Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
6000 conjugacy classes of subgroups; only the 1610 normal subgroups are shown.
This group has 6000 conjugacy classes of subgroups — too many to draw. Only its 1610 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C5×D12 | C2 | semidirect |
| 2. C22×C3×C42×C5 | C2 | semidirect |
| 3. C2×C5×#874 | C2 | direct (N × H) |
| 8. C22×C5×D12 | C22 | semidirect |
| 9. C2×C3×C42×C5 | C22 | semidirect |
| 10. C5×#874 | C22 | direct (N × H) |
| 11. C22×#874 | C5 | direct (N × H) |
| 14. C22×C42×C5 | D3 | semidirect |
| 18. C22×C3×C4×C5 | D4 | semidirect |
| 21. C2×C5×D12 | C23 | semidirect |
| 22. C3×C42×C5 | C23 | semidirect |
| 23. C23×D12 | C2×C5 | semidirect |
| 24. C22×C3×C42 | C2×C5 | semidirect |
| 25. C2×#874 | C2×C5 | direct (N × H) |
| 31. C2×C42×C5 | C2×D3 | semidirect |
| 38. C2×C3×C4×C5 | C2×D4 | semidirect |
| 44. C22×D12 | C22×C5 | semidirect |
| 45. C2×C3×C42 | C22×C5 | semidirect |
| 46. #874 | C22×C5 | direct (N × H) |
| 52. C22×C4×C5 | D12 | semidirect |
| 54. C42×C5 | C22×D3 | semidirect |
| 57. C22×C42 | C5×D3 | semidirect |
| 58. C22×C3×C5 | #127 | semidirect |
| 63. C3×C4×C5 | C22×D4 | semidirect |
| 67. C22×C3×C4 | C5×D4 | semidirect |
| 70. C2×D12 | C23×C5 | semidirect |
| 71. C3×C42 | C23×C5 | semidirect |
| 78. C2×C4×C5 | C2×D12 | semidirect |
| 85. C2×C42 | C2×C5×D3 | semidirect |
| 86. C2×C3×C5 | C2×#127 | semidirect |
| 94. C2×C3×C4 | C2×C5×D4 | semidirect |
| 99. C22×C5 | #874 | direct (N × H) |
| 102. C4×C5 | C22×D12 | semidirect |
| 108. C22×C4 | C5×D12 | semidirect |
| 110. C42 | C22×C5×D3 | semidirect |
| 111. C3×C5 | C22×#127 | semidirect |
| 112. C22×C3 | C5×#127 | semidirect |
| 117. C3×C4 | C22×C5×D4 | semidirect |
| 119. C2×C5 | C2×#874 | direct (N × H) |
| 127. C2×C4 | C2×C5×D12 | semidirect |
| 129. C2×C3 | C2×C5×#127 | semidirect |
| 132. C5 | C22×#874 | direct (N × H) |
| 135. C22 | C5×#874 | direct (N × H) |
| 138. C4 | C22×C5×D12 | semidirect |
| 139. C3 | C22×C5×#127 | semidirect |
| 141. C2 | C2×C5×#874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D12 | 2 |
| C22×C3×C42×C5 | 2 |
| C2×C5×#874 | 2 |
| C22×C5×#127 | 3 |
| C22×#874 | 5 |