Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 122 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. C2×C5×#208 | C2 | semidirect |
| 3. C5×#830 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. C4×C5×C3⋊C8 | C2 | semidirect |
| 16. #5012 | C5 | direct (N × H) |
| 32. C5×C3⋊C8 | D4 | semidirect |
| 34. C2×#208 | C2×C5 | semidirect |
| 35. #830 | C2×C5 | semidirect |
| 36. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 37. C4×C3⋊C8 | C2×C5 | semidirect |
| 54. C3×C4×C5 | M16 | semidirect |
| 96. C3⋊C8 | C5×D4 | semidirect |
| 103. C4×C5 | #208 | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 122. C3×C4 | C5×M16 | semidirect |
| 144. C5 | #5012 | direct (N × H) |
| 151. C4 | C5×#208 | semidirect |
| 154. C3 | C5×#436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C2×C5×#208 | 2 |
| C5×#830 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C4×C5×C3⋊C8 | 2 |
| C5×#436 | 3 |
| #5012 | 5 |