Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
600 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 101 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. #10600856 | C2 | semidirect |
| 5. #10600821 | C2 | semidirect |
| 6. #10598189 | C2 | semidirect |
| 7. #10598185 | C2 | semidirect |
| 9. C22×C22⋊Dic5 | C4 | semidirect |
| 13. #65536 | C4 | semidirect |
| 22. #65239 | C4 | semidirect |
| 24. C22⋊C4×Dic5 | C4 | semidirect |
| 90. C24×C5 | C4⋊C4 | semidirect |
| 129. C5×C22⋊C4 | C4⋊C4 | semidirect |
| 332. C24 | #683 | semidirect |
| 388. C22⋊C4 | #683 | semidirect |
| 470. C5 | #12795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614309 | 2 |
| C2×C5×AΣL(1,𝔽16) | 2 |
| C2×#64756 | 2 |
| #10600856 | 2 |
| #10600821 | 2 |
| #10598189 | 2 |
| #10598185 | 2 |
| #12795 | 5 |