Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#64847 | C2 | semidirect |
| 4. #10604082 | C2 | semidirect |
| 6. #10598660 | C2 | semidirect |
| 7. #10598621 | C2 | semidirect |
| 23. C5×#357 | C4 | semidirect |
| 24. #64782 | C4 | semidirect |
| 25. #64729 | C4 | semidirect |
| 26. #64711 | C4 | semidirect |
| 58. C2×C5×C16 | C2×C4 | semidirect |
| 59. C5×#107 | C2×C4 | semidirect |
| 60. #3950 | C2×C4 | semidirect |
| 61. C2×#672 | C2×C4 | semidirect |
| 133. #357 | AGL(1,𝔽5) | semidirect |
| 195. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 199. #107 | C2×AGL(1,𝔽5) | semidirect |
| 318. C5 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65731 | 2 |
| C2×#64906 | 2 |
| C2×#64847 | 2 |
| #10604082 | 2 |
| #10599983 | 2 |
| #10598660 | 2 |
| #10598621 | 2 |
| #12956 | 5 |