Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10598275 | C2 | semidirect |
| 4. C5×#533 | C4 | semidirect |
| 6. C5×#490 | C4 | semidirect |
| 10. C4×C5×M16 | C4 | semidirect |
| 23. C5×#125 | C2×C4 | semidirect |
| 31. C5×#97 | C2×C4 | semidirect |
| 64. #533 | Dic5 | semidirect |
| 66. #490 | Dic5 | semidirect |
| 71. C4×M16 | Dic5 | semidirect |
| 105. #125 | C2×Dic5 | semidirect |
| 115. #97 | C2×Dic5 | semidirect |
| 186. C5 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3138 | 2 |
| C2×#64765 | 2 |
| #10598275 | 2 |
| #13595 | 5 |