Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10602205 | C2 | semidirect |
| 3. C2×#64728 | C2 | semidirect |
| 4. #10601478 | C2 | semidirect |
| 5. #10601457 | C2 | semidirect |
| 6. #10601449 | C2 | semidirect |
| 7. C5×#1382 | C2 | semidirect |
| 74. #1382 | D5 | semidirect |
| 328. C5 | #13401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610987 | 2 |
| #10602205 | 2 |
| C2×#64728 | 2 |
| #10601478 | 2 |
| #10601457 | 2 |
| #10601449 | 2 |
| C5×#1382 | 2 |
| #13401 | 5 |