Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 54. C32×C5 | #125 | semidirect |
| 85. C3×C5 | #890 | semidirect |
| 97. C32 | #4016 | semidirect |
| 106. C5 | #63872 | semidirect |
| 112. C3 | #91381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C3⋊Dic3 | 2 |
| C3×C4⋊Dic15 | 2 |
| #10623831 | 2 |
| #91381 | 3 |
| #63872 | 5 |