Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
614 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 2. C8×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. #10598766 | C2 | semidirect |
| 6. C22×C8×D5 | C4 | semidirect |
| 13. C2×C4×C5×C8 | C4 | semidirect |
| 14. C2×#3952 | C4 | semidirect |
| 16. C2×C4⋊#168 | C4 | semidirect |
| 20. #64915 | C4 | semidirect |
| 21. #64913 | C4 | semidirect |
| 49. #3999 | C8 | direct (N × H) |
| 81. C22⋊AGL(1,𝔽5) | C2×C8 | semidirect |
| 116. C2×C4×C8 | AGL(1,𝔽5) | semidirect |
| 129. C22×D5 | C4×C8 | semidirect |
| 142. C2×C4×C5 | C4×C8 | semidirect |
| 159. C5×C8 | #99 | semidirect |
| 299. C2×C4 | C8×AGL(1,𝔽5) | semidirect |
| 307. C8 | #3999 | direct (N × H) |
| 308. C5 | C8×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D20 | 2 |
| C8×C22⋊AGL(1,𝔽5) | 2 |
| C4×#3999 | 2 |
| #10604160 | 2 |
| #10598766 | 2 |
| C8×#99 | 5 |