Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. C4×ΓL(1,𝔽16) | C2 | semidirect |
| 4. C3×C4×AGL(1,𝔽5) | C2 | semidirect |
| 5. Dic3×AGL(1,𝔽5) | C2 | semidirect |
| 10. D3×AGL(1,𝔽5) | C4 | direct (N × H) |
| 11. C4×D15 | C4 | semidirect |
| 12. C4×C5×D3 | C4 | semidirect |
| 14. #1200 | C4 | semidirect |
| 15. D3×Dic5 | C4 | semidirect |
| 22. C4×AGL(1,𝔽5) | D3 | direct (N × H) |
| 27. ΓL(1,𝔽16) | C2×C4 | semidirect |
| 28. C3×AGL(1,𝔽5) | C2×C4 | semidirect |
| 29. C3×C4×C5 | C2×C4 | semidirect |
| 30. Dic15 | C2×C4 | semidirect |
| 31. C3×Dic5 | C2×C4 | semidirect |
| 32. C5×Dic3 | C2×C4 | semidirect |
| 50. D15 | C42 | semidirect |
| 52. C5×D3 | C42 | semidirect |
| 62. C4×D3 | AGL(1,𝔽5) | direct (N × H) |
| 68. AGL(1,𝔽5) | C4×D3 | direct (N × H) |
| 70. C4×C5 | C4×D3 | semidirect |
| 72. Dic5 | C4×D3 | semidirect |
| 78. C3×C5 | C2×C42 | semidirect |
| 85. C3×C4 | C2×AGL(1,𝔽5) | semidirect |
| 88. Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 106. D3 | C4×AGL(1,𝔽5) | direct (N × H) |
| 107. C5 | C42×D3 | semidirect |
| 117. C4 | D3×AGL(1,𝔽5) | direct (N × H) |
| 118. C3 | C2×C4×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×AGL(1,𝔽5) | 2 |
| C4×D3×D5 | 2 |
| C4×ΓL(1,𝔽16) | 2 |
| C3×C4×AGL(1,𝔽5) | 2 |
| Dic3×AGL(1,𝔽5) | 2 |
| C2×C4×AGL(1,𝔽5) | 3 |
| C42×D3 | 5 |