Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 574 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×#1964 | C2 | semidirect |
| 3. #10602474 | C2 | semidirect |
| 4. #10600308 | C2 | semidirect |
| 5. #10600249 | C2 | semidirect |
| 6. #10600242 | C2 | semidirect |
| 7. #10598116 | C2 | semidirect |
| 84. #1964 | D5 | semidirect |
| 137. C5×C22⋊C4 | D8 | semidirect |
| 408. C22⋊C4 | #686 | semidirect |
| 489. C5 | #10564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614356 | 2 |
| C5×#1964 | 2 |
| #10602474 | 2 |
| #10600308 | 2 |
| #10600249 | 2 |
| #10600242 | 2 |
| #10598116 | 2 |
| #10564 | 5 |