Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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. #10602335 | C2 | semidirect |
| 3. #10602332 | C2 | semidirect |
| 4. #10598140 | C2 | semidirect |
| 5. #10598136 | C2 | semidirect |
| 6. C2×C5×#121 | C4 | semidirect |
| 9. C5×#397 | C4 | semidirect |
| 13. C5×#392 | C4 | semidirect |
| 16. C5×#380 | C4 | semidirect |
| 117. C2×#121 | Dic5 | semidirect |
| 121. #397 | Dic5 | semidirect |
| 125. #392 | Dic5 | semidirect |
| 128. #380 | Dic5 | semidirect |
| 396. C5 | #11799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2617 | 2 |
| #10602335 | 2 |
| #10602332 | 2 |
| #10598140 | 2 |
| #10598136 | 2 |
| #11799 | 5 |