Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 80 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. C5×D4×C3⋊D3 | C2 | semidirect |
| 2. C5×#3802 | C2 | semidirect |
| 3. C3×C5×#213 | C2 | semidirect |
| 4. C5×#3714 | C2 | semidirect |
| 5. C5×#3710 | C2 | semidirect |
| 9. C32×C5×D4 | C22 | semidirect |
| 11. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C3×C5×D12 | C22 | semidirect |
| 15. C3×C5×C3⋊C8 | C22 | semidirect |
| 16. #63926 | C5 | direct (N × H) |
| 22. C5×#213 | D3 | semidirect |
| 34. D4×C3⋊D3 | C2×C5 | semidirect |
| 35. #3802 | C2×C5 | semidirect |
| 36. C3×#213 | C2×C5 | semidirect |
| 37. #3714 | C2×C5 | semidirect |
| 38. #3710 | C2×C5 | semidirect |
| 44. C3×C5×D4 | C2×D3 | semidirect |
| 50. C5×D12 | C2×D3 | semidirect |
| 54. C5×C3⋊C8 | C2×D3 | semidirect |
| 59. C5×C3⋊D3 | D8 | semidirect |
| 68. C32×D4 | C22×C5 | semidirect |
| 70. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 72. C3×D12 | C22×C5 | semidirect |
| 74. C3×C3⋊C8 | C22×C5 | semidirect |
| 95. #213 | C5×D3 | semidirect |
| 98. C32×C5 | C2×D8 | semidirect |
| 105. C5×D4 | D32 | semidirect |
| 132. C3×D4 | C2×C5×D3 | semidirect |
| 138. D12 | C2×C5×D3 | semidirect |
| 142. C3⋊C8 | C2×C5×D3 | semidirect |
| 154. C3⋊D3 | C5×D8 | semidirect |
| 162. C3×C5 | D3×D8 | semidirect |
| 183. C32 | C2×C5×D8 | semidirect |
| 190. D4 | C5×D32 | semidirect |
| 203. C5 | #63926 | direct (N × H) |
| 213. C3 | C5×D3×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C3⋊D3 | 2 |
| C5×#3802 | 2 |
| C3×C5×#213 | 2 |
| C5×#3714 | 2 |
| C5×#3710 | 2 |
| C5×D3×D8 | 3 |
| #63926 | 5 |