Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 64 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. C22×C3×Dic5 | C2 | semidirect |
| 3. C2×#1200 | C2 | semidirect |
| 4. C5×#217 | C2 | semidirect |
| 5. #6669 | C2 | semidirect |
| 6. #6667 | C2 | semidirect |
| 7. Dic3×Dic5 | C2 | semidirect |
| 11. #1220 | C4 | semidirect |
| 21. C22×Dic5 | D3 | semidirect |
| 29. C22×C3×C5 | C2×C4 | semidirect |
| 33. C2×D15 | C2×C4 | semidirect |
| 34. Dic15 | C2×C4 | semidirect |
| 36. C3×Dic5 | D4 | semidirect |
| 42. #217 | D5 | semidirect |
| 74. C22×C5 | C4×D3 | semidirect |
| 83. Dic5 | #67 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 94. C22×C3 | C4×D5 | semidirect |
| 124. C5 | C4×#67 | semidirect |
| 130. C22 | #1200 | semidirect |
| 137. C3 | #4027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1220 | 2 |
| C22×C3×Dic5 | 2 |
| C2×#1200 | 2 |
| C5×#217 | 2 |
| #6669 | 2 |
| #6667 | 2 |
| Dic3×Dic5 | 2 |
| #4027 | 3 |
| C4×#67 | 5 |