Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 4. #10604976 | C2 | semidirect |
| 5. C2×Q8⋊#170 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 101. C2×C5×Q8 | M16 | semidirect |
| 123. C5×M16 | M16 | semidirect |
| 299. C2×Q8 | #704 | semidirect |
| 317. M16 | #704 | semidirect |
| 398. C5 | #9098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617545 | 2 |
| Dic5×#137 | 2 |
| #10605001 | 2 |
| #10604976 | 2 |
| C2×Q8⋊#170 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9098 | 5 |