Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 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. C22×Dic15 | C2 | semidirect |
| 3. C5×#217 | C2 | semidirect |
| 4. Dic3⋊Dic5 | C2 | semidirect |
| 5. #6665 | C2 | semidirect |
| 31. #217 | D5 | semidirect |
| 65. C3×C5 | #123 | semidirect |
| 89. C5 | #935 | semidirect |
| 98. C3 | #4032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic15 | 2 |
| C2×C3×C22⋊D5 | 2 |
| C5×#217 | 2 |
| Dic3⋊Dic5 | 2 |
| #6665 | 2 |
| #4032 | 3 |
| #935 | 5 |