Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. #10617115 | C2 | semidirect |
| 3. #10604932 | C2 | semidirect |
| 4. C2×D4⋊#170 | C2 | semidirect |
| 5. #10604360 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 97. C2×C5×D4 | M16 | semidirect |
| 148. #681 | M16 | semidirect |
| 314. C2×D4 | #700 | semidirect |
| 417. C5 | #9097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617115 | 2 |
| #10610645 | 2 |
| #10604932 | 2 |
| C2×D4⋊#170 | 2 |
| #10604360 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9097 | 5 |