Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 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. C2×C3×C22⋊D5 | C2 | semidirect |
| 2. C2×C3×C22⋊D5 | C2 | semidirect |
| 3. C2×C3×D20 | C2 | semidirect |
| 4. C2×C3×C4×D5 | C2 | semidirect |
| 5. C3×C5×C22⋊C4 | C2 | semidirect |
| 6. C3×#685 | C2 | semidirect |
| 7. C3×#683 | C2 | semidirect |
| 8. #4030 | C3 | direct (N × H) |
| 21. C2×C22⋊D5 | C2×C3 | semidirect |
| 22. C2×C22⋊D5 | C2×C3 | semidirect |
| 23. C2×D20 | C2×C3 | semidirect |
| 24. C2×C4×D5 | C2×C3 | semidirect |
| 25. C5×C22⋊C4 | C2×C3 | semidirect |
| 26. #685 | C2×C3 | semidirect |
| 27. #683 | C2×C3 | semidirect |
| 37. C2×C3×D5 | D4 | semidirect |
| 41. C3×Dic5 | D4 | semidirect |
| 48. C3×C22⋊C4 | D5 | semidirect |
| 87. C2×D5 | C3×D4 | semidirect |
| 91. Dic5 | C3×D4 | semidirect |
| 98. C22⋊C4 | C3×D5 | semidirect |
| 99. C3×C5 | #121 | semidirect |
| 137. C5 | C3×#121 | semidirect |
| 152. C3 | #4030 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊D5 | 2 |
| C2×C3×D20 | 2 |
| C2×C3×C4×D5 | 2 |
| C3×C5×C22⋊C4 | 2 |
| C3×#685 | 2 |
| C3×#683 | 2 |
| #4030 | 3 |
| C3×#121 | 5 |