Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #10601294 | C2 | semidirect |
| 4. #10601284 | C2 | semidirect |
| 5. #10601231 | C2 | semidirect |
| 7. C5×#1292 | C2 | semidirect |
| 74. #1292 | D5 | semidirect |
| 334. C5 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610790 | 2 |
| #10601320 | 2 |
| #10601294 | 2 |
| #10601284 | 2 |
| #10601231 | 2 |
| C2×#64703 | 2 |
| C5×#1292 | 2 |
| #10461 | 5 |