Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 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. C5×#1980 | C2 | semidirect |
| 3. #10602599 | C2 | semidirect |
| 4. #10600669 | C2 | semidirect |
| 5. #10600643 | C2 | semidirect |
| 6. #10600280 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 74. #1980 | D5 | semidirect |
| 110. C5×M16 | D8 | semidirect |
| 306. M16 | #686 | semidirect |
| 383. C5 | #10500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615033 | 2 |
| C5×#1980 | 2 |
| #10602599 | 2 |
| #10600669 | 2 |
| #10600643 | 2 |
| #10600280 | 2 |
| #10598111 | 2 |
| #10500 | 5 |