Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 310 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 |
|---|---|---|
| 12. C5×#627 | C4 | direct (N × H) |
| 13. C4×#627 | C5 | direct (N × H) |
| 23. C32×C4×C5 | Q8 | semidirect |
| 59. #627 | C4×C5 | direct (N × H) |
| 65. C3×C4×C5 | Dic6 | semidirect |
| 80. C32×C5 | C4×Q8 | semidirect |
| 88. C32×C4 | C5×Q8 | semidirect |
| 116. C4×C5 | #627 | direct (N × H) |
| 126. C3×C5 | C4×Dic6 | semidirect |
| 132. C3×C4 | C5×Dic6 | semidirect |
| 142. C32 | C4×C5×Q8 | semidirect |
| 155. C5 | C4×#627 | direct (N × H) |
| 161. C4 | C5×#627 | direct (N × H) |
| 163. C3 | C4×C5×Dic6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#627 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×#3724 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C4×C5×Dic6 | 3 |
| C4×#627 | 5 |