Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. #10604792 | C2 | semidirect |
| 2. #10604070 | C2 | semidirect |
| 4. #10598799 | C2 | semidirect |
| 5. #10598641 | C2 | semidirect |
| 6. #10598640 | C2 | semidirect |
| 7. #10598607 | C2 | semidirect |
| 63. C5×D8 | M16 | semidirect |
| 154. D8 | #700 | semidirect |
| 198. C5 | #12078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604792 | 2 |
| #10604070 | 2 |
| #10599970 | 2 |
| #10598799 | 2 |
| #10598641 | 2 |
| #10598640 | 2 |
| #10598607 | 2 |
| #12078 | 5 |