Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10598647 | C2 | semidirect |
| 5. #10598646 | C2 | semidirect |
| 6. #10598645 | C2 | semidirect |
| 7. #10598644 | C2 | semidirect |
| 72. C5×C16 | M16 | semidirect |
| 74. #672 | M16 | semidirect |
| 166. C16 | #704 | semidirect |
| 192. C5 | #12025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604699 | 2 |
| #10604697 | 2 |
| Dic5×M32 | 2 |
| #10598647 | 2 |
| #10598646 | 2 |
| #10598645 | 2 |
| #10598644 | 2 |
| #12025 | 5 |