Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
2988 conjugacy classes of subgroups; only the 470 normal subgroups are shown.
This group has 2988 conjugacy classes of subgroups — too many to draw. Only its 470 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. C2×C5×D4×C3⋊D3 | C2 | semidirect |
| 2. C32×C5×#127 | C2 | semidirect |
| 3. C5×#64149 | C2 | semidirect |
| 4. C5×#64083 | C2 | semidirect |
| 5. C42×C5×C3⋊D3 | C2 | semidirect |
| 8. C2×C32×C5×D4 | C22 | semidirect |
| 9. C2×C5×#638 | C22 | semidirect |
| 11. C2×C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C32×C42×C5 | C22 | semidirect |
| 14. C4×C5×C3⋊Dic3 | C22 | semidirect |
| 15. C3⋊D3×#127 | C5 | direct (N × H) |
| 17. C3×C5×#127 | D3 | semidirect |
| 30. C4×C5×C3⋊D3 | D4 | semidirect |
| 32. C2×D4×C3⋊D3 | C2×C5 | semidirect |
| 33. C32×#127 | C2×C5 | semidirect |
| 34. #64149 | C2×C5 | semidirect |
| 35. #64083 | C2×C5 | semidirect |
| 36. C42×C3⋊D3 | C2×C5 | semidirect |
| 38. C2×C3×C5×D4 | C2×D3 | semidirect |
| 43. C3×C42×C5 | C2×D3 | semidirect |
| 51. C32×C4×C5 | C2×D4 | semidirect |
| 52. C5×C3⋊Dic3 | C2×D4 | semidirect |
| 56. C5×#127 | C3⋊D3 | direct (N × H) |
| 59. C2×C32×D4 | C22×C5 | semidirect |
| 60. C2×#638 | C22×C5 | semidirect |
| 62. C2×C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 64. C32×C42 | C22×C5 | semidirect |
| 65. C4×C3⋊Dic3 | C22×C5 | semidirect |
| 77. C3×#127 | C5×D3 | semidirect |
| 84. C5×C3⋊D3 | #127 | direct (N × H) |
| 89. C2×C5×D4 | C2×C3⋊D3 | semidirect |
| 92. C42×C5 | C2×C3⋊D3 | semidirect |
| 102. C4×C3⋊D3 | C5×D4 | semidirect |
| 109. C3×C4×C5 | D3×D4 | semidirect |
| 112. C2×C3×D4 | C2×C5×D3 | semidirect |
| 117. C3×C42 | C2×C5×D3 | semidirect |
| 119. C32×C5 | C2×#127 | semidirect |
| 135. C32×C4 | C2×C5×D4 | semidirect |
| 136. C3⋊Dic3 | C2×C5×D4 | semidirect |
| 140. #127 | C5×C3⋊D3 | direct (N × H) |
| 162. C4×C5 | D4×C3⋊D3 | semidirect |
| 166. C3⋊D3 | C5×#127 | direct (N × H) |
| 171. C2×D4 | C2×C5×C3⋊D3 | semidirect |
| 174. C42 | C2×C5×C3⋊D3 | semidirect |
| 175. C3×C5 | D3×#127 | semidirect |
| 181. C3×C4 | C5×D3×D4 | semidirect |
| 187. C32 | C2×C5×#127 | semidirect |
| 202. C5 | C3⋊D3×#127 | direct (N × H) |
| 209. C4 | C5×D4×C3⋊D3 | semidirect |
| 210. C3 | C5×D3×#127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C3⋊D3 | 2 |
| C32×C5×#127 | 2 |
| C5×#64149 | 2 |
| C5×#64083 | 2 |
| C42×C5×C3⋊D3 | 2 |
| C5×D3×#127 | 3 |
| C3⋊D3×#127 | 5 |