Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 4. C5×C4⋊Dic3 | C2 | semidirect |
| 5. C5×Dic3⋊C4 | C2 | semidirect |
| 6. C5×Dic3⋊C4 | C2 | semidirect |
| 7. C4×C5×Dic3 | C2 | semidirect |
| 16. #879 | C5 | direct (N × H) |
| 37. C4⋊Dic3 | C2×C5 | semidirect |
| 38. Dic3⋊C4 | C2×C5 | semidirect |
| 39. Dic3⋊C4 | C2×C5 | semidirect |
| 40. C4×Dic3 | C2×C5 | semidirect |
| 77. C3×C5 | #126 | semidirect |
| 103. C5 | #879 | direct (N × H) |
| 114. C3 | C5×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C22⋊C4 | 2 |
| C5×#217 | 2 |
| C5×C4⋊Dic3 | 2 |
| C5×Dic3⋊C4 | 2 |
| C4×C5×Dic3 | 2 |
| C5×#126 | 3 |
| #879 | 5 |