Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 132 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. C2×C3×C5×Dic6 | C2 | semidirect |
| 3. C3×C5×#217 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 6. C5×#936 | C3 | direct (N × H) |
| 13. C3×#936 | C5 | direct (N × H) |
| 18. C2×C5×Dic6 | C2×C3 | semidirect |
| 21. C5×#217 | C2×C3 | semidirect |
| 22. C4×C5×Dic3 | C2×C3 | semidirect |
| 31. C2×C3×Dic6 | C2×C5 | semidirect |
| 32. C3×#217 | C2×C5 | semidirect |
| 33. C3×C4×Dic3 | C2×C5 | semidirect |
| 50. #936 | C3×C5 | direct (N × H) |
| 84. C2×Dic6 | C2×C3×C5 | semidirect |
| 87. #217 | C2×C3×C5 | semidirect |
| 88. C4×Dic3 | C2×C3×C5 | semidirect |
| 89. C32×C5 | #124 | semidirect |
| 141. C3×C5 | #936 | direct (N × H) |
| 142. C3×C5 | C3×#124 | semidirect |
| 162. C32 | C5×#124 | semidirect |
| 178. C5 | C3×#936 | direct (N × H) |
| 186. C3 | C5×#936 | direct (N × H) |
| 187. C3 | C3×C5×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C3×C5×Dic6 | 2 |
| C3×C5×#217 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C3×C5×#124 | 3 |
| C5×#936 | 3 |
| C3×#936 | 5 |