Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
340 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #10598273 | C2 | direct (N × H) |
| 5. C2×C5×#125 | C4 | semidirect |
| 9. C5×#488 | C4 | semidirect |
| 13. C2×C4×C5×C8 | C4 | semidirect |
| 26. C5×#125 | C2×C4 | semidirect |
| 43. C4×C5×C8 | C2×C4 | semidirect |
| 87. C2×#125 | Dic5 | semidirect |
| 91. #488 | Dic5 | semidirect |
| 97. C2×C4×C8 | Dic5 | semidirect |
| 137. #125 | C2×Dic5 | semidirect |
| 157. C4×C8 | C2×Dic5 | semidirect |
| 215. C2×C5 | #1414 | semidirect |
| 246. C5 | C2×#1414 | semidirect |
| 269. C2 | #10598273 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#488 | 2 |
| C2×#64762 | 2 |
| C2×#64761 | 2 |
| #10598273 | 2 |
| C2×#1414 | 5 |