Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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. C3×#711 | C2 | semidirect |
| 2. C3×D4×D5 | C2 | semidirect |
| 3. C3×C5×D8 | C2 | semidirect |
| 4. C3×#687 | C2 | semidirect |
| 5. C3×#686 | C2 | semidirect |
| 6. C3×#677 | C2 | semidirect |
| 7. C3×#676 | C2 | semidirect |
| 8. #4057 | C3 | direct (N × H) |
| 11. C3×C5×D4 | C22 | semidirect |
| 17. C3×Dic10 | C22 | semidirect |
| 18. C3×C5×C8 | C22 | semidirect |
| 19. C3×#168 | C22 | semidirect |
| 21. #711 | C2×C3 | semidirect |
| 22. D4×D5 | C2×C3 | semidirect |
| 23. C5×D8 | C2×C3 | semidirect |
| 24. #687 | C2×C3 | semidirect |
| 25. #686 | C2×C3 | semidirect |
| 26. #677 | C2×C3 | semidirect |
| 27. #676 | C2×C3 | semidirect |
| 41. C3×D8 | D5 | semidirect |
| 45. C5×D4 | C22×C3 | semidirect |
| 51. Dic10 | C22×C3 | semidirect |
| 52. C5×C8 | C22×C3 | semidirect |
| 53. #168 | C22×C3 | semidirect |
| 66. C3×D4 | C2×D5 | semidirect |
| 70. C3×C8 | C2×D5 | semidirect |
| 84. D8 | C3×D5 | semidirect |
| 86. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 106. D4 | C2×C3×D5 | semidirect |
| 110. C8 | C2×C3×D5 | semidirect |
| 116. C5 | C3×AGL(1,ℤ/8) | semidirect |
| 125. C3 | #4057 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#711 | 2 |
| C3×D4×D5 | 2 |
| C3×C5×D8 | 2 |
| C3×#687 | 2 |
| C3×#686 | 2 |
| C3×#677 | 2 |
| C3×#676 | 2 |
| #4057 | 3 |
| C3×AGL(1,ℤ/8) | 5 |