Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
206 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 9. C5×#634 | C4 | semidirect |
| 12. #63567 | C5 | direct (N × H) |
| 56. #634 | C4×C5 | semidirect |
| 80. C32×C5 | #103 | semidirect |
| 130. C3×C5 | #810 | semidirect |
| 131. C3×C5 | #816 | semidirect |
| 149. C32 | C5×#103 | semidirect |
| 165. C5 | #63567 | direct (N × H) |
| 172. C3 | C5×#810 | semidirect |
| 173. C3 | C5×#816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#634 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C2×C3×C5×C3⋊C8 | 2 |
| C5×#816 | 3 |
| C5×#810 | 3 |
| #63567 | 5 |