	6	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	6	yes	complemented
9	C₂×C₅×Dic₁₁	C₂²	1	6	yes	complemented
10	C₄×C₅×D₁₁	C₂²	1	16	yes	direct product factor
11	C₂²×C₄×D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₅×C₁₁	C₂×C₄	1	4	yes	complemented
13	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
14	C₂×C₅×D₁₁	C₂×C₄	1	24	yes	direct product factor
15	C₂×C₅×D₁₁	C₂³	1	4	yes	—
16	C₄×C₅×C₁₁	C₂³	1	4	yes	complemented
17	C₅×Dic₁₁	C₂³	1	4	yes	complemented
18	C₂³×D₁₁	C₂×C₅	1	1	yes	characteristic
19	C₂²×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
20	C₂²×Dic₁₁	C₂×C₅	1	1	yes	characteristic, complemented
21	C₂×C₄×D₁₁	C₂×C₅	1	12	yes	direct product factor
22	C₂³×C₄×C₅	—	11	1	no	maximal, Hall
23	C₂×C₅×C₁₁	C₂²×C₄	1	6	yes	complemented
24	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
25	C₅×D₁₁	C₂²×C₄	1	8	yes	direct product factor
26	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
27	C₂²×D₁₁	C₄×C₅	1	8	yes	direct product factor
28	C₂²×D₁₁	C₂²×C₅	1	6	yes	—
29	C₂×C₄×C₁₁	C₂²×C₅	1	6	yes	complemented
30	C₂×Dic₁₁	C₂²×C₅	1	6	yes	complemented
31	C₄×D₁₁	C₂²×C₅	1	16	yes	direct product factor
32	C₂⁴×C₅	—	11	1	no	—
33	C₂²×C₄×C₅	—	11	1	no	—
34	C₂²×C₄×C₅	—	11	12	no	—
35	C₂²×C₄×C₅	D₁₁	1	1	yes	characteristic, direct product factor
36	C₅×C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₁₁	C₂×C₄×C₅	1	4	yes	complemented
38	C₂²×C₁₁	C₂³×C₅	1	3	yes	—
39	C₂×D₁₁	C₂×C₄×C₅	1	24	yes	direct product factor
40	C₂×D₁₁	C₂³×C₅	1	4	yes	—
41	C₄×C₁₁	C₂³×C₅	1	4	yes	complemented
42	Dic₁₁	C₂³×C₅	1	4	yes	complemented
43	C₂³×C₅	—	11	6	no	—
44	C₂³×C₅	—	11	8	no	—
45	C₂³×C₅	C₂×D₁₁	1	1	yes	characteristic
46	C₂×C₄×C₅	—	11	6	no	—
47	C₂×C₄×C₅	—	11	16	no	—
48	C₂×C₄×C₅	C₂×D₁₁	1	6	yes	direct product factor
49	C₂³×C₄	—	11	1	no	Sylow
50	C₂×C₁₁	C₂²×C₄×C₅	1	6	yes	complemented
51	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
52	D₁₁	C₂²×C₄×C₅	1	8	yes	direct product factor
53	C₂²×C₅	—	11	24	no	—
54	C₂²×C₅	—	11	4	no	—
55	C₂²×C₅	C₄×D₁₁	1	4	yes	direct product factor
56	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
57	C₄×C₅	—	11	4	no	—
58	C₄×C₅	C₂²×D₁₁	1	4	yes	direct product factor
59	C₂⁴	—	11	1	no	—
60	C₂²×C₄	—	11	1	no	—
61	C₂²×C₄	—	11	12	no	—
62	C₂²×C₄	C₅×D₁₁	1	1	yes	characteristic, direct product factor
63	C₁₁	C₂³×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	—	11	8	no	—
65	C₂×C₅	C₂×C₄×D₁₁	1	6	yes	direct product factor
66	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
67	C₂³	—	11	8	no	—
68	C₂³	—	11	6	no	—
69	C₂³	C₂×C₅×D₁₁	1	1	yes	characteristic
70	C₂×C₄	—	11	6	no	—
71	C₂×C₄	—	11	16	no	—
72	C₂×C₄	C₂×C₅×D₁₁	1	6	yes	direct product factor
73	C₅	C₂²×C₄×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	11	24	no	—
75	C₂²	—	11	4	no	—
76	C₂²	C₄×C₅×D₁₁	1	4	yes	direct product factor
77	C₂²	C₂²×C₅×D₁₁	1	3	yes	—
78	C₄	—	11	4	no	—
79	C₄	C₂²×C₅×D₁₁	1	4	yes	direct product factor
80	C₂	—	11	8	no	—
81	C₂	C₂×C₄×C₅×D₁₁	1	6	yes	direct product factor
82	C₂	C₂³×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄×C₅	D₁₁
commutator, hypocenter	C₁₁	C₂³×C₄×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting	C₂²×C₄×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
prime radical	C₂³×C₅×D₁₁	C₂
cosocle	C₂×C₁₁	C₂⁴×C₅
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₅×C₁₁	C₂	semidirect
3. C₂²×C₅×Dic₁₁	C₂	semidirect
4. C₂×C₄×C₅×D₁₁	C₂	direct (N × H)
6. C₂²×C₅×D₁₁	C₄	direct (N × H)
8. C₂×C₄×C₅×C₁₁	C₂²	semidirect
9. C₂×C₅×Dic₁₁	C₂²	semidirect
10. C₄×C₅×D₁₁	C₂²	direct (N × H)
11. C₂²×C₄×D₁₁	C₅	direct (N × H)
12. C₂²×C₅×C₁₁	C₂×C₄	semidirect
14. C₂×C₅×D₁₁	C₂×C₄	direct (N × H)
16. C₄×C₅×C₁₁	C₂³	semidirect
17. C₅×Dic₁₁	C₂³	semidirect
19. C₂²×C₄×C₁₁	C₂×C₅	semidirect
20. C₂²×Dic₁₁	C₂×C₅	semidirect
21. C₂×C₄×D₁₁	C₂×C₅	direct (N × H)
23. C₂×C₅×C₁₁	C₂²×C₄	semidirect
25. C₅×D₁₁	C₂²×C₄	direct (N × H)
27. C₂²×D₁₁	C₄×C₅	direct (N × H)
29. C₂×C₄×C₁₁	C₂²×C₅	semidirect
30. C₂×Dic₁₁	C₂²×C₅	semidirect
31. C₄×D₁₁	C₂²×C₅	direct (N × H)
35. C₂²×C₄×C₅	D₁₁	direct (N × H)
36. C₅×C₁₁	C₂³×C₄	semidirect
37. C₂²×C₁₁	C₂×C₄×C₅	semidirect
39. C₂×D₁₁	C₂×C₄×C₅	direct (N × H)
41. C₄×C₁₁	C₂³×C₅	semidirect
42. Dic₁₁	C₂³×C₅	semidirect
48. C₂×C₄×C₅	C₂×D₁₁	direct (N × H)
50. C₂×C₁₁	C₂²×C₄×C₅	semidirect
52. D₁₁	C₂²×C₄×C₅	direct (N × H)
55. C₂²×C₅	C₄×D₁₁	direct (N × H)
58. C₄×C₅	C₂²×D₁₁	direct (N × H)
62. C₂²×C₄	C₅×D₁₁	direct (N × H)
63. C₁₁	C₂³×C₄×C₅	semidirect
65. C₂×C₅	C₂×C₄×D₁₁	direct (N × H)
72. C₂×C₄	C₂×C₅×D₁₁	direct (N × H)
73. C₅	C₂²×C₄×D₁₁	direct (N × H)
76. C₂²	C₄×C₅×D₁₁	direct (N × H)
79. C₄	C₂²×C₅×D₁₁	direct (N × H)
81. C₂	C₂×C₄×C₅×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×D₁₁	2
C₂²×C₄×C₅×C₁₁	2
C₂²×C₅×Dic₁₁	2
C₂×C₄×C₅×D₁₁	2
C₂²×C₄×D₁₁	5
C₂³×C₄×C₅	11

Subgroups — C22×C4×C5×D11 #13183411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₅×D₁₁ #13183411