Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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. #10602805 | C2 | semidirect |
| 4. #10598182 | C2 | semidirect |
| 5. C2×C5×#131 | C4 | semidirect |
| 10. C5×#423 | C4 | semidirect |
| 11. C5×#408 | C4 | semidirect |
| 13. C2×C5×#97 | C4 | semidirect |
| 91. C2×#131 | Dic5 | semidirect |
| 97. #423 | Dic5 | semidirect |
| 99. #408 | Dic5 | semidirect |
| 101. C2×#97 | Dic5 | semidirect |
| 250. C5 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2932 | 2 |
| #10602805 | 2 |
| #10602612 | 2 |
| #10598182 | 2 |
| #12808 | 5 |