Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×C5×M16 | C2 | semidirect |
| 2. C5×#930 | C2 | semidirect |
| 3. C2×C5×D24 | C2 | semidirect |
| 4. C5×#821 | C2 | semidirect |
| 5. C5×#817 | C2 | semidirect |
| 16. #5135 | C5 | direct (N × H) |
| 18. C2×C5×M16 | D3 | semidirect |
| 33. C3×C5×C8 | D4 | semidirect |
| 34. C2×C3×M16 | C2×C5 | semidirect |
| 35. #930 | C2×C5 | semidirect |
| 36. C2×D24 | C2×C5 | semidirect |
| 37. #821 | C2×C5 | semidirect |
| 38. #817 | C2×C5 | semidirect |
| 79. C5×C8 | #67 | semidirect |
| 81. C2×M16 | C5×D3 | semidirect |
| 100. C3×C8 | C5×D4 | semidirect |
| 120. C3×C5 | #469 | semidirect |
| 146. C8 | C5×#67 | semidirect |
| 151. C5 | #5135 | direct (N × H) |
| 162. C3 | C5×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| C5×#930 | 2 |
| C2×C5×D24 | 2 |
| C5×#821 | 2 |
| C5×#817 | 2 |
| C5×#469 | 3 |
| #5135 | 5 |