Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 17. #4849 | C5 | direct (N × H) |
| 52. C3×C4×C5 | Q16 | semidirect |
| 103. C4×C5 | Dic12 | semidirect |
| 116. C3×C5 | #462 | semidirect |
| 119. C3×C4 | C5×Q16 | semidirect |
| 142. C5 | #4849 | direct (N × H) |
| 148. C4 | C5×Dic12 | semidirect |
| 151. C3 | C5×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic12 | 2 |
| C5×#869 | 2 |
| C4×C5×Dic6 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C5×#816 | 2 |
| C5×#462 | 3 |
| #4849 | 5 |