Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×Dic30 | C2 | semidirect |
| 4. C4⋊Dic15 | C2 | semidirect |
| 5. #6712 | C2 | semidirect |
| 22. C22×C3×C5 | Q8 | semidirect |
| 54. C22×C5 | Dic6 | semidirect |
| 65. C3×C5 | C22⋊Q8 | semidirect |
| 68. C22×C3 | Dic10 | semidirect |
| 89. C5 | #924 | semidirect |
| 92. C22 | Dic30 | semidirect |
| 98. C3 | #4070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C5 | 2 |
| C2×Dic30 | 2 |
| #6719 | 2 |
| C4⋊Dic15 | 2 |
| #6712 | 2 |
| #4070 | 3 |
| #924 | 5 |