Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
236 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 4. C5×#818 | C2 | semidirect |
| 5. C5×#817 | C2 | semidirect |
| 9. C3×C5×M16 | C4 | semidirect |
| 17. #5121 | C5 | direct (N × H) |
| 32. C3×C5×C8 | C2×C4 | semidirect |
| 36. #818 | C2×C5 | semidirect |
| 37. #817 | C2×C5 | semidirect |
| 40. C5×M16 | Dic3 | semidirect |
| 61. C3×M16 | C4×C5 | semidirect |
| 78. C5×C8 | C2×Dic3 | semidirect |
| 97. C3×C8 | C2×C4×C5 | semidirect |
| 110. M16 | C5×Dic3 | semidirect |
| 118. C3×C5 | #428 | semidirect |
| 142. C8 | C2×C5×Dic3 | semidirect |
| 147. C5 | #5121 | direct (N × H) |
| 158. C3 | C5×#428 | 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×#926 | 2 |
| C2×C5×C4⋊Dic3 | 2 |
| C5×#818 | 2 |
| C5×#817 | 2 |
| C5×#428 | 3 |
| #5121 | 5 |