Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×C5×M16 | C2 | semidirect |
| 3. C3×#681 | C2 | semidirect |
| 4. C3×#676 | C2 | semidirect |
| 5. C3×C8×D5 | C2 | semidirect |
| 6. D5×M16 | C3 | direct (N × H) |
| 14. C3×C5×C8 | C22 | semidirect |
| 15. C3×#168 | C22 | semidirect |
| 18. C5×M16 | C2×C3 | semidirect |
| 19. #681 | C2×C3 | semidirect |
| 20. #676 | C2×C3 | semidirect |
| 21. C8×D5 | C2×C3 | semidirect |
| 33. C3×M16 | D5 | direct (N × H) |
| 42. C5×C8 | C22×C3 | semidirect |
| 43. #168 | C22×C3 | semidirect |
| 48. C3×D5 | M16 | direct (N × H) |
| 57. C3×C8 | C2×D5 | semidirect |
| 69. M16 | C3×D5 | direct (N × H) |
| 71. C3×C5 | C2×M16 | semidirect |
| 83. D5 | C3×M16 | direct (N × H) |
| 92. C8 | C2×C3×D5 | semidirect |
| 97. C5 | C2×C3×M16 | semidirect |
| 106. C3 | D5×M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D5 | 2 |
| C3×C5×M16 | 2 |
| C3×#681 | 2 |
| C3×#676 | 2 |
| C3×C8×D5 | 2 |
| D5×M16 | 3 |
| C2×C3×M16 | 5 |