Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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. #10604114 | C2 | semidirect |
| 4. #10604090 | C2 | semidirect |
| 6. #10598675 | C2 | semidirect |
| 7. #10598627 | C2 | semidirect |
| 13. #65731 | C4 | semidirect |
| 14. #65731 | C4 | semidirect |
| 22. #64904 | C4 | semidirect |
| 26. C5×#361 | C4 | semidirect |
| 27. #64783 | C4 | semidirect |
| 28. #64736 | C4 | semidirect |
| 29. #64715 | C4 | semidirect |
| 54. #3994 | C2×C4 | semidirect |
| 65. D5⋊C16 | C2×C4 | semidirect |
| 66. C5×M32 | C2×C4 | semidirect |
| 67. C5×#108 | C2×C4 | semidirect |
| 69. #3951 | C2×C4 | semidirect |
| 70. #3944 | C2×C4 | semidirect |
| 144. #361 | AGL(1,𝔽5) | semidirect |
| 208. M32 | C2×AGL(1,𝔽5) | semidirect |
| 213. #108 | C2×AGL(1,𝔽5) | semidirect |
| 333. 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 |
| #10604786 | 2 |
| #10604114 | 2 |
| #10604090 | 2 |
| D5×#361 | 2 |
| #10598675 | 2 |
| #10598627 | 2 |
| #12647 | 5 |