Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
298 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 14. #63918 | C5 | direct (N × H) |
| 27. C32×C4×C5 | Q8 | semidirect |
| 31. C3×C5×Dic3 | Q8 | semidirect |
| 75. C3×C4×C5 | Dic6 | semidirect |
| 76. C3×C4×C5 | Dic6 | semidirect |
| 81. C5×Dic3 | Dic6 | semidirect |
| 94. C32×C5 | C4⋊Q8 | semidirect |
| 102. C32×C4 | C5×Q8 | semidirect |
| 106. C3×Dic3 | C5×Q8 | semidirect |
| 136. C4×C5 | #627 | semidirect |
| 146. C3×C5 | #869 | semidirect |
| 147. C3×C5 | #888 | semidirect |
| 155. C3×C4 | C5×Dic6 | semidirect |
| 156. C3×C4 | C5×Dic6 | semidirect |
| 161. Dic3 | C5×Dic6 | semidirect |
| 166. C32 | C5×C4⋊Q8 | semidirect |
| 182. C5 | #63918 | direct (N × H) |
| 188. C4 | C5×#627 | semidirect |
| 190. C3 | C5×#869 | semidirect |
| 191. C3 | C5×#888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#627 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×#888 | 3 |
| C5×#869 | 3 |
| #63918 | 5 |