Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
104 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 26 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. #6763 | C2 | semidirect |
| 3. C3×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. C22×D15 | C4 | semidirect |
| 9. C2×C5×Dic3 | C4 | semidirect |
| 15. C22⋊AGL(1,𝔽5) | D3 | semidirect |
| 47. C2×Dic3 | AGL(1,𝔽5) | semidirect |
| 60. C3×C5 | #99 | semidirect |
| 87. C5 | #806 | semidirect |
| 97. C3 | #3999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1202 | 2 |
| #6763 | 2 |
| C3×C22⋊AGL(1,𝔽5) | 2 |
| #3999 | 3 |
| #806 | 5 |