Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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×#2216 | C2 | semidirect |
| 3. C2×#64742 | C2 | semidirect |
| 4. C2×#64741 | C2 | semidirect |
| 5. C22⋊#3926 | C2 | semidirect |
| 6. #10598069 | C2 | semidirect |
| 7. #10598068 | C2 | semidirect |
| 51. #2216 | D5 | semidirect |
| 202. C5 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65193 | 2 |
| C5×#2216 | 2 |
| C2×#64742 | 2 |
| C2×#64741 | 2 |
| C22⋊#3926 | 2 |
| #10598069 | 2 |
| #10598068 | 2 |
| #13666 | 5 |