Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
428 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10603885 | C2 | semidirect |
| 5. #10603872 | C2 | semidirect |
| 6. #10598606 | C2 | semidirect |
| 7. #10598604 | C2 | semidirect |
| 15. C5×#441 | C4 | semidirect |
| 16. #65473 | C4 | semidirect |
| 18. #65158 | C4 | semidirect |
| 22. #65000 | C4 | semidirect |
| 24. #64909 | C4 | semidirect |
| 25. #64907 | C4 | semidirect |
| 54. #3996 | C2×C4 | semidirect |
| 57. #3993 | C2×C4 | semidirect |
| 61. #3990 | C2×C4 | semidirect |
| 63. D5⋊C16 | C2×C4 | semidirect |
| 138. #441 | AGL(1,𝔽5) | semidirect |
| 332. C5 | #12649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611559 | 2 |
| #10604834 | 2 |
| #10604830 | 2 |
| #10603885 | 2 |
| #10603872 | 2 |
| #10598606 | 2 |
| #10598604 | 2 |
| #12649 | 5 |