Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C2×#64722 | C2 | semidirect |
| 3. #10601497 | C2 | semidirect |
| 6. C5×#1381 | C2 | semidirect |
| 7. #10598220 | C2 | semidirect |
| 19. #64729 | C4 | semidirect |
| 20. #64723 | C4 | semidirect |
| 61. #1381 | D5 | semidirect |
| 256. C5 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602205 | 2 |
| C2×#64722 | 2 |
| #10601497 | 2 |
| #10601489 | 2 |
| C2×#64717 | 2 |
| C5×#1381 | 2 |
| #10598220 | 2 |
| #13152 | 5 |