Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. #10601313 | C2 | semidirect |
| 5. #10601301 | C2 | semidirect |
| 6. C2×#64701 | C2 | semidirect |
| 7. #10598197 | C2 | semidirect |
| 315. C5 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615014 | 2 |
| C5×#1547 | 2 |
| #10602593 | 2 |
| #10601313 | 2 |
| #10601301 | 2 |
| C2×#64701 | 2 |
| #10598197 | 2 |
| #10551 | 5 |