Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 1. C22×C32×C4×C5 | C2 | semidirect |
| 3. C32×C22⋊Dic5 | C2 | semidirect |
| 4. C32×#685 | C2 | semidirect |
| 5. C32×#683 | C2 | semidirect |
| 6. C3×#4075 | C3 | direct (N × H) |
| 15. C22×C3×C4×C5 | C2×C3 | semidirect |
| 17. C3×C22⋊Dic5 | C2×C3 | semidirect |
| 18. C3×#685 | C2×C3 | semidirect |
| 19. C3×#683 | C2×C3 | semidirect |
| 28. #4075 | C32 | direct (N × H) |
| 30. C22×C32×C4 | D5 | semidirect |
| 46. C22×C4×C5 | C2×C32 | semidirect |
| 48. C22⋊Dic5 | C2×C32 | semidirect |
| 49. #685 | C2×C32 | semidirect |
| 50. #683 | C2×C32 | semidirect |
| 67. C22×C3×C4 | C3×D5 | semidirect |
| 71. C32×C5 | #123 | semidirect |
| 112. C22×C4 | C32×D5 | semidirect |
| 116. C3×C5 | C3×#123 | semidirect |
| 129. C32 | #4075 | direct (N × H) |
| 141. C5 | C32×#123 | semidirect |
| 150. C3 | C3×#4075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×C32×C22⋊D5 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×#685 | 2 |
| C32×#683 | 2 |
| C3×#4075 | 3 |
| C32×#123 | 5 |