Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 110 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×Q8×C3⋊D3 | C2 | semidirect |
| 3. C32×C5×Q16 | C2 | semidirect |
| 4. C5×#3756 | C2 | semidirect |
| 5. C5×#3755 | C2 | semidirect |
| 6. C5×#3744 | C2 | semidirect |
| 7. C5×#3743 | C2 | semidirect |
| 20. #64127 | C5 | direct (N × H) |
| 23. C3×C5×Q16 | D3 | semidirect |
| 37. Q8×C3⋊D3 | C2×C5 | semidirect |
| 38. C32×Q16 | C2×C5 | semidirect |
| 39. #3756 | C2×C5 | semidirect |
| 40. #3755 | C2×C5 | semidirect |
| 41. #3744 | C2×C5 | semidirect |
| 42. #3743 | C2×C5 | semidirect |
| 61. C5×Q16 | C3⋊D3 | semidirect |
| 85. C3×Q16 | C5×D3 | semidirect |
| 90. C32×C5 | #137 | semidirect |
| 137. Q16 | C5×C3⋊D3 | semidirect |
| 141. C3×C5 | #918 | semidirect |
| 152. C32 | C5×#137 | semidirect |
| 167. C5 | #64127 | direct (N × H) |
| 175. C3 | C5×#918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| C5×Q8×C3⋊D3 | 2 |
| C32×C5×Q16 | 2 |
| C5×#3756 | 2 |
| C5×#3755 | 2 |
| C5×#3744 | 2 |
| C5×#3743 | 2 |
| C5×#918 | 3 |
| #64127 | 5 |