Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
300 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 6. Dic5×Q32 | C3 | direct (N × H) |
| 9. C3×C5×Q32 | C4 | semidirect |
| 39. C5×Q32 | C3×C4 | semidirect |
| 58. C3×Q32 | Dic5 | direct (N × H) |
| 86. C3×Dic5 | Q32 | direct (N × H) |
| 110. Q32 | C3×Dic5 | direct (N × H) |
| 135. Dic5 | C3×Q32 | direct (N × H) |
| 147. C3×C5 | C4×Q32 | semidirect |
| 171. C5 | C3×C4×Q32 | semidirect |
| 179. C3 | Dic5×Q32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q32 | 2 |
| C3×Q16×Dic5 | 2 |
| C3×#64784 | 2 |
| C3×#64724 | 2 |
| C3×C16×Dic5 | 2 |
| Dic5×Q32 | 3 |
| C3×C4×Q32 | 5 |