Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
518 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10611019 | C2 | semidirect |
| 3. C5×#1517 | C2 | semidirect |
| 4. #10602593 | C2 | semidirect |
| 5. #10600349 | C2 | semidirect |
| 6. #10598236 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 14. #65372 | C4 | semidirect |
| 15. #65361 | C4 | semidirect |
| 72. #1517 | D5 | semidirect |
| 357. C5 | #9309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615028 | 2 |
| #10611019 | 2 |
| C5×#1517 | 2 |
| #10602593 | 2 |
| #10600349 | 2 |
| #10598236 | 2 |
| #10598122 | 2 |
| #9309 | 5 |