Subgroups — C₂²×C₁₁×C₂²⋊D₅ #13183439

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×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₂²⋊D₅	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₁×Dic₅	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×D₅×C₁₁	—	2	4	no	—
9	C₂²×D₅×C₁₁	C₂²	1	6	yes	complemented
10	C₁₁×C₂²⋊D₅	C₂²	1	16	yes	direct product factor
11	C₂×C₁₁×Dic₅	C₂²	1	6	yes	complemented
12	C₂²×D₄×C₁₁	—	5	1	no	maximal, 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×D₅×C₁₁	—	2	12	no	—
18	C₂×D₅×C₁₁	C₂³	1	4	yes	complemented
19	C₁₁×Dic₅	C₂³	1	4	yes	complemented
20	C₂⁴×C₁₁	—	5	1	no	—
21	C₂⁴×C₁₁	D₅	1	1	yes	characteristic, complemented
22	C₂×D₄×C₁₁	—	5	12	no	—
23	C₂²×C₄×C₁₁	—	5	1	no	—
24	C₂²×C₂²⋊D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, 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	D₅×C₁₁	—	2	4	no	—
29	C₂³×C₁₁	—	2	4	no	—
30	C₂³×C₁₁	—	5	6	no	—
31	C₂³×C₁₁	—	10	4	no	—
32	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
33	C₂³×C₁₁	C₂×D₅	1	6	yes	complemented
34	D₄×C₁₁	—	5	16	no	—
35	C₂×C₄×C₁₁	—	5	6	no	—
36	C₂⁴×C₅	C₂×C₁₁	1	1	yes	characteristic, complemented
37	C₂³×D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊D₅	C₂×C₁₁	1	12	yes	direct product factor
39	C₂²×Dic₅	C₂×C₁₁	1	1	yes	characteristic, complemented
40	C₅×C₁₁	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	2	12	no	—
42	C₂²×C₁₁	—	5	4	no	—
43	C₂²×C₁₁	—	10	12	no	—
44	C₂²×C₁₁	C₂²⋊D₅	1	4	yes	direct product factor
45	C₂²×C₁₁	C₂²×D₅	1	3	yes	—
46	C₂²×C₁₁	C₂²×D₅	1	4	yes	complemented
47	C₄×C₁₁	—	5	4	no	—
48	C₂³×C₅	—	2	4	no	—
49	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
50	C₂³×C₅	C₂²×C₁₁	1	6	yes	complemented
51	C₂²×D₅	—	2	4	no	—
52	C₂²×D₅	C₂²×C₁₁	1	6	yes	complemented
53	C₂²⋊D₅	C₂²×C₁₁	1	16	yes	direct product factor
54	C₂×Dic₅	C₂²×C₁₁	1	6	yes	complemented
55	C₂²×D₄	—	5	1	no	Sylow
56	C₂×C₁₁	—	2	4	no	—
57	C₂×C₁₁	—	10	4	no	—
58	C₂×C₁₁	C₂×C₂²⋊D₅	1	6	yes	direct product factor
59	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
60	C₂²×C₅	—	2	12	no	—
61	C₂²×C₅	D₄×C₁₁	1	4	yes	complemented
62	C₂²×C₅	C₂³×C₁₁	1	3	yes	—
63	C₂²×C₅	C₂³×C₁₁	1	4	yes	complemented
64	C₂×D₅	—	2	12	no	—
65	C₂×D₅	C₂³×C₁₁	1	4	yes	complemented
66	Dic₅	C₂³×C₁₁	1	4	yes	complemented
67	C₂⁴	—	5	1	no	—
68	C₂⁴	D₅×C₁₁	1	1	yes	characteristic, complemented
69	C₂×D₄	—	5	12	no	—
70	C₂²×C₄	—	5	1	no	—
71	C₁₁	C₂²×C₂²⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×C₅	—	2	4	no	—
73	C₂×C₅	C₂×D₄×C₁₁	1	6	yes	complemented
74	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
75	D₅	—	2	4	no	—
76	C₂³	—	2	4	no	—
77	C₂³	—	5	6	no	—
78	C₂³	—	10	4	no	—
79	C₂³	C₂×D₅×C₁₁	1	1	yes	characteristic
80	C₂³	C₂×D₅×C₁₁	1	6	yes	complemented
81	D₄	—	5	16	no	—
82	C₂×C₄	—	5	6	no	—
83	C₅	C₂²×D₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	2	12	no	—
85	C₂²	—	5	4	no	—
86	C₂²	—	10	12	no	—
87	C₂²	C₁₁×C₂²⋊D₅	1	4	yes	direct product factor
88	C₂²	C₂²×D₅×C₁₁	1	3	yes	—
89	C₂²	C₂²×D₅×C₁₁	1	4	yes	complemented
90	C₄	—	5	4	no	—
91	C₂	—	2	4	no	—
92	C₂	—	10	4	no	—
93	C₂	C₂×C₁₁×C₂²⋊D₅	1	6	yes	direct product factor
94	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₁₁	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₂⁴×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
hypercenter	C₂⁴×C₁₁	D₅
hypocenter	C₅	C₂²×D₄×C₁₁
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂⁴×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂³×D₅×C₁₁	C₂	semidirect
3. C₂×C₁₁×C₂²⋊D₅	C₂	direct (N × H)
4. C₂²×C₁₁×Dic₅	C₂	semidirect
7. C₂³×C₅×C₁₁	C₂²	semidirect
9. C₂²×D₅×C₁₁	C₂²	semidirect
10. C₁₁×C₂²⋊D₅	C₂²	direct (N × H)
11. C₂×C₁₁×Dic₅	C₂²	semidirect
14. C₂²×C₅×C₁₁	D₄	semidirect
16. C₂²×C₅×C₁₁	C₂³	semidirect
18. C₂×D₅×C₁₁	C₂³	semidirect
19. C₁₁×Dic₅	C₂³	semidirect
21. C₂⁴×C₁₁	D₅	semidirect
24. C₂²×C₂²⋊D₅	C₁₁	direct (N × H)
26. C₂×C₅×C₁₁	C₂×D₄	semidirect
33. C₂³×C₁₁	C₂×D₅	semidirect
36. C₂⁴×C₅	C₂×C₁₁	semidirect
37. C₂³×D₅	C₂×C₁₁	semidirect
38. C₂×C₂²⋊D₅	C₂×C₁₁	direct (N × H)
39. C₂²×Dic₅	C₂×C₁₁	semidirect
40. C₅×C₁₁	C₂²×D₄	semidirect
44. C₂²×C₁₁	C₂²⋊D₅	direct (N × H)
46. C₂²×C₁₁	C₂²×D₅	semidirect
50. C₂³×C₅	C₂²×C₁₁	semidirect
52. C₂²×D₅	C₂²×C₁₁	semidirect
53. C₂²⋊D₅	C₂²×C₁₁	direct (N × H)
54. C₂×Dic₅	C₂²×C₁₁	semidirect
58. C₂×C₁₁	C₂×C₂²⋊D₅	direct (N × H)
61. C₂²×C₅	D₄×C₁₁	semidirect
63. C₂²×C₅	C₂³×C₁₁	semidirect
65. C₂×D₅	C₂³×C₁₁	semidirect
66. Dic₅	C₂³×C₁₁	semidirect
68. C₂⁴	D₅×C₁₁	semidirect
71. C₁₁	C₂²×C₂²⋊D₅	direct (N × H)
73. C₂×C₅	C₂×D₄×C₁₁	semidirect
80. C₂³	C₂×D₅×C₁₁	semidirect
83. C₅	C₂²×D₄×C₁₁	semidirect
87. C₂²	C₁₁×C₂²⋊D₅	direct (N × H)
89. C₂²	C₂²×D₅×C₁₁	semidirect
93. C₂	C₂×C₁₁×C₂²⋊D₅	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×D₅×C₁₁	2
C₂×C₁₁×C₂²⋊D₅	2
C₂²×C₁₁×Dic₅	2
C₂²×D₄×C₁₁	5
C₂²×C₂²⋊D₅	11

Subgroups — C22×C11×C22⋊D5 #13183439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₂²⋊D₅ #13183439