Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
184 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×C4⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 4. C2×C4⋊AGL(1,𝔽5) | C3 | direct (N × H) |
| 8. C2×C3×C4×C5 | C4 | semidirect |
| 9. C2×C3×Dic5 | C4 | semidirect |
| 10. C3×C4×D5 | C4 | semidirect |
| 15. C4⋊AGL(1,𝔽5) | C2×C3 | direct (N × H) |
| 22. C3×C4×C5 | C2×C4 | semidirect |
| 23. C3×Dic5 | C2×C4 | semidirect |
| 30. C2×C4×C5 | C3×C4 | semidirect |
| 31. C2×Dic5 | C3×C4 | semidirect |
| 32. C4×D5 | C3×C4 | semidirect |
| 35. C2×C3×C5 | C4⋊C4 | semidirect |
| 37. C3×D5 | C4⋊C4 | semidirect |
| 46. C2×C3×C4 | AGL(1,𝔽5) | semidirect |
| 53. C4×C5 | C2×C3×C4 | semidirect |
| 54. Dic5 | C2×C3×C4 | semidirect |
| 58. C3×C5 | C2×C4⋊C4 | semidirect |
| 66. C3×C4 | C2×AGL(1,𝔽5) | semidirect |
| 67. C2×C5 | C3×C4⋊C4 | semidirect |
| 69. D5 | C3×C4⋊C4 | semidirect |
| 78. C2×C4 | C3×AGL(1,𝔽5) | semidirect |
| 82. C2×C3 | C4⋊AGL(1,𝔽5) | direct (N × H) |
| 84. C5 | C2×C3×C4⋊C4 | semidirect |
| 92. C4 | C2×C3×AGL(1,𝔽5) | semidirect |
| 93. C3 | C2×C4⋊AGL(1,𝔽5) | direct (N × H) |
| 97. C2 | C3×C4⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×AGL(1,𝔽5) | 2 |
| C2×C3×C4×D5 | 2 |
| C3×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4⋊AGL(1,𝔽5) | 3 |
| C2×C3×C4⋊C4 | 5 |