Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
358 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 13. #64850 | C4 | semidirect |
| 14. #64849 | C4 | semidirect |
| 15. C5×#346 | C4 | semidirect |
| 16. #64722 | C4 | semidirect |
| 17. #64722 | C4 | semidirect |
| 18. #64681 | C4 | semidirect |
| 71. C5×C16 | C42 | semidirect |
| 73. #672 | C42 | semidirect |
| 85. #346 | AGL(1,𝔽5) | semidirect |
| 171. C16 | C4×AGL(1,𝔽5) | semidirect |
| 200. C5 | #12674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64850 | 2 |
| C2×#64849 | 2 |
| C4×#3994 | 2 |
| D5×#346 | 2 |
| #10598664 | 2 |
| #12674 | 5 |