Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 4. C32×C4⋊Dic5 | C2 | semidirect |
| 5. C32×#683 | C2 | semidirect |
| 6. C32×#683 | C2 | semidirect |
| 7. C32×C4×Dic5 | C2 | semidirect |
| 8. C3×#4025 | C3 | direct (N × H) |
| 20. C3×C4⋊Dic5 | C2×C3 | semidirect |
| 21. C3×#683 | C2×C3 | semidirect |
| 22. C3×#683 | C2×C3 | semidirect |
| 23. C3×C4×Dic5 | C2×C3 | semidirect |
| 34. #4025 | C32 | direct (N × H) |
| 57. C4⋊Dic5 | C2×C32 | semidirect |
| 58. #683 | C2×C32 | semidirect |
| 59. #683 | C2×C32 | semidirect |
| 60. C4×Dic5 | C2×C32 | semidirect |
| 85. C32×C5 | #126 | semidirect |
| 136. C3×C5 | C3×#126 | semidirect |
| 151. C32 | #4025 | direct (N × H) |
| 163. C5 | C32×#126 | semidirect |
| 174. C3 | C3×#4025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C22⋊C4 | 2 |
| C32×C22⋊Dic5 | 2 |
| C32×C4⋊Dic5 | 2 |
| C32×#683 | 2 |
| C32×C4×Dic5 | 2 |
| C3×#4025 | 3 |
| C32×#126 | 5 |