Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
250 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. C5×#1313 | C2 | semidirect |
| 5. #10598002 | C2 | semidirect |
| 6. #10598002 | C2 | semidirect |
| 7. #10597933 | C2 | semidirect |
| 50. #1313 | D5 | semidirect |
| 70. C5×C16 | M16 | semidirect |
| 159. C16 | #676 | semidirect |
| 183. C5 | #11413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599866 | 2 |
| D5×#346 | 2 |
| #10598862 | 2 |
| C5×#1313 | 2 |
| #10598002 | 2 |
| #10597933 | 2 |
| #11413 | 5 |