Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10603883 | C2 | semidirect |
| 4. #10603882 | C2 | semidirect |
| 6. #10598545 | C2 | semidirect |
| 7. #10598545 | C2 | semidirect |
| 27. C5×#329 | C4 | semidirect |
| 28. #64760 | C4 | semidirect |
| 29. #64684 | C4 | semidirect |
| 30. #64684 | C4 | semidirect |
| 71. C5×#97 | C2×C4 | semidirect |
| 72. C5×#97 | C2×C4 | semidirect |
| 75. #3935 | C2×C4 | semidirect |
| 76. #3935 | C2×C4 | semidirect |
| 166. #329 | AGL(1,𝔽5) | semidirect |
| 256. #97 | C2×AGL(1,𝔽5) | semidirect |
| 257. #97 | C2×AGL(1,𝔽5) | semidirect |
| 415. C5 | #8911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617328 | 2 |
| #10604567 | 2 |
| #10603883 | 2 |
| #10603882 | 2 |
| D5×#329 | 2 |
| #10598545 | 2 |
| #8911 | 5 |