Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
770 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 111 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. #10615805 | C2 | semidirect |
| 3. #10602932 | C2 | semidirect |
| 4. #10602467 | C2 | semidirect |
| 5. #10598107 | C2 | semidirect |
| 7. C2×C5×#127 | C4 | semidirect |
| 8. C2×C5×#124 | C4 | semidirect |
| 13. C5×#391 | C4 | semidirect |
| 14. C5×#390 | C4 | semidirect |
| 69. C22⋊#168 | D4 | semidirect |
| 145. C2×#127 | Dic5 | semidirect |
| 146. C2×#124 | Dic5 | semidirect |
| 155. #391 | Dic5 | semidirect |
| 156. #390 | Dic5 | semidirect |
| 447. C5 | #9445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2431 | 2 |
| #10615805 | 2 |
| #10602932 | 2 |
| #10602467 | 2 |
| #10598107 | 2 |
| #9445 | 5 |