Subgroups — C₂×C₃×C₄×C₅×C₁₁×C₁₃ #72195044

Order 17160.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₄×C₁₁×C₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₁₁×C₁₃	C₂	1	2	yes	maximal, direct product factor
5	C₂×C₃×C₅×C₁₁×C₁₃	C₄	1	2	yes	direct product factor
6	C₂×C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₄×C₅×C₁₁×C₁₃	C₂×C₃	1	2	yes	direct product factor
9	C₃×C₅×C₁₁×C₁₃	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂²×C₃×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic
11	C₃×C₄×C₁₁×C₁₃	C₂×C₅	1	2	yes	direct product factor
12	C₂×C₃×C₄×C₅×C₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁×C₁₃	C₃×C₄	1	2	yes	direct product factor
14	C₂×C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄×C₅×C₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₄×C₁₁×C₁₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₁×C₁₃	C₄×C₅	1	2	yes	direct product factor
18	C₂×C₃×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic
20	C₃×C₄×C₅×C₁₃	C₂×C₁₁	1	2	yes	direct product factor
21	C₅×C₁₁×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₃×C₅×C₁₁	C₂×C₁₃	1	1	yes	characteristic
23	C₃×C₄×C₅×C₁₁	C₂×C₁₃	1	2	yes	direct product factor
24	C₂²×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic
25	C₄×C₁₁×C₁₃	C₂×C₃×C₅	1	2	yes	direct product factor
26	C₂×C₄×C₅×C₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₄×C₅×C₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₁₁×C₁₃	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃×C₅×C₁₃	C₄×C₁₁	1	2	yes	direct product factor
30	C₂×C₃×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₁	C₄×C₁₃	1	2	yes	direct product factor
32	C₂×C₃×C₅×C₁₁	C₂²×C₁₃	1	1	yes	characteristic
33	C₂×C₃×C₄×C₁₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₁×C₁₃	C₃×C₄×C₅	1	2	yes	direct product factor
35	C₂×C₁₁×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic
36	C₂×C₃×C₄×C₁₁	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂²×C₅×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
38	C₄×C₅×C₁₃	C₂×C₃×C₁₁	1	2	yes	direct product factor
39	C₂²×C₅×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic
40	C₄×C₅×C₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
41	C₃×C₅×C₁₃	C₂×C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
42	C₃×C₅×C₁₁	C₂×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂²×C₃×C₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic
44	C₃×C₄×C₁₃	C₂×C₅×C₁₁	1	2	yes	direct product factor
45	C₁₁×C₁₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
46	C₂²×C₃×C₁₁	C₂×C₅×C₁₃	1	1	yes	characteristic
47	C₃×C₄×C₁₁	C₂×C₅×C₁₃	1	2	yes	direct product factor
48	C₂×C₅×C₁₃	C₃×C₄×C₁₁	1	2	yes	direct product factor
49	C₂×C₅×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic
50	C₂×C₃×C₄×C₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₅×C₁₁	C₃×C₄×C₁₃	1	2	yes	direct product factor
52	C₂×C₅×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₄×C₁₁	C₃×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
55	C₂×C₃×C₁₃	C₄×C₅×C₁₁	1	2	yes	direct product factor
56	C₂×C₃×C₁₃	C₂²×C₅×C₁₁	1	1	yes	characteristic
57	C₂×C₃×C₁₁	C₄×C₅×C₁₃	1	2	yes	direct product factor
58	C₂×C₃×C₁₁	C₂²×C₅×C₁₃	1	1	yes	characteristic
59	C₅×C₁₃	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
60	C₂²×C₃×C₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic
61	C₃×C₄×C₅	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
62	C₅×C₁₁	C₂×C₃×C₄×C₁₃	1	1	yes	characteristic, direct product factor, Hall
63	C₂²×C₁₃	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
64	C₄×C₁₃	C₂×C₃×C₅×C₁₁	1	2	yes	direct product factor
65	C₂²×C₁₁	C₂×C₃×C₅×C₁₃	1	1	yes	characteristic
66	C₄×C₁₁	C₂×C₃×C₅×C₁₃	1	2	yes	direct product factor
67	C₂×C₄×C₅	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
68	C₃×C₁₃	C₂×C₄×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
69	C₃×C₁₁	C₂×C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
70	C₂×C₃×C₅	C₄×C₁₁×C₁₃	1	2	yes	direct product factor
71	C₂×C₃×C₅	C₂²×C₁₁×C₁₃	1	1	yes	characteristic
72	C₂×C₁₃	C₃×C₄×C₅×C₁₁	1	2	yes	direct product factor
73	C₂×C₁₃	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic
74	C₂×C₃×C₄	C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
75	C₂×C₁₁	C₃×C₄×C₅×C₁₃	1	2	yes	direct product factor
76	C₂×C₁₁	C₂²×C₃×C₅×C₁₃	1	1	yes	characteristic
77	C₂²×C₅	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic
78	C₄×C₅	C₂×C₃×C₁₁×C₁₃	1	2	yes	direct product factor
79	C₃×C₅	C₂×C₄×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
80	C₁₃	C₂×C₃×C₄×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₃	C₂×C₅×C₁₁×C₁₃	1	1	yes	characteristic
82	C₃×C₄	C₂×C₅×C₁₁×C₁₃	1	2	yes	direct product factor
83	C₁₁	C₂×C₃×C₄×C₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
84	C₂×C₅	C₃×C₄×C₁₁×C₁₃	1	2	yes	direct product factor
85	C₂×C₅	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic
86	C₂×C₄	C₃×C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₃	C₄×C₅×C₁₁×C₁₃	1	2	yes	direct product factor
88	C₂×C₃	C₂²×C₅×C₁₁×C₁₃	1	1	yes	characteristic
89	C₅	C₂×C₃×C₄×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²	C₂×C₃×C₅×C₁₁×C₁₃	1	1	yes	characteristic
91	C₄	C₂×C₃×C₅×C₁₁×C₁₃	1	2	yes	direct product factor
92	C₃	C₂×C₄×C₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
93	C₂	C₃×C₄×C₅×C₁₁×C₁₃	1	2	yes	direct product factor
94	C₂	C₂²×C₃×C₅×C₁₁×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₅×C₁₁×C₁₃
socle, prime radical	C₂²×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×C₁₁×C₁₃	C₃	direct (N × H)
2. C₂×C₃×C₄×C₁₁×C₁₃	C₅	direct (N × H)
4. C₃×C₄×C₅×C₁₁×C₁₃	C₂	direct (N × H)
5. C₂×C₃×C₅×C₁₁×C₁₃	C₄	direct (N × H)
8. C₄×C₅×C₁₁×C₁₃	C₂×C₃	direct (N × H)
9. C₃×C₅×C₁₁×C₁₃	C₂×C₄	direct (N × H)
11. C₃×C₄×C₁₁×C₁₃	C₂×C₅	direct (N × H)
12. C₂×C₃×C₄×C₅×C₁₃	C₁₁	direct (N × H)
13. C₂×C₅×C₁₁×C₁₃	C₃×C₄	direct (N × H)
15. C₂×C₃×C₄×C₅×C₁₁	C₁₃	direct (N × H)
16. C₂×C₄×C₁₁×C₁₃	C₃×C₅	direct (N × H)
17. C₂×C₃×C₁₁×C₁₃	C₄×C₅	direct (N × H)
20. C₃×C₄×C₅×C₁₃	C₂×C₁₁	direct (N × H)
21. C₅×C₁₁×C₁₃	C₂×C₃×C₄	direct (N × H)
23. C₃×C₄×C₅×C₁₁	C₂×C₁₃	direct (N × H)
25. C₄×C₁₁×C₁₃	C₂×C₃×C₅	direct (N × H)
26. C₂×C₄×C₅×C₁₃	C₃×C₁₁	direct (N × H)
27. C₂×C₄×C₅×C₁₁	C₃×C₁₃	direct (N × H)
28. C₃×C₁₁×C₁₃	C₂×C₄×C₅	direct (N × H)
29. C₂×C₃×C₅×C₁₃	C₄×C₁₁	direct (N × H)
31. C₂×C₃×C₅×C₁₁	C₄×C₁₃	direct (N × H)
33. C₂×C₃×C₄×C₁₃	C₅×C₁₁	direct (N × H)
34. C₂×C₁₁×C₁₃	C₃×C₄×C₅	direct (N × H)
36. C₂×C₃×C₄×C₁₁	C₅×C₁₃	direct (N × H)
38. C₄×C₅×C₁₃	C₂×C₃×C₁₁	direct (N × H)
40. C₄×C₅×C₁₁	C₂×C₃×C₁₃	direct (N × H)
41. C₃×C₅×C₁₃	C₂×C₄×C₁₁	direct (N × H)
42. C₃×C₅×C₁₁	C₂×C₄×C₁₃	direct (N × H)
44. C₃×C₄×C₁₃	C₂×C₅×C₁₁	direct (N × H)
45. C₁₁×C₁₃	C₂×C₃×C₄×C₅	direct (N × H)
47. C₃×C₄×C₁₁	C₂×C₅×C₁₃	direct (N × H)
48. C₂×C₅×C₁₃	C₃×C₄×C₁₁	direct (N × H)
50. C₂×C₃×C₄×C₅	C₁₁×C₁₃	direct (N × H)
51. C₂×C₅×C₁₁	C₃×C₄×C₁₃	direct (N × H)
53. C₂×C₄×C₁₃	C₃×C₅×C₁₁	direct (N × H)
54. C₂×C₄×C₁₁	C₃×C₅×C₁₃	direct (N × H)
55. C₂×C₃×C₁₃	C₄×C₅×C₁₁	direct (N × H)
57. C₂×C₃×C₁₁	C₄×C₅×C₁₃	direct (N × H)
59. C₅×C₁₃	C₂×C₃×C₄×C₁₁	direct (N × H)
61. C₃×C₄×C₅	C₂×C₁₁×C₁₃	direct (N × H)
62. C₅×C₁₁	C₂×C₃×C₄×C₁₃	direct (N × H)
64. C₄×C₁₃	C₂×C₃×C₅×C₁₁	direct (N × H)
66. C₄×C₁₁	C₂×C₃×C₅×C₁₃	direct (N × H)
67. C₂×C₄×C₅	C₃×C₁₁×C₁₃	direct (N × H)
68. C₃×C₁₃	C₂×C₄×C₅×C₁₁	direct (N × H)
69. C₃×C₁₁	C₂×C₄×C₅×C₁₃	direct (N × H)
70. C₂×C₃×C₅	C₄×C₁₁×C₁₃	direct (N × H)
72. C₂×C₁₃	C₃×C₄×C₅×C₁₁	direct (N × H)
74. C₂×C₃×C₄	C₅×C₁₁×C₁₃	direct (N × H)
75. C₂×C₁₁	C₃×C₄×C₅×C₁₃	direct (N × H)
78. C₄×C₅	C₂×C₃×C₁₁×C₁₃	direct (N × H)
79. C₃×C₅	C₂×C₄×C₁₁×C₁₃	direct (N × H)
80. C₁₃	C₂×C₃×C₄×C₅×C₁₁	direct (N × H)
82. C₃×C₄	C₂×C₅×C₁₁×C₁₃	direct (N × H)
83. C₁₁	C₂×C₃×C₄×C₅×C₁₃	direct (N × H)
84. C₂×C₅	C₃×C₄×C₁₁×C₁₃	direct (N × H)
86. C₂×C₄	C₃×C₅×C₁₁×C₁₃	direct (N × H)
87. C₂×C₃	C₄×C₅×C₁₁×C₁₃	direct (N × H)
89. C₅	C₂×C₃×C₄×C₁₁×C₁₃	direct (N × H)
91. C₄	C₂×C₃×C₅×C₁₁×C₁₃	direct (N × H)
92. C₃	C₂×C₄×C₅×C₁₁×C₁₃	direct (N × H)
93. C₂	C₃×C₄×C₅×C₁₁×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₁₁×C₁₃	3
C₂×C₃×C₄×C₁₁×C₁₃	5
C₂²×C₃×C₅×C₁₁×C₁₃	2
C₃×C₄×C₅×C₁₁×C₁₃	2
C₂×C₃×C₄×C₅×C₁₃	11
C₂×C₃×C₄×C₅×C₁₁	13

Subgroups — C2×C3×C4×C5×C11×C13 #72195044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄×C₅×C₁₁×C₁₃ #72195044