Subgroups — C₂²×C₅×C₂²⋊D₁₁ #13183424

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂²⋊D₁₁	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₅×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₅×C₁₁	—	2	4	no	—
6	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₅×C₁₁	C₂²	1	6	yes	complemented
8	C₂²×C₅×D₁₁	—	2	4	no	—
9	C₂²×C₅×D₁₁	C₂²	1	6	yes	complemented
10	C₅×C₂²⋊D₁₁	C₂²	1	16	yes	direct product factor
11	C₂×C₅×Dic₁₁	C₂²	1	6	yes	complemented
12	C₂²×C₂²⋊D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₁₁	—	2	12	no	—
14	C₂²×C₅×C₁₁	D₄	1	4	yes	complemented
15	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
16	C₂²×C₅×C₁₁	C₂³	1	4	yes	complemented
17	C₂×C₅×D₁₁	—	2	12	no	—
18	C₂×C₅×D₁₁	C₂³	1	4	yes	complemented
19	C₅×Dic₁₁	C₂³	1	4	yes	complemented
20	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
21	C₂³×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊D₁₁	C₂×C₅	1	12	yes	direct product factor
23	C₂²×Dic₁₁	C₂×C₅	1	1	yes	characteristic, complemented
24	C₂²×C₅×D₄	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	—	2	4	no	—
26	C₂×C₅×C₁₁	C₂×D₄	1	6	yes	complemented
27	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₅×D₁₁	—	2	4	no	—
29	C₂³×C₁₁	—	2	4	no	—
30	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
31	C₂³×C₁₁	C₂²×C₅	1	6	yes	complemented
32	C₂²×D₁₁	—	2	4	no	—
33	C₂²×D₁₁	C₂²×C₅	1	6	yes	complemented
34	C₂²⋊D₁₁	C₂²×C₅	1	16	yes	direct product factor
35	C₂×Dic₁₁	C₂²×C₅	1	6	yes	complemented
36	C₂⁴×C₅	—	11	1	no	—
37	C₂⁴×C₅	D₁₁	1	1	yes	characteristic, complemented
38	C₂×C₅×D₄	—	11	12	no	—
39	C₂²×C₄×C₅	—	11	1	no	—
40	C₅×C₁₁	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	12	no	—
42	C₂²×C₁₁	C₅×D₄	1	4	yes	complemented
43	C₂²×C₁₁	C₂³×C₅	1	3	yes	—
44	C₂²×C₁₁	C₂³×C₅	1	4	yes	complemented
45	C₂×D₁₁	—	2	12	no	—
46	C₂×D₁₁	C₂³×C₅	1	4	yes	complemented
47	Dic₁₁	C₂³×C₅	1	4	yes	complemented
48	C₂³×C₅	—	2	4	no	—
49	C₂³×C₅	—	11	6	no	—
50	C₂³×C₅	—	22	4	no	—
51	C₂³×C₅	C₂×D₁₁	1	1	yes	characteristic
52	C₂³×C₅	C₂×D₁₁	1	6	yes	complemented
53	C₅×D₄	—	11	16	no	—
54	C₂×C₄×C₅	—	11	6	no	—
55	C₂²×D₄	—	11	1	no	Sylow
56	C₂×C₁₁	—	2	4	no	—
57	C₂×C₁₁	C₂×C₅×D₄	1	6	yes	complemented
58	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
59	D₁₁	—	2	4	no	—
60	C₂²×C₅	—	2	12	no	—
61	C₂²×C₅	—	11	4	no	—
62	C₂²×C₅	—	22	12	no	—
63	C₂²×C₅	C₂²⋊D₁₁	1	4	yes	direct product factor
64	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
65	C₂²×C₅	C₂²×D₁₁	1	4	yes	complemented
66	C₄×C₅	—	11	4	no	—
67	C₂⁴	—	11	1	no	—
68	C₂⁴	C₅×D₁₁	1	1	yes	characteristic, complemented
69	C₂×D₄	—	11	12	no	—
70	C₂²×C₄	—	11	1	no	—
71	C₁₁	C₂²×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₅	—	2	4	no	—
73	C₂×C₅	—	22	4	no	—
74	C₂×C₅	C₂×C₂²⋊D₁₁	1	6	yes	direct product factor
75	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
76	C₂³	—	2	4	no	—
77	C₂³	—	11	6	no	—
78	C₂³	—	22	4	no	—
79	C₂³	C₂×C₅×D₁₁	1	1	yes	characteristic
80	C₂³	C₂×C₅×D₁₁	1	6	yes	complemented
81	D₄	—	11	16	no	—
82	C₂×C₄	—	11	6	no	—
83	C₅	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²	—	2	12	no	—
85	C₂²	—	11	4	no	—
86	C₂²	—	22	12	no	—
87	C₂²	C₅×C₂²⋊D₁₁	1	4	yes	direct product factor
88	C₂²	C₂²×C₅×D₁₁	1	3	yes	—
89	C₂²	C₂²×C₅×D₁₁	1	4	yes	complemented
90	C₄	—	11	4	no	—
91	C₂	—	2	4	no	—
92	C₂	—	22	4	no	—
93	C₂	C₂×C₅×C₂²⋊D₁₁	1	6	yes	direct product factor
94	C₂	C₂³×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting	C₂⁴×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
hypercenter	C₂⁴×C₅	D₁₁
hypocenter	C₁₁	C₂²×C₅×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂⁴×C₅

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂³×C₅×D₁₁	C₂	semidirect
3. C₂×C₅×C₂²⋊D₁₁	C₂	direct (N × H)
4. C₂²×C₅×Dic₁₁	C₂	semidirect
7. C₂³×C₅×C₁₁	C₂²	semidirect
9. C₂²×C₅×D₁₁	C₂²	semidirect
10. C₅×C₂²⋊D₁₁	C₂²	direct (N × H)
11. C₂×C₅×Dic₁₁	C₂²	semidirect
12. C₂²×C₂²⋊D₁₁	C₅	direct (N × H)
14. C₂²×C₅×C₁₁	D₄	semidirect
16. C₂²×C₅×C₁₁	C₂³	semidirect
18. C₂×C₅×D₁₁	C₂³	semidirect
19. C₅×Dic₁₁	C₂³	semidirect
20. C₂⁴×C₁₁	C₂×C₅	semidirect
21. C₂³×D₁₁	C₂×C₅	semidirect
22. C₂×C₂²⋊D₁₁	C₂×C₅	direct (N × H)
23. C₂²×Dic₁₁	C₂×C₅	semidirect
26. C₂×C₅×C₁₁	C₂×D₄	semidirect
31. C₂³×C₁₁	C₂²×C₅	semidirect
33. C₂²×D₁₁	C₂²×C₅	semidirect
34. C₂²⋊D₁₁	C₂²×C₅	direct (N × H)
35. C₂×Dic₁₁	C₂²×C₅	semidirect
37. C₂⁴×C₅	D₁₁	semidirect
40. C₅×C₁₁	C₂²×D₄	semidirect
42. C₂²×C₁₁	C₅×D₄	semidirect
44. C₂²×C₁₁	C₂³×C₅	semidirect
46. C₂×D₁₁	C₂³×C₅	semidirect
47. Dic₁₁	C₂³×C₅	semidirect
52. C₂³×C₅	C₂×D₁₁	semidirect
57. C₂×C₁₁	C₂×C₅×D₄	semidirect
63. C₂²×C₅	C₂²⋊D₁₁	direct (N × H)
65. C₂²×C₅	C₂²×D₁₁	semidirect
68. C₂⁴	C₅×D₁₁	semidirect
71. C₁₁	C₂²×C₅×D₄	semidirect
74. C₂×C₅	C₂×C₂²⋊D₁₁	direct (N × H)
80. C₂³	C₂×C₅×D₁₁	semidirect
83. C₅	C₂²×C₂²⋊D₁₁	direct (N × H)
87. C₂²	C₅×C₂²⋊D₁₁	direct (N × H)
89. C₂²	C₂²×C₅×D₁₁	semidirect
93. C₂	C₂×C₅×C₂²⋊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
C₂⁴×C₅×C₁₁	2
C₂³×C₅×D₁₁	2
C₂×C₅×C₂²⋊D₁₁	2
C₂²×C₅×Dic₁₁	2
C₂²×C₂²⋊D₁₁	5
C₂²×C₅×D₄	11

Subgroups — C22×C5×C22⋊D11 #13183424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₂²⋊D₁₁ #13183424