Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
336 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 16. #64098 | C5 | direct (N × H) |
| 80. C32×C5 | #125 | semidirect |
| 125. C3×C5 | #889 | semidirect |
| 137. C32 | C5×#125 | semidirect |
| 148. C5 | #64098 | direct (N × H) |
| 157. C3 | C5×#889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C4⋊C4 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×#3750 | 2 |
| C4×C5×C3⋊Dic3 | 2 |
| C5×#889 | 3 |
| #64098 | 5 |