Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
374 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 7. C5×C8×A4 | C4 | semidirect |
| 8. C5×A4⋊C8 | C4 | semidirect |
| 10. C8×SL(2,ℤ/4) | C5 | direct (N × H) |
| 21. C5×SL(2,ℤ/4) | C8 | direct (N × H) |
| 34. C22×C5×C8 | Dic3 | semidirect |
| 53. C8×A4 | C4×C5 | semidirect |
| 54. A4⋊C8 | C4×C5 | semidirect |
| 91. C5×A4 | C4×C8 | semidirect |
| 98. SL(2,ℤ/4) | C5×C8 | direct (N × H) |
| 125. C5×C8 | SL(2,ℤ/4) | direct (N × H) |
| 132. C22×C8 | C5×Dic3 | semidirect |
| 157. C22×C5 | C8×Dic3 | semidirect |
| 194. A4 | C4×C5×C8 | semidirect |
| 226. C8 | C5×SL(2,ℤ/4) | direct (N × H) |
| 229. C5 | C8×SL(2,ℤ/4) | direct (N × H) |
| 237. C22 | C5×C8×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×A4 | 2 |
| C4×C5×SL(2,ℤ/4) | 2 |
| C2×C5×A4⋊C8 | 2 |
| C5×C8×C22⋊C4 | 3 |
| C5×C8×Dic3 | 4 |
| C8×SL(2,ℤ/4) | 5 |