Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 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×C5×C82 | C2 | semidirect |
| 3. C2×#64675 | C2 | semidirect |
| 4. #10598843 | C2 | direct (N × H) |
| 12. C5×C82 | C22 | semidirect |
| 13. #64675 | C22 | semidirect |
| 32. C2×C82 | D5 | semidirect |
| 39. C2×C5×C8 | M16 | semidirect |
| 56. C82 | C2×D5 | semidirect |
| 67. C5×C8 | C2×M16 | semidirect |
| 99. C2×C8 | #676 | semidirect |
| 105. C2×C5 | #1455 | semidirect |
| 119. C8 | C2×#676 | semidirect |
| 120. C5 | C2×#1455 | semidirect |
| 129. C2 | #10598843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#676 | 2 |
| C2×C5×C82 | 2 |
| C2×#64675 | 2 |
| #10598843 | 2 |
| C2×#1455 | 5 |