Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22×C3×C4×C5 | C2 | semidirect |
| 3. C2×C4×D15 | C2 | semidirect |
| 4. #6719 | C2 | semidirect |
| 5. #6714 | C2 | semidirect |
| 6. #6712 | C2 | semidirect |
| 7. C4×Dic15 | C2 | semidirect |
| 14. #1220 | C4 | direct (N × H) |
| 20. C22×C4×C5 | D3 | semidirect |
| 29. C22×C3×C5 | C2×C4 | semidirect |
| 33. C2×D15 | C2×C4 | semidirect |
| 35. C3×C4×C5 | D4 | semidirect |
| 38. Dic15 | C2×C4 | semidirect |
| 39. C22×C3×C4 | D5 | semidirect |
| 74. C22×C5 | C4×D3 | semidirect |
| 80. C4×C5 | #67 | semidirect |
| 86. C22×C4 | D15 | semidirect |
| 91. C3×C5 | C4×D4 | semidirect |
| 94. C22×C3 | C4×D5 | semidirect |
| 100. C3×C4 | C22⋊D5 | semidirect |
| 124. C5 | C4×#67 | semidirect |
| 130. C22 | C4×D15 | semidirect |
| 136. C4 | #1220 | direct (N × H) |
| 137. C3 | C4×C22⋊D5 | semidirect |
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×#1220 | 2 |
| C2×C4×D15 | 2 |
| #6719 | 2 |
| #6714 | 2 |
| #6712 | 2 |
| C4×Dic15 | 2 |
| C4×C22⋊D5 | 3 |
| C4×#67 | 5 |