Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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×D5×Dic3 | C2 | semidirect |
| 3. #6719 | C2 | semidirect |
| 4. C5×#217 | C2 | semidirect |
| 5. #6665 | C2 | semidirect |
| 9. C22×C3×D5 | C4 | semidirect |
| 12. C2×Dic15 | C22 | semidirect |
| 13. C2×C5×Dic3 | C22 | semidirect |
| 22. C22×C3×C5 | C2×C4 | semidirect |
| 27. C2×C3×D5 | C2×C4 | semidirect |
| 35. #217 | D5 | direct (N × H) |
| 38. C22×D5 | Dic3 | semidirect |
| 49. C3×D5 | C22⋊C4 | semidirect |
| 57. C2×Dic3 | C2×D5 | semidirect |
| 59. C22×C5 | C2×Dic3 | semidirect |
| 64. C2×D5 | C2×Dic3 | semidirect |
| 73. C3×C5 | C2×C22⋊C4 | semidirect |
| 80. C22×C3 | C4×D5 | semidirect |
| 88. D5 | #217 | direct (N × H) |
| 102. C5 | C2×#217 | semidirect |
| 109. C22 | D5×Dic3 | semidirect |
| 113. C3 | D5×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D5 | 2 |
| C2×D5×Dic3 | 2 |
| #6719 | 2 |
| C5×#217 | 2 |
| #6665 | 2 |
| D5×C22⋊C4 | 3 |
| C2×#217 | 5 |