Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
524 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 6. C2×C4×C5×Q8 | C4 | semidirect |
| 8. C5×#391 | C4 | semidirect |
| 12. C5×#384 | C4 | semidirect |
| 13. C5×#376 | C4 | semidirect |
| 54. C2×C5×Q8 | C4⋊C4 | semidirect |
| 84. C42×C5 | C4⋊C4 | semidirect |
| 89. C2×C4×Q8 | Dic5 | semidirect |
| 92. #391 | Dic5 | semidirect |
| 96. #384 | Dic5 | semidirect |
| 98. #376 | Dic5 | semidirect |
| 192. C2×Q8 | C4⋊Dic5 | semidirect |
| 225. C42 | C4⋊Dic5 | semidirect |
| 271. C5 | #12800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2326 | 2 |
| C2×#64761 | 2 |
| #10602412 | 2 |
| #10598132 | 2 |
| #12800 | 5 |