Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
148 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C3×Dic10 | C2 | semidirect |
| 4. C3×C4⋊Dic5 | C2 | semidirect |
| 5. C3×#683 | C2 | semidirect |
| 6. #4070 | C3 | direct (N × H) |
| 16. C2×Dic10 | C2×C3 | semidirect |
| 18. C4⋊Dic5 | C2×C3 | semidirect |
| 19. #683 | C2×C3 | semidirect |
| 22. C22×C3×C5 | Q8 | semidirect |
| 54. C22×C5 | C3×Q8 | semidirect |
| 65. C3×C5 | C22⋊Q8 | semidirect |
| 68. C22×C3 | Dic10 | semidirect |
| 89. C5 | C3×C22⋊Q8 | semidirect |
| 92. C22 | C3×Dic10 | semidirect |
| 98. C3 | #4070 | direct (N × H) |
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×C3×Dic10 | 2 |
| C3×C22⋊Dic5 | 2 |
| C3×C4⋊Dic5 | 2 |
| C3×#683 | 2 |
| #4070 | 3 |
| C3×C22⋊Q8 | 5 |