Subgroups — C₂×C₁₁×C₁₃×D₄₅ #38787926

Order 25740.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×D₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₃×D₁₅	—	3	1	no	maximal
4	C₅×C₉×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₃×D₉	—	5	1	no	maximal, Hall
6	C₁₁×C₁₃×D₁₅	—	3	2	no	—
7	C₂×C₃×C₅×C₁₁×C₁₃	D₃	1	1	yes	characteristic
8	C₂×D₅×C₁₁×C₁₃	—	9	1	no	Hall
9	C₁₁×C₁₃×D₉	—	5	2	no	—
10	C₂×C₉×C₁₁×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₂×C₁₃×D₄₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic
13	C₂×C₁₁×D₄₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×D₃×C₁₁×C₁₃	—	15	1	no	—
15	C₂×C₅×C₁₁×C₁₃	D₉	1	1	yes	characteristic, complemented
16	D₅×C₁₁×C₁₃	—	9	2	no	—
17	C₉×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₁₃×D₄₅	C₂×C₁₁	1	2	yes	direct product factor
20	C₂×C₅×C₉×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₁₁×D₄₅	C₂×C₁₃	1	2	yes	direct product factor
22	C₂×C₃×C₁₁×C₁₃	D₁₅	1	1	yes	characteristic
23	D₃×C₁₁×C₁₃	—	15	2	no	—
24	C₂×C₁₃×D₁₅	—	3	1	no	—
25	C₅×C₁₁×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₁₁×D₁₅	—	3	1	no	—
27	C₅×C₉×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁×C₁₃	—	45	1	no	Hall
29	C₅×C₉×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×D₉	—	5	1	no	Hall
31	C₃×C₁₁×C₁₃	C₂×D₁₅	1	1	yes	characteristic
32	C₂×C₁₁×D₉	—	5	1	no	Hall
33	C₂×C₃×C₅×C₁₃	D₃×C₁₁	1	1	yes	characteristic
34	C₁₃×D₁₅	—	3	2	no	—
35	C₂×C₃×C₅×C₁₁	D₃×C₁₃	1	1	yes	characteristic
36	C₁₁×D₁₅	—	3	2	no	—
37	C₂×C₁₁×C₁₃	—	45	2	no	—
38	C₂×C₁₁×C₁₃	D₄₅	1	1	yes	characteristic, direct product factor
39	C₂×D₅×C₁₃	—	9	1	no	Hall
40	C₂×C₉×C₁₃	D₅×C₁₁	1	1	yes	characteristic, complemented
41	C₁₃×D₉	—	5	2	no	—
42	C₂×D₅×C₁₁	—	9	1	no	Hall
43	C₂×C₉×C₁₁	D₅×C₁₃	1	1	yes	characteristic, complemented
44	C₁₁×D₉	—	5	2	no	—
45	C₃×C₅×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic
46	C₂×D₄₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
47	C₃×C₅×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic
48	C₂×D₃×C₁₃	—	15	1	no	—
49	C₁₁×C₁₃	C₂×D₄₅	1	1	yes	characteristic, direct product factor, Hall
50	C₂×D₃×C₁₁	—	15	1	no	—
51	C₂×C₅×C₁₃	C₁₁×D₉	1	1	yes	characteristic, complemented
52	D₅×C₁₃	—	9	2	no	—
53	C₉×C₁₃	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
54	C₂×C₅×C₁₁	C₁₃×D₉	1	1	yes	characteristic, complemented
55	D₅×C₁₁	—	9	2	no	—
56	C₉×C₁₁	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₅×C₉	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
58	D₄₅	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
59	C₂×C₃×C₁₃	C₁₁×D₁₅	1	1	yes	characteristic
60	D₃×C₁₃	—	15	2	no	—
61	C₂×C₃×C₁₁	C₁₃×D₁₅	1	1	yes	characteristic
62	D₃×C₁₁	—	15	2	no	—
63	C₅×C₁₃	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Hall
64	C₂×D₁₅	—	3	1	no	—
65	C₅×C₁₁	C₂×C₁₃×D₉	1	1	yes	characteristic, complemented, Hall
66	C₂²×C₁₃	—	45	1	no	Hall
67	C₅×C₉	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
68	C₂²×C₁₁	—	45	1	no	Hall
69	C₃×C₁₃	C₂×C₁₁×D₁₅	1	1	yes	characteristic
70	C₂×D₉	—	5	1	no	Hall
71	C₃×C₁₁	C₂×C₁₃×D₁₅	1	1	yes	characteristic
72	C₂×C₃×C₅	D₃×C₁₁×C₁₃	1	1	yes	characteristic
73	D₁₅	—	3	2	no	—
74	C₂×C₁₃	—	45	2	no	—
75	C₂×C₁₃	C₁₁×D₄₅	1	1	yes	characteristic, direct product factor
76	C₂×C₁₁	—	45	2	no	—
77	C₂×C₁₁	C₁₃×D₄₅	1	1	yes	characteristic, direct product factor
78	C₂×D₅	—	9	1	no	Hall
79	C₂×C₉	D₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented
80	D₉	—	5	2	no	—
81	C₃×C₅	C₂×D₃×C₁₁×C₁₃	1	1	yes	characteristic
82	C₁₃	C₂×C₁₁×D₄₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×D₃	—	15	1	no	—
84	C₁₁	C₂×C₁₃×D₄₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	C₁₁×C₁₃×D₉	1	1	yes	characteristic, complemented
86	D₅	—	9	2	no	—
87	C₉	C₂×D₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₁₁×C₁₃×D₁₅	1	1	yes	characteristic
89	D₃	—	15	2	no	—
90	C₅	C₂×C₁₁×C₁₃×D₉	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	45	1	no	Sylow
92	C₃	C₂×C₁₁×C₁₃×D₁₅	1	1	yes	characteristic
93	C₂	—	45	2	no	—
94	C₂	C₁₁×C₁₃×D₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₁₁×C₁₃
Frattini	C₃	C₂×C₁₁×C₁₃×D₁₅
Fitting	C₂×C₅×C₉×C₁₁×C₁₃	C₂
socle	C₂×C₃×C₅×C₁₁×C₁₃	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₁×C₁₃×D₄₅	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₁×C₁₃	C₂	semidirect
4. C₅×C₉×C₁₁×C₁₃	C₂²	semidirect
10. C₂×C₉×C₁₁×C₁₃	D₅	semidirect
11. C₂×C₁₃×D₄₅	C₁₁	direct (N × H)
13. C₂×C₁₁×D₄₅	C₁₃	direct (N × H)
15. C₂×C₅×C₁₁×C₁₃	D₉	semidirect
17. C₉×C₁₁×C₁₃	C₂×D₅	semidirect
18. C₂×C₅×C₉×C₁₃	C₂×C₁₁	semidirect
19. C₁₃×D₄₅	C₂×C₁₁	direct (N × H)
20. C₂×C₅×C₉×C₁₁	C₂×C₁₃	semidirect
21. C₁₁×D₄₅	C₂×C₁₃	direct (N × H)
25. C₅×C₁₁×C₁₃	C₂×D₉	semidirect
27. C₅×C₉×C₁₃	C₂²×C₁₁	semidirect
29. C₅×C₉×C₁₁	C₂²×C₁₃	semidirect
38. C₂×C₁₁×C₁₃	D₄₅	direct (N × H)
40. C₂×C₉×C₁₃	D₅×C₁₁	semidirect
43. C₂×C₉×C₁₁	D₅×C₁₃	semidirect
46. C₂×D₄₅	C₁₁×C₁₃	direct (N × H)
49. C₁₁×C₁₃	C₂×D₄₅	direct (N × H)
51. C₂×C₅×C₁₃	C₁₁×D₉	semidirect
53. C₉×C₁₃	C₂×D₅×C₁₁	semidirect
54. C₂×C₅×C₁₁	C₁₃×D₉	semidirect
56. C₉×C₁₁	C₂×D₅×C₁₃	semidirect
57. C₂×C₅×C₉	C₂×C₁₁×C₁₃	semidirect
58. D₄₅	C₂×C₁₁×C₁₃	direct (N × H)
63. C₅×C₁₃	C₂×C₁₁×D₉	semidirect
65. C₅×C₁₁	C₂×C₁₃×D₉	semidirect
67. C₅×C₉	C₂²×C₁₁×C₁₃	semidirect
75. C₂×C₁₃	C₁₁×D₄₅	direct (N × H)
77. C₂×C₁₁	C₁₃×D₄₅	direct (N × H)
79. C₂×C₉	D₅×C₁₁×C₁₃	semidirect
82. C₁₃	C₂×C₁₁×D₄₅	direct (N × H)
84. C₁₁	C₂×C₁₃×D₄₅	direct (N × H)
85. C₂×C₅	C₁₁×C₁₃×D₉	semidirect
87. C₉	C₂×D₅×C₁₁×C₁₃	semidirect
90. C₅	C₂×C₁₁×C₁₃×D₉	semidirect
94. C₂	C₁₁×C₁₃×D₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×D₄₅	2
C₂×C₅×C₉×C₁₁×C₁₃	2
C₂×C₁₁×C₁₃×D₁₅	3
C₂×C₁₁×C₁₃×D₉	5
C₂×C₁₃×D₄₅	11
C₂×C₁₁×D₄₅	13

Subgroups — C2×C11×C13×D45 #38787926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₁₃×D₄₅ #38787926