Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
400 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 226 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 |
|---|---|---|
| 21. #5569 | C5 | direct (N × H) |
| 29. C3×C5×Q8 | Q8 | semidirect |
| 79. C5×Q8 | Dic6 | semidirect |
| 97. C3×Q8 | C5×Q8 | semidirect |
| 126. C3×C5 | #557 | semidirect |
| 139. Q8 | C5×Dic6 | semidirect |
| 150. C5 | #5569 | direct (N × H) |
| 159. C3 | C5×#557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C5×Q8×Dic3 | 2 |
| C5×#890 | 2 |
| C5×#888 | 2 |
| C5×#870 | 2 |
| C4×C5×Dic6 | 2 |
| C5×#557 | 3 |
| #5569 | 5 |