Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
13310 conjugacy classes of subgroups; only the 6264 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 6264 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. C24×#170 | C2 | semidirect |
| 3. C23×#700 | C2 | direct (N × H) |
| 9. C23×#170 | C22 | semidirect |
| 10. C22×#700 | C22 | direct (N × H) |
| 20. C22×#170 | C23 | semidirect |
| 21. C2×#700 | C23 | direct (N × H) |
| 25. C24×C5 | M16 | semidirect |
| 34. C2×#170 | C24 | semidirect |
| 35. #700 | C24 | direct (N × H) |
| 43. C23×C5 | C2×M16 | semidirect |
| 52. #170 | C25 | semidirect |
| 63. C22×C5 | C22×M16 | semidirect |
| 72. C24 | #700 | direct (N × H) |
| 81. C2×C5 | C23×M16 | semidirect |
| 86. C23 | C2×#700 | direct (N × H) |
| 94. C5 | C24×M16 | semidirect |
| 97. C22 | C22×#700 | direct (N × H) |
| 103. C2 | C23×#700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×D5 | 2 |
| C24×#170 | 2 |
| C23×#700 | 2 |
| C24×M16 | 5 |