Subgroups — C₂×C₅×C₇×C₁₁×D₇ #24924800

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₁×D₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₁×D₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₅×C₇×C₁₁	—	7	1	no	maximal
6	C₂×C₅×C₁₁×D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₇×C₁₁×D₇	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₅×C₇×D₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₇×C₁₁	—	2	3	no	—
11	C₂×C₅×C₇×C₁₁	—	7	2	no	—
12	C₂×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₅×C₁₁×D₇	C₂×C₇	1	2	yes	direct product factor
15	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇²	C₂×C₁₁	1	1	yes	characteristic, complemented
17	C₅×C₇×D₇	C₂×C₁₁	1	2	yes	direct product factor
18	C₅×C₇×C₁₁	—	2	3	no	—
19	C₅×C₇×C₁₁	C₂×D₇	1	1	yes	characteristic, direct product factor
20	C₅×C₇×C₁₁	C₂²×C₇	1	1	yes	characteristic, complemented
21	C₂²×C₇×C₁₁	—	7	1	no	—
22	C₂×C₁₁×D₇	C₅×C₇	1	1	yes	characteristic, direct product factor
23	C₅×C₇²	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₅×C₁₁	—	7	1	no	Hall
25	C₂×C₇×D₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₇×C₁₁	—	2	3	no	—
27	C₂×C₇×C₁₁	—	7	2	no	—
28	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic, direct product factor
29	C₂×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
30	C₁₁×D₇	C₂×C₅×C₇	1	2	yes	direct product factor
31	C₂²×C₅×C₇	—	7	1	no	—
32	C₂×C₅×D₇	C₇×C₁₁	1	1	yes	characteristic, direct product factor
33	C₂×C₅×C₁₁	—	7	2	no	—
34	C₂×C₅×C₁₁	C₇×D₇	1	1	yes	characteristic, direct product factor
35	C₂×C₇²	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
36	C₇×D₇	C₂×C₅×C₁₁	1	2	yes	direct product factor
37	C₇×C₁₁	—	2	3	no	—
38	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, direct product factor
39	C₇×C₁₁	C₂²×C₅×C₇	1	1	yes	characteristic, complemented
40	C₂×C₅×C₇	—	2	3	no	—
41	C₂×C₅×C₇	—	7	2	no	—
42	C₂×C₅×C₇	C₁₁×D₇	1	1	yes	characteristic, direct product factor
43	C₂×C₅×C₇	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented
44	C₅×D₇	C₂×C₇×C₁₁	1	2	yes	direct product factor
45	C₅×C₁₁	C₂×C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
46	C₇²	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₁₁	—	7	1	no	Hall
48	C₅×C₇	—	2	3	no	—
49	C₅×C₇	C₂×C₁₁×D₇	1	1	yes	characteristic, direct product factor
50	C₅×C₇	C₂²×C₇×C₁₁	1	1	yes	characteristic, complemented
51	C₂²×C₇	—	7	1	no	—
52	C₂×D₇	C₅×C₇×C₁₁	1	1	yes	characteristic, direct product factor
53	C₂×C₁₁	—	7	2	no	—
54	C₂×C₁₁	C₅×C₇×D₇	1	1	yes	characteristic, direct product factor
55	C₂²×C₅	—	7	1	no	Hall
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	7	2	no	—
58	C₂×C₇	C₅×C₁₁×D₇	1	1	yes	characteristic, direct product factor
59	C₂×C₇	C₂×C₅×C₇×C₁₁	1	1	yes	characteristic, complemented
60	D₇	C₂×C₅×C₇×C₁₁	1	2	yes	direct product factor
61	C₁₁	C₂×C₅×C₇×D₇	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₅	—	7	2	no	—
63	C₂×C₅	C₇×C₁₁×D₇	1	1	yes	characteristic, direct product factor
64	C₇	—	2	3	no	—
65	C₇	C₂×C₅×C₁₁×D₇	1	1	yes	characteristic, direct product factor
66	C₇	C₂²×C₅×C₇×C₁₁	1	1	yes	characteristic, complemented
67	C₅	C₂×C₇×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²	—	7	1	no	Sylow
69	C₂	—	7	2	no	—
70	C₂	C₅×C₇×C₁₁×D₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₁	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₅×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₅×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₁×D₇	C₂	direct (N × H)
2. C₂×C₅×C₇²×C₁₁	C₂	semidirect
3. C₅×C₇²×C₁₁	C₂²	semidirect
4. C₂×C₇×C₁₁×D₇	C₅	direct (N × H)
6. C₂×C₅×C₁₁×D₇	C₇	direct (N × H)
7. C₂×C₇²×C₁₁	C₂×C₅	semidirect
8. C₇×C₁₁×D₇	C₂×C₅	direct (N × H)
9. C₂×C₅×C₇×D₇	C₁₁	direct (N × H)
12. C₂×C₅×C₇×C₁₁	D₇	direct (N × H)
13. C₂×C₅×C₇×C₁₁	C₂×C₇	semidirect
14. C₅×C₁₁×D₇	C₂×C₇	direct (N × H)
15. C₇²×C₁₁	C₂²×C₅	semidirect
16. C₂×C₅×C₇²	C₂×C₁₁	semidirect
17. C₅×C₇×D₇	C₂×C₁₁	direct (N × H)
19. C₅×C₇×C₁₁	C₂×D₇	direct (N × H)
20. C₅×C₇×C₁₁	C₂²×C₇	semidirect
22. C₂×C₁₁×D₇	C₅×C₇	direct (N × H)
23. C₅×C₇²	C₂²×C₁₁	semidirect
25. C₂×C₇×D₇	C₅×C₁₁	direct (N × H)
28. C₂×C₇×C₁₁	C₅×D₇	direct (N × H)
29. C₂×C₇×C₁₁	C₂×C₅×C₇	semidirect
30. C₁₁×D₇	C₂×C₅×C₇	direct (N × H)
32. C₂×C₅×D₇	C₇×C₁₁	direct (N × H)
34. C₂×C₅×C₁₁	C₇×D₇	direct (N × H)
35. C₂×C₇²	C₂×C₅×C₁₁	semidirect
36. C₇×D₇	C₂×C₅×C₁₁	direct (N × H)
38. C₇×C₁₁	C₂×C₅×D₇	direct (N × H)
39. C₇×C₁₁	C₂²×C₅×C₇	semidirect
42. C₂×C₅×C₇	C₁₁×D₇	direct (N × H)
43. C₂×C₅×C₇	C₂×C₇×C₁₁	semidirect
44. C₅×D₇	C₂×C₇×C₁₁	direct (N × H)
45. C₅×C₁₁	C₂×C₇×D₇	direct (N × H)
46. C₇²	C₂²×C₅×C₁₁	semidirect
49. C₅×C₇	C₂×C₁₁×D₇	direct (N × H)
50. C₅×C₇	C₂²×C₇×C₁₁	semidirect
52. C₂×D₇	C₅×C₇×C₁₁	direct (N × H)
54. C₂×C₁₁	C₅×C₇×D₇	direct (N × H)
58. C₂×C₇	C₅×C₁₁×D₇	direct (N × H)
59. C₂×C₇	C₂×C₅×C₇×C₁₁	semidirect
60. D₇	C₂×C₅×C₇×C₁₁	direct (N × H)
61. C₁₁	C₂×C₅×C₇×D₇	direct (N × H)
63. C₂×C₅	C₇×C₁₁×D₇	direct (N × H)
65. C₇	C₂×C₅×C₁₁×D₇	direct (N × H)
66. C₇	C₂²×C₅×C₇×C₁₁	semidirect
67. C₅	C₂×C₇×C₁₁×D₇	direct (N × H)
70. C₂	C₅×C₇×C₁₁×D₇	direct (N × H)

Subgroups — C2×C5×C7×C11×D7 #24924800

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅×C₇×C₁₁×D₇ #24924800