Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
534 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 117 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. C5×#1997 | C2 | semidirect |
| 3. #10602567 | C2 | semidirect |
| 5. #10601284 | C2 | semidirect |
| 7. #10600640 | C2 | semidirect |
| 63. #1997 | D5 | semidirect |
| 157. #168 | #100 | semidirect |
| 285. C5 | #9805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65374 | 2 |
| C5×#1997 | 2 |
| #10602567 | 2 |
| #10601295 | 2 |
| #10601284 | 2 |
| #10600669 | 2 |
| #10600640 | 2 |
| #9805 | 5 |