Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2141 | C2 | semidirect |
| 3. C2×#64785 | C2 | semidirect |
| 5. #10601455 | C2 | semidirect |
| 7. #10598301 | C2 | semidirect |
| 67. #2141 | D5 | semidirect |
| 298. C5 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65480 | 2 |
| C5×#2141 | 2 |
| C2×#64785 | 2 |
| C2×#64736 | 2 |
| #10601455 | 2 |
| #10601445 | 2 |
| #10598301 | 2 |
| #13414 | 5 |