Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 114 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×Q16 | C2 | semidirect |
| 3. C5×#3756 | C2 | semidirect |
| 4. C5×#3746 | C2 | semidirect |
| 14. Q16×C3⋊D3 | C5 | direct (N × H) |
| 16. C3×C5×Q16 | D3 | semidirect |
| 27. C32×Q16 | C2×C5 | semidirect |
| 28. #3756 | C2×C5 | semidirect |
| 29. #3746 | C2×C5 | semidirect |
| 40. C5×C3⋊D3 | Q16 | direct (N × H) |
| 44. C5×Q16 | C3⋊D3 | direct (N × H) |
| 59. C3×Q16 | C5×D3 | semidirect |
| 63. C32×C5 | C2×Q16 | semidirect |
| 92. C3⋊D3 | C5×Q16 | direct (N × H) |
| 96. Q16 | C5×C3⋊D3 | direct (N × H) |
| 98. C3×C5 | D3×Q16 | semidirect |
| 106. C32 | C2×C5×Q16 | semidirect |
| 116. C5 | Q16×C3⋊D3 | direct (N × H) |
| 122. C3 | C5×D3×Q16 | 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 |
| C32×C5×Q16 | 2 |
| C5×#3756 | 2 |
| C5×#3746 | 2 |
| C5×C8×C3⋊D3 | 2 |
| C5×D3×Q16 | 3 |
| Q16×C3⋊D3 | 5 |