Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 11. #64849 | C4 | direct (N × H) |
| 12. C4×C5×C16 | C4 | semidirect |
| 13. C16×Dic5 | C4 | semidirect |
| 14. C16×Dic5 | C4 | semidirect |
| 15. C4×#672 | C4 | semidirect |
| 58. C5×C16 | C42 | semidirect |
| 60. #672 | C42 | semidirect |
| 70. C4×C16 | AGL(1,𝔽5) | semidirect |
| 117. C4×C5 | #366 | semidirect |
| 121. Dic5 | #366 | semidirect |
| 144. C16 | C4×AGL(1,𝔽5) | semidirect |
| 170. C5 | C4×#366 | semidirect |
| 181. C4 | #64849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64849 | 2 |
| C4×#3994 | 2 |
| C4×D5×C16 | 2 |
| #10598664 | 2 |
| C4×#366 | 5 |