Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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×C5×#41 | C2 | semidirect |
| 2. C2×C3×D20 | C2 | semidirect |
| 3. C3×#688 | C2 | semidirect |
| 4. C3×#686 | C2 | semidirect |
| 5. C3×#681 | C2 | semidirect |
| 6. #4095 | C3 | direct (N × H) |
| 8. C3×C5×Q8 | C22 | semidirect |
| 10. C3×C5×D4 | C22 | semidirect |
| 15. C3×#168 | C22 | semidirect |
| 17. C5×#41 | C2×C3 | semidirect |
| 18. C2×D20 | C2×C3 | semidirect |
| 19. #688 | C2×C3 | semidirect |
| 20. #686 | C2×C3 | semidirect |
| 21. #681 | C2×C3 | semidirect |
| 29. C3×#41 | D5 | semidirect |
| 35. C5×Q8 | C22×C3 | semidirect |
| 37. C5×D4 | C22×C3 | semidirect |
| 42. #168 | C22×C3 | semidirect |
| 49. C3×Q8 | C2×D5 | semidirect |
| 53. C3×D4 | C2×D5 | semidirect |
| 64. #41 | C3×D5 | semidirect |
| 69. C3×C5 | AGL(1,ℤ/8) | semidirect |
| 82. Q8 | C2×C3×D5 | semidirect |
| 86. D4 | C2×C3×D5 | semidirect |
| 94. C5 | C3×AGL(1,ℤ/8) | semidirect |
| 102. C3 | #4095 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#41 | 2 |
| C2×C3×D20 | 2 |
| C3×#688 | 2 |
| C3×#686 | 2 |
| C3×#681 | 2 |
| #4095 | 3 |
| C3×AGL(1,ℤ/8) | 5 |