Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
658 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10603911 | C2 | semidirect |
| 4. #10603802 | C2 | semidirect |
| 6. #10598551 | C2 | semidirect |
| 7. #10598504 | C2 | semidirect |
| 27. C5×#327 | C4 | semidirect |
| 28. #64757 | C4 | semidirect |
| 29. #64690 | C4 | semidirect |
| 30. #64671 | C4 | semidirect |
| 74. C5×C22⋊C8 | C2×C4 | semidirect |
| 75. C5×#95 | C2×C4 | semidirect |
| 77. #3963 | C2×C4 | semidirect |
| 78. C22⋊#168 | C2×C4 | semidirect |
| 190. #327 | AGL(1,𝔽5) | semidirect |
| 311. C22⋊C8 | C2×AGL(1,𝔽5) | semidirect |
| 321. #95 | C2×AGL(1,𝔽5) | semidirect |
| 545. C5 | #8870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617251 | 2 |
| #10604491 | 2 |
| #10603911 | 2 |
| #10603802 | 2 |
| D5×#327 | 2 |
| #10598551 | 2 |
| #10598504 | 2 |
| #8870 | 5 |