Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
780 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 202 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. C24×C32×C5 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C5×#3757 | C2 | semidirect |
| 7. C22×C5×C3⋊D3 | C22 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 10. #64162 | C5 | direct (N × H) |
| 11. C24×C3×C5 | D3 | semidirect |
| 16. C22×C32×C5 | D4 | semidirect |
| 21. C24×C32 | C2×C5 | semidirect |
| 22. C2×#638 | C2×C5 | semidirect |
| 23. #3757 | C2×C5 | semidirect |
| 33. C24×C5 | C3⋊D3 | semidirect |
| 38. C22×C3⋊D3 | C22×C5 | semidirect |
| 40. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 43. C22×C3×C5 | #67 | semidirect |
| 47. C24×C3 | C5×D3 | semidirect |
| 50. C32×C5 | #120 | semidirect |
| 58. C22×C32 | C5×D4 | semidirect |
| 74. C22×C5 | #638 | semidirect |
| 80. C24 | C5×C3⋊D3 | semidirect |
| 83. C3×C5 | #953 | semidirect |
| 86. C22×C3 | C5×#67 | semidirect |
| 93. C32 | C5×#120 | semidirect |
| 102. C5 | #64162 | direct (N × H) |
| 106. C22 | C5×#638 | semidirect |
| 109. C3 | C5×#953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C5 | 2 |
| C2×C5×#638 | 2 |
| C5×#3757 | 2 |
| C5×#953 | 3 |
| #64162 | 5 |