Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
568 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10602385 | C2 | semidirect |
| 3. #10602364 | C2 | semidirect |
| 4. #10598136 | C2 | semidirect |
| 5. C2×C5×#127 | C4 | semidirect |
| 10. C5×#394 | C4 | semidirect |
| 14. C5×#382 | C4 | semidirect |
| 100. C2×#127 | Dic5 | semidirect |
| 106. #394 | Dic5 | semidirect |
| 110. #382 | Dic5 | semidirect |
| 318. C5 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2619 | 2 |
| #10602385 | 2 |
| #10602364 | 2 |
| #10598136 | 2 |
| #11693 | 5 |