Subgroups — C₂×C₅×C₁₁×C₁₃×C₃⋊D₃ #38788316

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₃×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₁₁×C₁₃	—	3	4	no	maximal
4	C₃²×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₁₃×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₁₁×C₁₃	—	3	8	no	—
7	C₂×C₃×C₅×C₁₁×C₁₃	D₃	1	4	yes	complemented
8	C₂²×C₅×C₁₁×C₁₃	—	9	1	no	Hall
9	C₁₁×C₁₃×C₃⋊D₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃²×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₁₃×C₃⋊D₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₁₁×C₁₃	C₂×D₃	1	4	yes	complemented
13	C₂×C₅×C₁₁×C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×D₃×C₁₁×C₁₃	—	3	4	no	—
15	C₂×C₅×C₁₁×C₁₃	—	9	2	no	—
16	C₂×C₅×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
17	C₃²×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₅×C₁₃×C₃⋊D₃	C₂×C₁₁	1	2	yes	direct product factor
20	C₂×C₃²×C₅×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
21	C₅×C₁₁×C₃⋊D₃	C₂×C₁₃	1	2	yes	direct product factor
22	C₂×C₃×C₁₁×C₁₃	C₅×D₃	1	4	yes	complemented
23	D₃×C₁₁×C₁₃	—	3	8	no	—
24	C₂×C₅×D₃×C₁₃	—	3	4	no	—
25	C₅×C₁₁×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅×D₃×C₁₁	—	3	4	no	—
27	C₃²×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁×C₁₃	—	9	1	no	Hall
29	C₃²×C₅×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃×C₃⋊D₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₁₁×C₁₃	C₂×C₅×D₃	1	4	yes	complemented
32	C₂×C₁₁×C₃⋊D₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₅×C₁₃	D₃×C₁₁	1	4	yes	complemented
34	C₅×D₃×C₁₃	—	3	8	no	—
35	C₂×C₃×C₅×C₁₁	D₃×C₁₃	1	4	yes	complemented
36	C₅×D₃×C₁₁	—	3	8	no	—
37	C₂×C₁₁×C₁₃	—	9	2	no	—
38	C₂×C₁₁×C₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
39	C₂²×C₅×C₁₃	—	9	1	no	Hall
40	C₂×C₃²×C₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
41	C₁₃×C₃⋊D₃	C₂×C₅×C₁₁	1	2	yes	direct product factor
42	C₂²×C₅×C₁₁	—	9	1	no	Hall
43	C₂×C₃²×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
44	C₁₁×C₃⋊D₃	C₂×C₅×C₁₃	1	2	yes	direct product factor
45	C₃×C₅×C₁₃	C₂×D₃×C₁₁	1	4	yes	complemented
46	C₂×C₅×C₃⋊D₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
47	C₃×C₅×C₁₁	C₂×D₃×C₁₃	1	4	yes	complemented
48	C₂×D₃×C₁₃	—	3	4	no	—
49	C₁₁×C₁₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
50	C₂×D₃×C₁₁	—	3	4	no	—
51	C₂×C₅×C₁₃	—	9	2	no	—
52	C₂×C₅×C₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor
53	C₃²×C₁₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
54	C₂×C₅×C₁₁	—	9	2	no	—
55	C₂×C₅×C₁₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
56	C₃²×C₁₁	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃²×C₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
58	C₅×C₃⋊D₃	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
59	C₂×C₃×C₁₃	C₅×D₃×C₁₁	1	4	yes	complemented
60	D₃×C₁₃	—	3	8	no	—
61	C₂×C₃×C₁₁	C₅×D₃×C₁₃	1	4	yes	complemented
62	D₃×C₁₁	—	3	8	no	—
63	C₅×C₁₃	C₂×C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
64	C₂×C₅×D₃	—	3	4	no	—
65	C₅×C₁₁	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
66	C₂²×C₁₃	—	9	1	no	Hall
67	C₃²×C₅	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
68	C₂²×C₁₁	—	9	1	no	Hall
69	C₃×C₁₃	C₂×C₅×D₃×C₁₁	1	4	yes	complemented
70	C₂×C₃⋊D₃	C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
71	C₃×C₁₁	C₂×C₅×D₃×C₁₃	1	4	yes	complemented
72	C₂×C₃×C₅	D₃×C₁₁×C₁₃	1	4	yes	complemented
73	C₅×D₃	—	3	8	no	—
74	C₂×C₁₃	—	9	2	no	—
75	C₂×C₁₃	C₅×C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor
76	C₂×C₁₁	—	9	2	no	—
77	C₂×C₁₁	C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
78	C₂²×C₅	—	9	1	no	Hall
79	C₂×C₃²	C₂×C₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented
80	C₃⋊D₃	C₂×C₅×C₁₁×C₁₃	1	2	yes	direct product factor
81	C₃×C₅	C₂×D₃×C₁₁×C₁₃	1	4	yes	complemented
82	C₁₃	C₂×C₅×C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×D₃	—	3	4	no	—
84	C₁₁	C₂×C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	—	9	2	no	—
86	C₂×C₅	C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
87	C₃²	C₂²×C₅×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₅×D₃×C₁₁×C₁₃	1	4	yes	complemented
89	D₃	—	3	8	no	—
90	C₅	C₂×C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	9	1	no	Sylow
92	C₃	C₂×C₅×D₃×C₁₁×C₁₃	1	4	yes	complemented
93	C₂	—	9	2	no	—
94	C₂	C₅×C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₃×C₃⋊D₃	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₃	C₂	semidirect
4. C₃²×C₅×C₁₁×C₁₃	C₂²	semidirect
5. C₂×C₁₁×C₁₃×C₃⋊D₃	C₅	direct (N × H)
7. C₂×C₃×C₅×C₁₁×C₁₃	D₃	semidirect
9. C₁₁×C₁₃×C₃⋊D₃	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₁₁×C₁₃	C₂×C₅	semidirect
11. C₂×C₅×C₁₃×C₃⋊D₃	C₁₁	direct (N × H)
12. C₃×C₅×C₁₁×C₁₃	C₂×D₃	semidirect
13. C₂×C₅×C₁₁×C₃⋊D₃	C₁₃	direct (N × H)
16. C₂×C₅×C₁₁×C₁₃	C₃⋊D₃	direct (N × H)
17. C₃²×C₁₁×C₁₃	C₂²×C₅	semidirect
18. C₂×C₃²×C₅×C₁₃	C₂×C₁₁	semidirect
19. C₅×C₁₃×C₃⋊D₃	C₂×C₁₁	direct (N × H)
20. C₂×C₃²×C₅×C₁₁	C₂×C₁₃	semidirect
21. C₅×C₁₁×C₃⋊D₃	C₂×C₁₃	direct (N × H)
22. C₂×C₃×C₁₁×C₁₃	C₅×D₃	semidirect
25. C₅×C₁₁×C₁₃	C₂×C₃⋊D₃	direct (N × H)
27. C₃²×C₅×C₁₃	C₂²×C₁₁	semidirect
29. C₃²×C₅×C₁₁	C₂²×C₁₃	semidirect
30. C₂×C₁₃×C₃⋊D₃	C₅×C₁₁	direct (N × H)
31. C₃×C₁₁×C₁₃	C₂×C₅×D₃	semidirect
32. C₂×C₁₁×C₃⋊D₃	C₅×C₁₃	direct (N × H)
33. C₂×C₃×C₅×C₁₃	D₃×C₁₁	semidirect
35. C₂×C₃×C₅×C₁₁	D₃×C₁₃	semidirect
38. C₂×C₁₁×C₁₃	C₅×C₃⋊D₃	direct (N × H)
40. C₂×C₃²×C₁₃	C₂×C₅×C₁₁	semidirect
41. C₁₃×C₃⋊D₃	C₂×C₅×C₁₁	direct (N × H)
43. C₂×C₃²×C₁₁	C₂×C₅×C₁₃	semidirect
44. C₁₁×C₃⋊D₃	C₂×C₅×C₁₃	direct (N × H)
45. C₃×C₅×C₁₃	C₂×D₃×C₁₁	semidirect
46. C₂×C₅×C₃⋊D₃	C₁₁×C₁₃	direct (N × H)
47. C₃×C₅×C₁₁	C₂×D₃×C₁₃	semidirect
49. C₁₁×C₁₃	C₂×C₅×C₃⋊D₃	direct (N × H)
52. C₂×C₅×C₁₃	C₁₁×C₃⋊D₃	direct (N × H)
53. C₃²×C₁₃	C₂²×C₅×C₁₁	semidirect
55. C₂×C₅×C₁₁	C₁₃×C₃⋊D₃	direct (N × H)
56. C₃²×C₁₁	C₂²×C₅×C₁₃	semidirect
57. C₂×C₃²×C₅	C₂×C₁₁×C₁₃	semidirect
58. C₅×C₃⋊D₃	C₂×C₁₁×C₁₃	direct (N × H)
59. C₂×C₃×C₁₃	C₅×D₃×C₁₁	semidirect
61. C₂×C₃×C₁₁	C₅×D₃×C₁₃	semidirect
63. C₅×C₁₃	C₂×C₁₁×C₃⋊D₃	direct (N × H)
65. C₅×C₁₁	C₂×C₁₃×C₃⋊D₃	direct (N × H)
67. C₃²×C₅	C₂²×C₁₁×C₁₃	semidirect
69. C₃×C₁₃	C₂×C₅×D₃×C₁₁	semidirect
70. C₂×C₃⋊D₃	C₅×C₁₁×C₁₃	direct (N × H)
71. C₃×C₁₁	C₂×C₅×D₃×C₁₃	semidirect
72. C₂×C₃×C₅	D₃×C₁₁×C₁₃	semidirect
75. C₂×C₁₃	C₅×C₁₁×C₃⋊D₃	direct (N × H)
77. C₂×C₁₁	C₅×C₁₃×C₃⋊D₃	direct (N × H)
79. C₂×C₃²	C₂×C₅×C₁₁×C₁₃	semidirect
80. C₃⋊D₃	C₂×C₅×C₁₁×C₁₃	direct (N × H)
81. C₃×C₅	C₂×D₃×C₁₁×C₁₃	semidirect
82. C₁₃	C₂×C₅×C₁₁×C₃⋊D₃	direct (N × H)
84. C₁₁	C₂×C₅×C₁₃×C₃⋊D₃	direct (N × H)
86. C₂×C₅	C₁₁×C₁₃×C₃⋊D₃	direct (N × H)
87. C₃²	C₂²×C₅×C₁₁×C₁₃	semidirect
88. C₂×C₃	C₅×D₃×C₁₁×C₁₃	semidirect
90. C₅	C₂×C₁₁×C₁₃×C₃⋊D₃	direct (N × H)
92. C₃	C₂×C₅×D₃×C₁₁×C₁₃	semidirect
94. C₂	C₅×C₁₁×C₁₃×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×C₁₃×C₃⋊D₃	2
C₂×C₃²×C₅×C₁₁×C₁₃	2
C₂×C₅×D₃×C₁₁×C₁₃	3
C₂×C₁₁×C₁₃×C₃⋊D₃	5
C₂×C₅×C₁₃×C₃⋊D₃	11
C₂×C₅×C₁₁×C₃⋊D₃	13

Subgroups — C2×C5×C11×C13×C3⋊D3 #38788316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₁×C₁₃×C₃⋊D₃ #38788316