Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
488 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 488 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. #10604976 | C2 | semidirect |
| 4. C2×Q8⋊#170 | C2 | semidirect |
| 6. #10598793 | C2 | semidirect |
| 7. #10598787 | C2 | semidirect |
| 96. C2×C5×Q8 | M16 | semidirect |
| 146. #681 | M16 | semidirect |
| 300. C2×Q8 | #700 | semidirect |
| 398. C5 | #9098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617115 | 2 |
| #10610677 | 2 |
| #10604976 | 2 |
| C2×Q8⋊#170 | 2 |
| #10604360 | 2 |
| #10598793 | 2 |
| #10598787 | 2 |
| #9098 | 5 |