Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
638 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 3. C5×#1295 | C2 | semidirect |
| 4. #10598150 | C2 | semidirect |
| 5. #10598121 | C2 | semidirect |
| 16. #64994 | C4 | semidirect |
| 36. C5×#97 | C2×C4 | semidirect |
| 43. #3935 | C2×C4 | semidirect |
| 48. #1295 | D5 | semidirect |
| 140. #97 | C4×D5 | semidirect |
| 223. C5 | #8030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64994 | 2 |
| D5×#382 | 2 |
| C5×#1295 | 2 |
| #10598150 | 2 |
| #10598121 | 2 |
| #8030 | 5 |