Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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×#214 | C2 | semidirect |
| 3. C4×C5×Dic6 | C2 | semidirect |
| 4. C5×#832 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C8) | C2 | semidirect |
| 17. #5075 | C5 | direct (N × H) |
| 34. C5×Dic6 | D4 | semidirect |
| 37. C2×#214 | C2×C5 | semidirect |
| 38. C4×Dic6 | C2×C5 | semidirect |
| 39. #832 | C2×C5 | semidirect |
| 40. C4⋊(C3⋊C8) | C2×C5 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 105. Dic6 | C5×D4 | semidirect |
| 114. C4×C5 | #214 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 133. C3×C4 | C5×SD16 | semidirect |
| 159. C5 | #5075 | direct (N × H) |
| 167. C4 | C5×#214 | semidirect |
| 170. C3 | C5×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| C2×C5×#214 | 2 |
| C4×C5×Dic6 | 2 |
| C5×#832 | 2 |
| C5×C4⋊(C3⋊C8) | 2 |
| C5×#460 | 3 |
| #5075 | 5 |