Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
100 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 30 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. C4⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×D5⋊C8 | C2 | semidirect |
| 7. D60 | C4 | semidirect |
| 8. C5×D12 | C4 | semidirect |
| 15. D5⋊C8 | D3 | semidirect |
| 45. D12 | AGL(1,𝔽5) | semidirect |
| 58. C3×C5 | #102 | semidirect |
| 84. C5 | #821 | semidirect |
| 93. C3 | #4007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×D12 | 2 |
| C4⋊ΓL(1,𝔽16) | 2 |
| C3×D5⋊C8 | 2 |
| #4007 | 3 |
| #821 | 5 |