Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
246 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 93 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. #10601671 | C2 | semidirect |
| 3. #10598253 | C2 | semidirect |
| 4. #10598004 | C2 | semidirect |
| 5. #10598002 | C2 | semidirect |
| 20. C5×D16 | C8 | semidirect |
| 38. C5×D8 | C2×C8 | semidirect |
| 48. C5×C16 | C2×C8 | semidirect |
| 76. D16 | #168 | semidirect |
| 97. D8 | C2×#168 | semidirect |
| 108. C16 | C2×#168 | semidirect |
| 125. C5 | #12067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2177 | 2 |
| #10601671 | 2 |
| #10598253 | 2 |
| #10598004 | 2 |
| #10598002 | 2 |
| #12067 | 5 |