Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
420 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 174 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×#634 | C4 | semidirect |
| 13. #64096 | C5 | direct (N × H) |
| 24. C5×C3⋊Dic3 | Q8 | semidirect |
| 51. #634 | C4×C5 | semidirect |
| 63. C32×C5 | C4×Q8 | semidirect |
| 75. C3⋊Dic3 | C5×Q8 | semidirect |
| 100. C3×C5 | #887 | semidirect |
| 110. C32 | C4×C5×Q8 | semidirect |
| 120. C5 | #64096 | direct (N × H) |
| 127. C3 | C5×#887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#634 | 2 |
| C32×C5×C4⋊C4 | 2 |
| C5×#3750 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#887 | 3 |
| #64096 | 5 |