Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
454 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10604739 | C2 | semidirect |
| 4. #10604738 | C2 | semidirect |
| 6. #10598787 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 104. C5×M16 | M16 | semidirect |
| 118. #681 | M16 | semidirect |
| 262. M16 | #704 | semidirect |
| 328. C5 | #8837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617500 | 2 |
| #10604948 | 2 |
| #10604739 | 2 |
| #10604738 | 2 |
| Dic5×#100 | 2 |
| #10598787 | 2 |
| #8837 | 5 |