Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
636 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 636 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. AGL(1,𝔽5)×#100 | C2 | semidirect |
| 4. AGL(1,𝔽5)×#99 | C2 | semidirect |
| 6. #10598573 | C2 | semidirect |
| 7. #10598567 | C2 | semidirect |
| 8. C22×C22⋊AGL(1,𝔽5) | C4 | semidirect |
| 11. #65800 | C4 | semidirect |
| 20. #65699 | C4 | semidirect |
| 22. C22⋊C4×AGL(1,𝔽5) | C4 | semidirect |
| 25. #64934 | C4 | semidirect |
| 28. #64864 | C4 | semidirect |
| 29. C5×AΣL(1,𝔽16) | C4 | semidirect |
| 30. #64756 | C4 | semidirect |
| 31. #64695 | C4 | semidirect |
| 32. #64691 | C4 | semidirect |
| 92. C24×C5 | C42 | semidirect |
| 99. C23×D5 | C42 | semidirect |
| 155. C5×C22⋊C4 | C42 | semidirect |
| 158. C22⋊Dic5 | C42 | semidirect |
| 188. AΣL(1,𝔽16) | AGL(1,𝔽5) | semidirect |
| 374. C24 | C4×AGL(1,𝔽5) | semidirect |
| 434. C22⋊C4 | C4×AGL(1,𝔽5) | semidirect |
| 527. C5 | #12622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617222 | 2 |
| D5⋊AΣL(1,𝔽16) | 2 |
| AGL(1,𝔽5)×#100 | 2 |
| AGL(1,𝔽5)×#99 | 2 |
| D5×AΣL(1,𝔽16) | 2 |
| #10598573 | 2 |
| #10598567 | 2 |
| #12622 | 5 |