Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C2×C5×SD64 | C2 | semidirect |
| 2. Dic5×Q32 | C2 | semidirect |
| 3. C2×#64741 | C2 | semidirect |
| 5. #10598315 | C2 | semidirect |
| 6. #10598087 | C2 | semidirect |
| 7. #10598081 | C2 | semidirect |
| 29. C5×Q32 | D4 | semidirect |
| 43. C2×SD64 | D5 | semidirect |
| 108. Q32 | C22⋊D5 | semidirect |
| 133. Dic5 | SD64 | semidirect |
| 178. C5 | #13686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD64 | 2 |
| Dic5×Q32 | 2 |
| C2×#64741 | 2 |
| #10602257 | 2 |
| #10598315 | 2 |
| #10598087 | 2 |
| #10598081 | 2 |
| #13686 | 5 |