Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. C5×#1812 | C2 | semidirect |
| 3. #10602800 | C2 | semidirect |
| 4. #10597972 | C2 | semidirect |
| 7. C22×D40 | C4 | semidirect |
| 10. #65424 | C4 | semidirect |
| 15. #65395 | C4 | semidirect |
| 17. C5×H(3,ℤ/4) | C22 | semidirect |
| 19. #64773 | C22 | semidirect |
| 56. #1812 | D5 | semidirect |
| 113. H(3,ℤ/4) | C2×D5 | semidirect |
| 276. C5 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615530 | 2 |
| C5×#1812 | 2 |
| #10602800 | 2 |
| #10597972 | 2 |
| #11868 | 5 |