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 |
|---|---|---|
| 1. C5×Q8×C3⋊D3 | C2 | semidirect |
| 3. C32×C5×SD16 | C2 | semidirect |
| 4. C5×#3756 | C2 | semidirect |
| 5. C5×#3754 | C2 | semidirect |
| 6. C5×#3746 | C2 | semidirect |
| 7. C5×#3743 | C2 | semidirect |
| 20. #64124 | C5 | direct (N × H) |
| 23. C3×C5×SD16 | D3 | semidirect |
| 36. Q8×C3⋊D3 | C2×C5 | semidirect |
| 38. C32×SD16 | C2×C5 | semidirect |
| 39. #3756 | C2×C5 | semidirect |
| 40. #3754 | C2×C5 | semidirect |
| 41. #3746 | C2×C5 | semidirect |
| 42. #3743 | C2×C5 | semidirect |
| 63. C5×SD16 | C3⋊D3 | semidirect |
| 85. C3×SD16 | C5×D3 | semidirect |
| 90. C32×C5 | #137 | semidirect |
| 139. SD16 | C5×C3⋊D3 | semidirect |
| 141. C3×C5 | #915 | semidirect |
| 152. C32 | C5×#137 | semidirect |
| 167. C5 | #64124 | direct (N × H) |
| 175. C3 | C5×#915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C5×#3830 | 2 |
| C32×C5×SD16 | 2 |
| C5×#3756 | 2 |
| C5×#3754 | 2 |
| C5×#3746 | 2 |
| C5×#3743 | 2 |
| C5×#915 | 3 |
| #64124 | 5 |