Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10604090 | C2 | semidirect |
| 6. #10598666 | C2 | semidirect |
| 7. #10598632 | C2 | semidirect |
| 11. #65739 | C4 | semidirect |
| 13. #65731 | C4 | semidirect |
| 21. #64907 | C4 | semidirect |
| 22. #64903 | C4 | semidirect |
| 25. C5×#359 | C4 | semidirect |
| 26. #64787 | C4 | semidirect |
| 27. #64730 | C4 | semidirect |
| 28. #64717 | C4 | semidirect |
| 57. #3993 | C2×C4 | semidirect |
| 63. #3990 | C2×C4 | semidirect |
| 64. C2×C5×C16 | C2×C4 | semidirect |
| 65. C5×#108 | C2×C4 | semidirect |
| 67. #3951 | C2×C4 | semidirect |
| 68. C2×#672 | C2×C4 | semidirect |
| 146. #359 | AGL(1,𝔽5) | semidirect |
| 211. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 214. #108 | C2×AGL(1,𝔽5) | semidirect |
| 332. C5 | #12649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617439 | 2 |
| #10604854 | 2 |
| C2×#64845 | 2 |
| #10604090 | 2 |
| #10600034 | 2 |
| #10598666 | 2 |
| #10598632 | 2 |
| #12649 | 5 |