Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 2. C5×#2155 | C2 | semidirect |
| 3. #10602241 | C2 | semidirect |
| 4. #10602224 | C2 | semidirect |
| 5. #10601504 | C2 | semidirect |
| 6. #10601480 | C2 | semidirect |
| 7. #10598218 | C2 | semidirect |
| 55. C2×C5×C16 | D4 | semidirect |
| 69. #2155 | D5 | semidirect |
| 212. C2×C16 | D20 | semidirect |
| 336. C5 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610911 | 2 |
| C5×#2155 | 2 |
| #10602241 | 2 |
| #10602224 | 2 |
| #10601504 | 2 |
| #10601480 | 2 |
| #10598218 | 2 |
| #13395 | 5 |