Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. C2×C3×Dic10 | C2 | semidirect |
| 4. C5×Dic3⋊C4 | C2 | semidirect |
| 5. #6669 | C2 | semidirect |
| 6. #6668 | C2 | semidirect |
| 20. C2×Dic10 | D3 | semidirect |
| 29. C2×D15 | Q8 | semidirect |
| 42. Dic3⋊C4 | D5 | semidirect |
| 83. C3×C5 | C22⋊Q8 | semidirect |
| 111. C5 | #946 | semidirect |
| 122. C3 | #4042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic10 | 2 |
| C2×#1200 | 2 |
| #6714 | 2 |
| C5×Dic3⋊C4 | 2 |
| #6669 | 2 |
| #6668 | 2 |
| #6667 | 2 |
| #4042 | 3 |
| #946 | 5 |