Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
302 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 302 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. C2×#64724 | C2 | semidirect |
| 3. C2×#64719 | C2 | semidirect |
| 4. #10598317 | C2 | semidirect |
| 5. #10598315 | C2 | semidirect |
| 8. C5×#508 | C4 | semidirect |
| 28. C5×Q32 | C2×C4 | semidirect |
| 31. C5×D16 | C2×C4 | semidirect |
| 68. #508 | Dic5 | semidirect |
| 105. Q32 | C2×Dic5 | semidirect |
| 108. D16 | C2×Dic5 | semidirect |
| 173. C5 | #13616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#508 | 2 |
| C2×#64724 | 2 |
| C2×#64719 | 2 |
| #10598317 | 2 |
| #10598315 | 2 |
| #13616 | 5 |