Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 17. C5×#334 | C4 | semidirect |
| 18. #64700 | C4 | semidirect |
| 19. #64677 | C4 | semidirect |
| 96. #334 | AGL(1,𝔽5) | semidirect |
| 120. C5×C8 | #106 | semidirect |
| 123. #168 | #106 | semidirect |
| 228. C8 | #3993 | semidirect |
| 229. C5 | #9612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604031 | 2 |
| #10603847 | 2 |
| C8×C4⋊AGL(1,𝔽5) | 2 |
| D5×#334 | 2 |
| #10598586 | 2 |
| #9612 | 5 |