Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
258 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. C5×#3756 | C2 | semidirect |
| 4. C3×C5×#216 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 6. C5×#3718 | C2 | semidirect |
| 21. D3×#216 | C5 | direct (N × H) |
| 33. C5×#216 | D3 | direct (N × H) |
| 47. #3756 | C2×C5 | semidirect |
| 48. C3×#216 | C2×C5 | semidirect |
| 49. #3719 | C2×C5 | semidirect |
| 50. #3718 | C2×C5 | semidirect |
| 80. C3×C5×D3 | Q16 | semidirect |
| 127. #216 | C5×D3 | direct (N × H) |
| 131. C32×C5 | C2×Q16 | semidirect |
| 155. C5×D3 | #216 | direct (N × H) |
| 189. C3×D3 | C5×Q16 | semidirect |
| 198. C3×C5 | D3×Q16 | semidirect |
| 199. C3×C5 | C2×#216 | semidirect |
| 219. C32 | C2×C5×Q16 | semidirect |
| 235. D3 | C5×#216 | direct (N × H) |
| 236. C5 | D3×#216 | direct (N × H) |
| 245. C3 | C5×D3×Q16 | semidirect |
| 246. C3 | C2×C5×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D3×Q8 | 2 |
| C5×D3×Dic6 | 2 |
| C5×#3756 | 2 |
| C3×C5×#216 | 2 |
| C5×#3719 | 2 |
| C5×#3718 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C2×C5×#216 | 3 |
| C5×D3×Q16 | 3 |
| D3×#216 | 5 |