Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
678 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 678 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 |
|---|---|---|
| 4. #10604345 | C2 | semidirect |
| 5. #10604282 | C2 | semidirect |
| 6. #10598552 | C2 | semidirect |
| 7. #10598551 | C2 | semidirect |
| 22. C5×#480 | C4 | semidirect |
| 23. #65322 | C4 | semidirect |
| 24. #65256 | C4 | semidirect |
| 29. #65025 | C4 | semidirect |
| 56. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 60. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 84. C5×C22⋊C8 | C2×C4 | semidirect |
| 86. C22⋊#168 | C2×C4 | semidirect |
| 191. #480 | AGL(1,𝔽5) | semidirect |
| 321. C2×C4⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 340. C22⋊C8 | C2×AGL(1,𝔽5) | semidirect |
| 575. C5 | #9043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617251 | 2 |
| D5×#480 | 2 |
| D5⋊#327 | 2 |
| #10604345 | 2 |
| #10604282 | 2 |
| #10598552 | 2 |
| #10598551 | 2 |
| #9043 | 5 |