Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 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. #63840 | C5 | direct (N × H) |
| 28. C3×C5×Dic3 | Q8 | semidirect |
| 74. C5×Dic3 | Dic6 | semidirect |
| 83. C32×C5 | C4⋊Q8 | semidirect |
| 96. C3×Dic3 | C5×Q8 | semidirect |
| 130. C3×C5 | #888 | semidirect |
| 142. Dic3 | C5×Dic6 | semidirect |
| 145. C32 | C5×C4⋊Q8 | semidirect |
| 158. C5 | #63840 | direct (N × H) |
| 166. 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×#634 | 2 |
| C2×C5×#627 | 2 |
| C3×C5×Dic3⋊C4 | 2 |
| C5×Dic3⋊Dic3 | 2 |
| C5×Dic32 | 2 |
| C5×#888 | 3 |
| #63840 | 5 |