Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 20. #4856 | C5 | direct (N × H) |
| 36. C3×C5×C8 | Q8 | semidirect |
| 37. C5×C3⋊C8 | Q8 | semidirect |
| 86. C5×C8 | Dic6 | semidirect |
| 105. C3×C8 | C5×Q8 | semidirect |
| 106. C3⋊C8 | C5×Q8 | semidirect |
| 127. C3×C5 | #501 | semidirect |
| 149. C8 | C5×Dic6 | semidirect |
| 153. C5 | #4856 | direct (N × H) |
| 163. C3 | C5×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#890 | 2 |
| C5×#888 | 2 |
| C3×C5×#106 | 2 |
| C5×#818 | 2 |
| C5×#815 | 2 |
| C5×#808 | 2 |
| C5×#807 | 2 |
| C5×#501 | 3 |
| #4856 | 5 |