Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2112 | C2 | semidirect |
| 3. #10602770 | C2 | semidirect |
| 4. #10602241 | C2 | semidirect |
| 5. #10602235 | C2 | semidirect |
| 6. #10602220 | C2 | semidirect |
| 7. #10598313 | C2 | semidirect |
| 58. C2×C5×C16 | D4 | semidirect |
| 72. #2112 | D5 | semidirect |
| 212. C2×C16 | C22⋊D5 | semidirect |
| 336. C5 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615473 | 2 |
| C5×#2112 | 2 |
| #10602770 | 2 |
| #10602241 | 2 |
| #10602235 | 2 |
| #10602220 | 2 |
| #10598313 | 2 |
| #13395 | 5 |