Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C5×C8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×D3×C8 | C2 | semidirect |
| 4. C5×#3712 | C2 | semidirect |
| 5. C5×#3711 | C2 | semidirect |
| 15. #63803 | C5 | direct (N × H) |
| 23. C5×D3×C8 | D3 | semidirect |
| 31. C8×C3⋊D3 | C2×C5 | semidirect |
| 32. C3×D3×C8 | C2×C5 | semidirect |
| 33. #3712 | C2×C5 | semidirect |
| 34. #3711 | C2×C5 | semidirect |
| 83. D3×C8 | C5×D3 | semidirect |
| 84. C32×C5 | #131 | semidirect |
| 133. C3×C5 | #901 | semidirect |
| 147. C32 | C5×#131 | semidirect |
| 162. C5 | #63803 | direct (N × H) |
| 169. C3 | C5×#901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3798 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C3×C5×D3×C8 | 2 |
| C5×#3712 | 2 |
| C5×#3711 | 2 |
| C5×#901 | 3 |
| #63803 | 5 |