Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
372 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 146 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. C32×C5×M16 | C2 | semidirect |
| 3. C2×C5×C3⋊(C3⋊C8) | C2 | semidirect |
| 4. C5×#3743 | C2 | semidirect |
| 5. C5×C8×C3⋊D3 | C2 | semidirect |
| 15. #64116 | C5 | direct (N × H) |
| 17. C3×C5×M16 | D3 | semidirect |
| 28. C32×M16 | C2×C5 | semidirect |
| 29. C2×C3⋊(C3⋊C8) | C2×C5 | semidirect |
| 30. #3743 | C2×C5 | semidirect |
| 31. C8×C3⋊D3 | C2×C5 | semidirect |
| 46. C5×M16 | C3⋊D3 | semidirect |
| 63. C3×M16 | C5×D3 | semidirect |
| 67. C32×C5 | #131 | semidirect |
| 103. M16 | C5×C3⋊D3 | semidirect |
| 106. C3×C5 | #907 | semidirect |
| 115. C32 | C5×#131 | semidirect |
| 127. C5 | #64116 | direct (N × H) |
| 133. C3 | C5×#907 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3828 | 2 |
| C32×C5×M16 | 2 |
| C2×C5×C3⋊(C3⋊C8) | 2 |
| C5×#3743 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C5×#907 | 3 |
| #64116 | 5 |