Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 116 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×D5×C3⋊Dic3 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic15) | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C32×#685 | C2 | semidirect |
| 6. #10623773 | C2 | semidirect |
| 7. #10623771 | C2 | semidirect |
| 23. C3×#685 | D3 | semidirect |
| 43. #3752 | D5 | semidirect |
| 65. #685 | C3⋊D3 | semidirect |
| 96. C32×C5 | #123 | semidirect |
| 157. C3×C5 | #886 | semidirect |
| 175. C32 | #4029 | semidirect |
| 190. C5 | #64095 | semidirect |
| 203. C3 | #91414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67138 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C4⋊(C3⋊Dic15) | 2 |
| C5×#3752 | 2 |
| C32×#685 | 2 |
| #10623773 | 2 |
| #10623771 | 2 |
| #91414 | 3 |
| #64095 | 5 |