Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×C5×#216 | C2 | semidirect |
| 4. C5×#3719 | C2 | semidirect |
| 16. #63944 | C5 | direct (N × H) |
| 22. C5×#216 | D3 | semidirect |
| 34. C3×#216 | C2×C5 | semidirect |
| 35. #3719 | C2×C5 | semidirect |
| 55. C5×C3⋊D3 | Q16 | semidirect |
| 87. #216 | C5×D3 | semidirect |
| 90. C32×C5 | C2×Q16 | semidirect |
| 134. C3⋊D3 | C5×Q16 | semidirect |
| 141. C3×C5 | D3×Q16 | semidirect |
| 156. C32 | C2×C5×Q16 | semidirect |
| 170. C5 | #63944 | direct (N × H) |
| 178. 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 |
| C5×#3797 | 2 |
| C3×C5×#216 | 2 |
| C5×#3719 | 2 |
| C5×#3710 | 2 |
| C5×D3×Q16 | 3 |
| #63944 | 5 |