Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. #10603874 | C2 | semidirect |
| 3. #10603864 | C2 | semidirect |
| 4. #10598816 | C2 | semidirect |
| 5. #10598815 | C2 | semidirect |
| 6. #10598624 | C2 | semidirect |
| 7. #10598623 | C2 | semidirect |
| 21. #64889 | C22 | semidirect |
| 22. #64889 | C22 | semidirect |
| 24. #64879 | C22 | semidirect |
| 25. C8×#170 | C22 | semidirect |
| 87. C5×Q16 | M16 | semidirect |
| 89. C5×D8 | M16 | semidirect |
| 107. Dic20 | M16 | semidirect |
| 108. D40 | M16 | semidirect |
| 239. Q16 | #700 | semidirect |
| 246. D8 | #700 | semidirect |
| 314. C5 | #11669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611629 | 2 |
| #10603874 | 2 |
| #10603864 | 2 |
| #10598816 | 2 |
| #10598815 | 2 |
| #10598624 | 2 |
| #10598623 | 2 |
| #11669 | 5 |