Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 15. #64713 | C4 | direct (N × H) |
| 109. C4×C5 | #368 | semidirect |
| 149. C5 | C4×#368 | semidirect |
| 154. C4 | #64713 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#108 | 2 |
| C2×#64713 | 2 |
| C4×#3951 | 2 |
| C2×C4×#672 | 2 |
| #10598219 | 2 |
| C4×#368 | 5 |