Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
260 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 62 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. C3×D5×Dic6 | C2 | semidirect |
| 3. #10623827 | C2 | semidirect |
| 4. #10623807 | C2 | semidirect |
| 5. #10623802 | C2 | semidirect |
| 6. C5×#3715 | C2 | semidirect |
| 7. #10623754 | C2 | semidirect |
| 25. D5×Dic6 | D3 | semidirect |
| 51. #3715 | D5 | semidirect |
| 132. C32×C5 | #137 | semidirect |
| 203. C3×C5 | #942 | semidirect |
| 204. C3×C5 | #951 | semidirect |
| 225. C32 | #4061 | semidirect |
| 245. C5 | #63827 | semidirect |
| 254. C3 | #91484 | semidirect |
| 255. C3 | #91513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6772 | 2 |
| C3×D5×Dic6 | 2 |
| #10623827 | 2 |
| #10623807 | 2 |
| #10623802 | 2 |
| C5×#3715 | 2 |
| #10623754 | 2 |
| #91513 | 3 |
| #91484 | 3 |
| #63827 | 5 |