Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
156 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 62 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×C4×D5 | C2 | semidirect |
| 3. C3×C5×C4⋊C4 | C2 | semidirect |
| 4. C3×#685 | C2 | semidirect |
| 5. C3×#685 | C2 | semidirect |
| 6. C3×#685 | C2 | semidirect |
| 7. C3×#683 | C2 | semidirect |
| 8. #4040 | C3 | direct (N × H) |
| 20. C2×C4×D5 | C2×C3 | semidirect |
| 21. C5×C4⋊C4 | C2×C3 | semidirect |
| 22. #685 | C2×C3 | semidirect |
| 23. #685 | C2×C3 | semidirect |
| 24. #685 | C2×C3 | semidirect |
| 25. #683 | C2×C3 | semidirect |
| 41. C3×C4⋊C4 | D5 | semidirect |
| 84. C4⋊C4 | C3×D5 | semidirect |
| 88. C3×C5 | #123 | semidirect |
| 120. C5 | C3×#123 | semidirect |
| 133. C3 | #4040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D20 | 2 |
| C2×C3×C4×D5 | 2 |
| C3×C5×C4⋊C4 | 2 |
| C3×#685 | 2 |
| C3×#683 | 2 |
| #4040 | 3 |
| C3×#123 | 5 |