Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #10600834 | C2 | semidirect |
| 4. C5×#1391 | C2 | semidirect |
| 5. #10598182 | C2 | semidirect |
| 8. C2×#4053 | C4 | semidirect |
| 12. #65407 | C4 | semidirect |
| 13. #65399 | C4 | semidirect |
| 14. C2×#3947 | C4 | semidirect |
| 58. #1391 | D5 | semidirect |
| 269. C5 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610389 | 2 |
| #10600853 | 2 |
| #10600834 | 2 |
| C5×#1391 | 2 |
| #10598182 | 2 |
| #12808 | 5 |