Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1040 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 296 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×C52×D3 | C2 | semidirect |
| 2. C2×C52×#67 | C2 | semidirect |
| 3. C2×C52×D12 | C2 | semidirect |
| 4. C3×C52×C22⋊C4 | C2 | semidirect |
| 5. C52×(C2×D3)⋊C4 | C2 | semidirect |
| 11. C22×C52×D3 | C22 | semidirect |
| 12. C2×C3×C4×C52 | C22 | semidirect |
| 14. C2×C52×Dic3 | C22 | semidirect |
| 16. C5×#882 | C5 | direct (N × H) |
| 21. C52×C22⋊C4 | D3 | semidirect |
| 23. C22×C3×C52 | D4 | semidirect |
| 30. C2×C52×D3 | D4 | semidirect |
| 33. C23×C5×D3 | C2×C5 | semidirect |
| 34. C2×C5×#67 | C2×C5 | semidirect |
| 35. C2×C5×D12 | C2×C5 | semidirect |
| 36. C3×C5×C22⋊C4 | C2×C5 | semidirect |
| 37. C5×(C2×D3)⋊C4 | C2×C5 | semidirect |
| 46. C2×C4×C52 | C2×D3 | semidirect |
| 57. C22×C5×D3 | C22×C5 | semidirect |
| 58. C2×C3×C4×C5 | C22×C5 | semidirect |
| 60. C2×C5×Dic3 | C22×C5 | semidirect |
| 69. C22×C52 | D12 | semidirect |
| 73. #882 | C52 | direct (N × H) |
| 78. C5×C22⋊C4 | C5×D3 | semidirect |
| 79. C3×C52 | #120 | semidirect |
| 81. C22×C3×C5 | C5×D4 | semidirect |
| 88. C2×C5×D3 | C5×D4 | semidirect |
| 96. C23×D3 | C2×C52 | semidirect |
| 97. C2×#67 | C2×C52 | semidirect |
| 98. C2×D12 | C2×C52 | semidirect |
| 99. C3×C22⋊C4 | C2×C52 | semidirect |
| 100. (C2×D3)⋊C4 | C2×C52 | semidirect |
| 109. C2×C4×C5 | C2×C5×D3 | semidirect |
| 116. C52 | #882 | direct (N × H) |
| 121. C22×D3 | C22×C52 | semidirect |
| 122. C2×C3×C4 | C22×C52 | semidirect |
| 124. C2×Dic3 | C22×C52 | semidirect |
| 133. C22×C5 | C5×D12 | semidirect |
| 141. C22⋊C4 | C52×D3 | semidirect |
| 142. C3×C5 | C5×#120 | semidirect |
| 144. C22×C3 | C52×D4 | semidirect |
| 151. C2×D3 | C52×D4 | semidirect |
| 167. C2×C4 | C2×C52×D3 | semidirect |
| 173. C5 | C5×#882 | direct (N × H) |
| 181. C22 | C52×D12 | semidirect |
| 185. C3 | C52×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C52×D3 | 2 |
| C2×C52×#67 | 2 |
| C2×C52×D12 | 2 |
| C3×C52×C22⋊C4 | 2 |
| C52×(C2×D3)⋊C4 | 2 |
| C52×#120 | 3 |
| C5×#882 | 5 |