Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
186 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 33 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 |
|---|---|---|
| 1. A4×D20 | C2 | semidirect |
| 2. C5×C8×A4 | C2 | semidirect |
| 3. C22×D40 | C3 | semidirect |
| 8. C22×D20 | C2×C3 | semidirect |
| 9. C22×C5×C8 | C2×C3 | semidirect |
| 18. C8×A4 | D5 | semidirect |
| 29. D40 | A4 | direct (N × H) |
| 32. C5×A4 | D8 | semidirect |
| 47. D20 | C2×A4 | semidirect |
| 49. C5×C8 | C2×A4 | semidirect |
| 54. C22×C8 | C3×D5 | semidirect |
| 63. C22×C5 | C3×D8 | semidirect |
| 85. A4 | D40 | direct (N × H) |
| 104. C8 | D5×A4 | semidirect |
| 107. C5 | A4×D8 | semidirect |
| 116. C22 | C3×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×D20 | 2 |
| C5×C8×A4 | 2 |
| C22×D40 | 3 |
| C3×D40 | 4 |
| A4×D8 | 5 |