Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
418 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 89 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. C5×#1348 | C2 | semidirect |
| 5. #10598267 | C2 | semidirect |
| 6. #10598019 | C2 | semidirect |
| 7. #10597977 | C2 | semidirect |
| 8. C2×D5×Q16 | C4 | semidirect |
| 12. #65477 | C4 | semidirect |
| 18. #65176 | C4 | semidirect |
| 19. D5×#107 | C4 | semidirect |
| 71. #1348 | D5 | semidirect |
| 339. C5 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#467 | 2 |
| D5×C22⋊C16 | 2 |
| #10599662 | 2 |
| C5×#1348 | 2 |
| #10598267 | 2 |
| #10598019 | 2 |
| #10597977 | 2 |
| #11887 | 5 |