Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10601624 | C2 | semidirect |
| 5. C2×#64685 | C2 | semidirect |
| 6. C5×#1302 | C2 | semidirect |
| 7. #10598232 | C2 | semidirect |
| 94. #1302 | D5 | semidirect |
| 361. C5 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611005 | 2 |
| #10610212 | 2 |
| #10601624 | 2 |
| #10601600 | 2 |
| C2×#64685 | 2 |
| C5×#1302 | 2 |
| #10598232 | 2 |
| #9266 | 5 |