Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
678 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 248 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. C2×C3×C5×Dic6 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 5. C5×#3797 | C2 | direct (N × H) |
| 12. C3×C5×Dic6 | C22 | semidirect |
| 13. C5×#627 | C22 | semidirect |
| 15. C2×#3797 | C5 | direct (N × H) |
| 22. C2×C5×Dic6 | D3 | semidirect |
| 24. C2×C5×C3⋊D3 | Q8 | semidirect |
| 31. C2×C3×Dic6 | C2×C5 | semidirect |
| 32. C2×#627 | C2×C5 | semidirect |
| 34. #3797 | C2×C5 | direct (N × H) |
| 48. C5×Dic6 | C2×D3 | semidirect |
| 50. C2×C32×C5 | C2×Q8 | semidirect |
| 52. C5×C3⋊D3 | C2×Q8 | semidirect |
| 63. C3×Dic6 | C22×C5 | semidirect |
| 64. #627 | C22×C5 | semidirect |
| 84. C2×Dic6 | C5×D3 | semidirect |
| 85. C32×C5 | C22×Q8 | semidirect |
| 95. C2×C3⋊D3 | C5×Q8 | semidirect |
| 103. C2×C3×C5 | D3×Q8 | semidirect |
| 120. Dic6 | C2×C5×D3 | semidirect |
| 127. C2×C32 | C2×C5×Q8 | semidirect |
| 129. C3⋊D3 | C2×C5×Q8 | semidirect |
| 136. C3×C5 | C2×D3×Q8 | semidirect |
| 150. C2×C5 | #3797 | direct (N × H) |
| 152. C32 | C22×C5×Q8 | semidirect |
| 163. C2×C3 | C5×D3×Q8 | semidirect |
| 167. C5 | C2×#3797 | direct (N × H) |
| 175. C3 | C2×C5×D3×Q8 | semidirect |
| 177. C2 | C5×#3797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C2×C5×#627 | 2 |
| C2×C5×#624 | 2 |
| C5×#3797 | 2 |
| C2×C5×D3×Q8 | 3 |
| C2×#3797 | 5 |