Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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×#64845 | C2 | semidirect |
| 4. #10604078 | C2 | semidirect |
| 6. #10598663 | C2 | semidirect |
| 7. #10598621 | C2 | semidirect |
| 12. #65731 | C4 | semidirect |
| 20. #64906 | C4 | semidirect |
| 23. C5×#357 | C4 | semidirect |
| 24. #64782 | C4 | semidirect |
| 25. #64729 | C4 | semidirect |
| 26. #64711 | C4 | semidirect |
| 51. #3995 | C2×C4 | semidirect |
| 57. #3990 | C2×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 |
| 132. #357 | AGL(1,𝔽5) | semidirect |
| 195. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 199. #107 | C2×AGL(1,𝔽5) | semidirect |
| 318. C5 | #12647 | 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×#64845 | 2 |
| #10604078 | 2 |
| #10599983 | 2 |
| #10598663 | 2 |
| #10598621 | 2 |
| #12647 | 5 |