Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
628 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 628 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)×#99 | C2 | semidirect |
| 5. #10598568 | C2 | semidirect |
| 6. C2×D4×AGL(1,𝔽5) | C4 | semidirect |
| 9. #65780 | C4 | semidirect |
| 15. #65689 | C4 | semidirect |
| 16. #65686 | C4 | semidirect |
| 18. #64922 | C4 | semidirect |
| 20. #64853 | C4 | semidirect |
| 21. C5×#353 | C4 | semidirect |
| 22. #64765 | C4 | semidirect |
| 23. #64694 | C4 | semidirect |
| 54. #3999 | C2×C4 | semidirect |
| 55. C5×#99 | C2×C4 | semidirect |
| 56. #3966 | C2×C4 | semidirect |
| 77. C2×C5×D4 | C42 | semidirect |
| 90. C2×D20 | C42 | semidirect |
| 107. C42×C5 | C42 | semidirect |
| 111. C4×Dic5 | C42 | semidirect |
| 128. #353 | AGL(1,𝔽5) | semidirect |
| 210. #99 | C2×AGL(1,𝔽5) | semidirect |
| 262. C2×D4 | C4×AGL(1,𝔽5) | semidirect |
| 294. C42 | C4×AGL(1,𝔽5) | semidirect |
| 356. C5 | #12628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617368 | 2 |
| D5⋊#353 | 2 |
| AGL(1,𝔽5)×#99 | 2 |
| D5×#353 | 2 |
| #10598568 | 2 |
| #12628 | 5 |