Subgroups — C₂×C₅×D₃×C₇²×C₁₁ #44568943

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₇²×C₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×C₇²×C₁₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₇²×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇²×C₁₁	—	3	2	no	—
7	C₂×C₅×C₇²×C₁₁	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₅×D₃×C₇×C₁₁	C₇	1	8	yes	maximal, direct product factor
9	D₃×C₇²×C₁₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×D₃×C₇²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₇²×C₁₁	C₂×D₃	1	1	yes	characteristic, direct product factor, Hall
13	C₅×D₃×C₇×C₁₁	C₂×C₇	1	16	yes	direct product factor
14	C₂×C₃×C₅×C₇×C₁₁	C₂×C₇	1	8	yes	complemented
15	C₂²×C₇²×C₁₁	—	3	1	no	Hall
16	C₃×C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₅×C₇×C₁₁	—	3	8	no	—
18	C₂×C₃×C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₅×D₃×C₇²	C₂×C₁₁	1	2	yes	direct product factor
20	C₃×C₅×C₇×C₁₁	C₂²×C₇	1	8	yes	complemented
21	C₂×C₇²×C₁₁	—	3	2	no	—
22	C₂×C₇²×C₁₁	C₅×D₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₅×C₇²	—	3	1	no	Hall
24	C₂×D₃×C₇×C₁₁	C₅×C₇	1	8	yes	direct product factor
25	C₂×C₅×C₇×C₁₁	—	3	16	no	—
26	C₂×C₅×C₇×C₁₁	D₃×C₇	1	8	yes	direct product factor
27	C₃×C₅×C₇²	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×D₃×C₁₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
29	C₂×D₃×C₇²	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₇²×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₅×C₇²	—	3	2	no	—
32	C₂×C₅×C₇²	D₃×C₁₁	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₇×C₁₁	C₂×C₅×C₇	1	8	yes	complemented
34	D₃×C₇×C₁₁	C₂×C₅×C₇	1	16	yes	direct product factor
35	C₂×C₅×D₃×C₇	C₇×C₁₁	1	8	yes	direct product factor
36	C₅×C₇×C₁₁	C₂×D₃×C₇	1	8	yes	direct product factor
37	C₂×C₃×C₅×C₁₁	C₂×C₇²	1	1	yes	characteristic, complemented
38	C₅×D₃×C₁₁	C₂×C₇²	1	2	yes	direct product factor
39	C₂²×C₇×C₁₁	—	3	8	no	—
40	C₂×C₃×C₇²	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
41	D₃×C₇²	C₂×C₅×C₁₁	1	2	yes	direct product factor
42	C₅×C₇²	C₂×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
43	C₃×C₇×C₁₁	C₂²×C₅×C₇	1	8	yes	complemented
44	C₂²×C₅×C₁₁	—	3	1	no	Hall
45	C₂×C₃×C₅×C₇	C₂×C₇×C₁₁	1	8	yes	complemented
46	C₅×D₃×C₇	C₂×C₇×C₁₁	1	16	yes	direct product factor
47	C₂²×C₇²	—	3	1	no	Hall
48	C₃×C₅×C₁₁	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₁	—	3	16	no	—
50	C₂×C₇×C₁₁	C₅×D₃×C₇	1	8	yes	direct product factor
51	C₃×C₇²	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
52	C₂²×C₅×C₇	—	3	8	no	—
53	C₂×D₃×C₁₁	C₅×C₇²	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₅×C₁₁	—	3	2	no	—
55	C₂×C₅×C₁₁	D₃×C₇²	1	1	yes	characteristic, direct product factor
56	C₃×C₅×C₇	C₂²×C₇×C₁₁	1	8	yes	complemented
57	C₂×C₇²	—	3	2	no	—
58	C₂×C₇²	C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor
59	C₂×D₃×C₇	C₅×C₇×C₁₁	1	8	yes	direct product factor
60	C₇×C₁₁	C₂×C₅×D₃×C₇	1	8	yes	direct product factor
61	C₂×C₅×C₇	—	3	16	no	—
62	C₂×C₅×C₇	D₃×C₇×C₁₁	1	8	yes	direct product factor
63	C₂×C₃×C₁₁	C₂×C₅×C₇²	1	1	yes	characteristic, complemented
64	D₃×C₁₁	C₂×C₅×C₇²	1	2	yes	direct product factor
65	C₂×C₅×D₃	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
66	C₅×C₁₁	C₂×D₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
67	C₇²	C₂×C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²×C₁₁	—	3	1	no	Hall
69	C₂×C₃×C₇	C₂×C₅×C₇×C₁₁	1	8	yes	complemented
70	D₃×C₇	C₂×C₅×C₇×C₁₁	1	16	yes	direct product factor
71	C₅×C₇	C₂×D₃×C₇×C₁₁	1	8	yes	direct product factor
72	C₃×C₁₁	C₂²×C₅×C₇²	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃×C₅	C₂×C₇²×C₁₁	1	1	yes	characteristic, complemented
74	C₅×D₃	C₂×C₇²×C₁₁	1	2	yes	direct product factor
75	C₂²×C₇	—	3	8	no	—
76	C₂×C₁₁	—	3	2	no	—
77	C₂×C₁₁	C₅×D₃×C₇²	1	1	yes	characteristic, direct product factor
78	C₃×C₇	C₂²×C₅×C₇×C₁₁	1	8	yes	complemented
79	C₂²×C₅	—	3	1	no	Hall
80	C₃×C₅	C₂²×C₇²×C₁₁	1	1	yes	characteristic, complemented, Hall
81	C₂×C₇	—	3	16	no	—
82	C₂×C₇	C₅×D₃×C₇×C₁₁	1	8	yes	direct product factor
83	C₂×D₃	C₅×C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
84	C₁₁	C₂×C₅×D₃×C₇²	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	—	3	2	no	—
86	C₂×C₅	D₃×C₇²×C₁₁	1	1	yes	characteristic, direct product factor
87	C₇	C₂×C₅×D₃×C₇×C₁₁	1	8	yes	direct product factor
88	C₂×C₃	C₂×C₅×C₇²×C₁₁	1	1	yes	characteristic, complemented
89	D₃	C₂×C₅×C₇²×C₁₁	1	2	yes	direct product factor
90	C₅	C₂×D₃×C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	3	1	no	Sylow
92	C₃	C₂²×C₅×C₇²×C₁₁	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	3	2	no	—
94	C₂	C₅×D₃×C₇²×C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇²×C₁₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₇²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×C₇²×C₁₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇²×C₁₁	C₂	semidirect
4. C₃×C₅×C₇²×C₁₁	C₂²	semidirect
5. C₂×D₃×C₇²×C₁₁	C₅	direct (N × H)
7. C₂×C₅×C₇²×C₁₁	D₃	direct (N × H)
8. C₂×C₅×D₃×C₇×C₁₁	C₇	direct (N × H)
9. D₃×C₇²×C₁₁	C₂×C₅	direct (N × H)
10. C₂×C₃×C₇²×C₁₁	C₂×C₅	semidirect
11. C₂×C₅×D₃×C₇²	C₁₁	direct (N × H)
12. C₅×C₇²×C₁₁	C₂×D₃	direct (N × H)
13. C₅×D₃×C₇×C₁₁	C₂×C₇	direct (N × H)
14. C₂×C₃×C₅×C₇×C₁₁	C₂×C₇	semidirect
16. C₃×C₇²×C₁₁	C₂²×C₅	semidirect
18. C₂×C₃×C₅×C₇²	C₂×C₁₁	semidirect
19. C₅×D₃×C₇²	C₂×C₁₁	direct (N × H)
20. C₃×C₅×C₇×C₁₁	C₂²×C₇	semidirect
22. C₂×C₇²×C₁₁	C₅×D₃	direct (N × H)
24. C₂×D₃×C₇×C₁₁	C₅×C₇	direct (N × H)
26. C₂×C₅×C₇×C₁₁	D₃×C₇	direct (N × H)
27. C₃×C₅×C₇²	C₂²×C₁₁	semidirect
28. C₂×C₅×D₃×C₁₁	C₇²	direct (N × H)
29. C₂×D₃×C₇²	C₅×C₁₁	direct (N × H)
30. C₇²×C₁₁	C₂×C₅×D₃	direct (N × H)
32. C₂×C₅×C₇²	D₃×C₁₁	direct (N × H)
33. C₂×C₃×C₇×C₁₁	C₂×C₅×C₇	semidirect
34. D₃×C₇×C₁₁	C₂×C₅×C₇	direct (N × H)
35. C₂×C₅×D₃×C₇	C₇×C₁₁	direct (N × H)
36. C₅×C₇×C₁₁	C₂×D₃×C₇	direct (N × H)
37. C₂×C₃×C₅×C₁₁	C₂×C₇²	semidirect
38. C₅×D₃×C₁₁	C₂×C₇²	direct (N × H)
40. C₂×C₃×C₇²	C₂×C₅×C₁₁	semidirect
41. D₃×C₇²	C₂×C₅×C₁₁	direct (N × H)
42. C₅×C₇²	C₂×D₃×C₁₁	direct (N × H)
43. C₃×C₇×C₁₁	C₂²×C₅×C₇	semidirect
45. C₂×C₃×C₅×C₇	C₂×C₇×C₁₁	semidirect
46. C₅×D₃×C₇	C₂×C₇×C₁₁	direct (N × H)
48. C₃×C₅×C₁₁	C₂²×C₇²	semidirect
50. C₂×C₇×C₁₁	C₅×D₃×C₇	direct (N × H)
51. C₃×C₇²	C₂²×C₅×C₁₁	semidirect
53. C₂×D₃×C₁₁	C₅×C₇²	direct (N × H)
55. C₂×C₅×C₁₁	D₃×C₇²	direct (N × H)
56. C₃×C₅×C₇	C₂²×C₇×C₁₁	semidirect
58. C₂×C₇²	C₅×D₃×C₁₁	direct (N × H)
59. C₂×D₃×C₇	C₅×C₇×C₁₁	direct (N × H)
60. C₇×C₁₁	C₂×C₅×D₃×C₇	direct (N × H)
62. C₂×C₅×C₇	D₃×C₇×C₁₁	direct (N × H)
63. C₂×C₃×C₁₁	C₂×C₅×C₇²	semidirect
64. D₃×C₁₁	C₂×C₅×C₇²	direct (N × H)
65. C₂×C₅×D₃	C₇²×C₁₁	direct (N × H)
66. C₅×C₁₁	C₂×D₃×C₇²	direct (N × H)
67. C₇²	C₂×C₅×D₃×C₁₁	direct (N × H)
69. C₂×C₃×C₇	C₂×C₅×C₇×C₁₁	semidirect
70. D₃×C₇	C₂×C₅×C₇×C₁₁	direct (N × H)
71. C₅×C₇	C₂×D₃×C₇×C₁₁	direct (N × H)
72. C₃×C₁₁	C₂²×C₅×C₇²	semidirect
73. C₂×C₃×C₅	C₂×C₇²×C₁₁	semidirect
74. C₅×D₃	C₂×C₇²×C₁₁	direct (N × H)
77. C₂×C₁₁	C₅×D₃×C₇²	direct (N × H)
78. C₃×C₇	C₂²×C₅×C₇×C₁₁	semidirect
80. C₃×C₅	C₂²×C₇²×C₁₁	semidirect
82. C₂×C₇	C₅×D₃×C₇×C₁₁	direct (N × H)
83. C₂×D₃	C₅×C₇²×C₁₁	direct (N × H)
84. C₁₁	C₂×C₅×D₃×C₇²	direct (N × H)
86. C₂×C₅	D₃×C₇²×C₁₁	direct (N × H)
87. C₇	C₂×C₅×D₃×C₇×C₁₁	direct (N × H)
88. C₂×C₃	C₂×C₅×C₇²×C₁₁	semidirect
89. D₃	C₂×C₅×C₇²×C₁₁	direct (N × H)
90. C₅	C₂×D₃×C₇²×C₁₁	direct (N × H)
92. C₃	C₂²×C₅×C₇²×C₁₁	semidirect
94. C₂	C₅×D₃×C₇²×C₁₁	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×D₃×C₇²×C₁₁	2
C₂×C₃×C₅×C₇²×C₁₁	2
C₂²×C₅×C₇²×C₁₁	3
C₂×D₃×C₇²×C₁₁	5
C₂×C₅×D₃×C₇×C₁₁	7
C₂×C₅×D₃×C₇²	11

Subgroups — C2×C5×D3×C72×C11 #44568943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×C₇²×C₁₁ #44568943