Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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×C3×C4×C5 | C2 | semidirect |
| 3. C5×#217 | C2 | semidirect |
| 4. C5×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C5×Dic3⋊C4 | C2 | semidirect |
| 14. #929 | C5 | direct (N × H) |
| 16. C22×C4×C5 | D3 | semidirect |
| 28. C22×C3×C4 | C2×C5 | semidirect |
| 30. #217 | C2×C5 | semidirect |
| 31. (C2×D3)⋊C4 | C2×C5 | semidirect |
| 32. Dic3⋊C4 | C2×C5 | semidirect |
| 61. C22×C4 | C5×D3 | semidirect |
| 65. C3×C5 | #123 | semidirect |
| 89. C5 | #929 | direct (N × H) |
| 98. C3 | C5×#123 | 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×C5×#67 | 2 |
| C5×#217 | 2 |
| C5×(C2×D3)⋊C4 | 2 |
| C5×Dic3⋊C4 | 2 |
| C5×#123 | 3 |
| #929 | 5 |