Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 120 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×#3724 | C2 | semidirect |
| 4. C5×Dic32 | C2 | semidirect |
| 7. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 11. #63957 | C5 | direct (N × H) |
| 27. #3724 | C2×C5 | semidirect |
| 28. Dic32 | C2×C5 | semidirect |
| 48. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 70. C32×C5 | #117 | semidirect |
| 113. C3×C5 | #877 | semidirect |
| 129. C32 | C5×#117 | semidirect |
| 141. C5 | #63957 | direct (N × H) |
| 149. C3 | C5×#877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C3×C5×#217 | 2 |
| C5×#3724 | 2 |
| C5×Dic32 | 2 |
| C5×#877 | 3 |
| #63957 | 5 |