Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
628 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. C4×#3966 | C2 | semidirect |
| 4. #10598132 | C2 | semidirect |
| 6. C2×C4×C5×D4 | C4 | semidirect |
| 8. C5×#390 | C4 | semidirect |
| 12. C5×#382 | C4 | semidirect |
| 13. C5×#376 | C4 | semidirect |
| 16. #64765 | C4 | semidirect |
| 43. #3966 | C2×C4 | semidirect |
| 59. C2×C5×D4 | C42 | semidirect |
| 84. C42×C5 | C42 | semidirect |
| 89. C2×C4×D4 | Dic5 | semidirect |
| 92. #390 | Dic5 | semidirect |
| 96. #382 | Dic5 | semidirect |
| 98. #376 | Dic5 | semidirect |
| 201. C2×D4 | C4×Dic5 | semidirect |
| 229. C42 | C4×Dic5 | semidirect |
| 277. C5 | #12628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2328 | 2 |
| C2×#64765 | 2 |
| C4×#3966 | 2 |
| #10598132 | 2 |
| #12628 | 5 |