Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
212 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 32 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. C5×C22⋊#157 | C2 | semidirect |
| 3. C23×C32×C5 | C4 | semidirect |
| 7. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 8. #63786 | C5 | direct (N × H) |
| 19. C22⋊#157 | C2×C5 | semidirect |
| 30. C23×C32 | C4×C5 | semidirect |
| 34. C2×C3⋊Dic3 | C4×C5 | semidirect |
| 42. C32×C5 | #99 | semidirect |
| 44. C23×C5 | #157 | semidirect |
| 88. C32 | C5×#99 | semidirect |
| 90. C23 | C5×#157 | semidirect |
| 98. C5 | #63786 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C5×C22⋊#157 | 2 |
| #63786 | 5 |
| C5×#99 | 9 |