Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
188 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 12. #67558 | C5 | direct (N × H) |
| 43. C5×Dic6 | C16 | semidirect |
| 113. Dic6 | C5×C16 | semidirect |
| 136. C3×C5 | Q8⋊C16 | semidirect |
| 162. C5 | #67558 | direct (N × H) |
| 171. C3 | C5×Q8⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C8×Dic6 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C4×C5×C3⋊C16 | 2 |
| C5×Q8⋊C16 | 3 |
| #67558 | 5 |