Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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×C5×Dic6 | C2 | semidirect |
| 3. #6710 | C2 | semidirect |
| 4. #6661 | C2 | semidirect |
| 5. #6655 | C2 | semidirect |
| 29. C2×Dic6 | D5 | semidirect |
| 66. C3×C5 | #137 | semidirect |
| 88. C5 | #951 | semidirect |
| 95. C3 | #4088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic6 | 2 |
| C3×#709 | 2 |
| #6710 | 2 |
| #6661 | 2 |
| #6655 | 2 |
| #4088 | 3 |
| #951 | 5 |