Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 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 |
|---|---|---|
| 2. C22×C3×AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×C22⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 4. C2×C22⋊AGL(1,𝔽5) | C3 | direct (N × H) |
| 5. C23×C3×C5 | C4 | semidirect |
| 7. C22×C3×D5 | C4 | semidirect |
| 8. C22×C3×D5 | C4 | semidirect |
| 12. C2×C3×AGL(1,𝔽5) | C22 | semidirect |
| 15. C22×AGL(1,𝔽5) | C2×C3 | semidirect |
| 16. C22⋊AGL(1,𝔽5) | C2×C3 | direct (N × H) |
| 19. C22×C3×C5 | C2×C4 | semidirect |
| 24. C2×C3×D5 | C2×C4 | semidirect |
| 31. C23×C5 | C3×C4 | semidirect |
| 33. C22×D5 | C3×C4 | semidirect |
| 34. C22×D5 | C3×C4 | semidirect |
| 38. C2×AGL(1,𝔽5) | C22×C3 | semidirect |
| 41. C2×C3×C5 | C22⋊C4 | semidirect |
| 44. C3×D5 | C22⋊C4 | semidirect |
| 51. C23×C3 | AGL(1,𝔽5) | semidirect |
| 56. C22×C5 | C2×C3×C4 | semidirect |
| 61. C2×D5 | C2×C3×C4 | semidirect |
| 68. C3×C5 | C2×C22⋊C4 | semidirect |
| 78. C22×C3 | C2×AGL(1,𝔽5) | semidirect |
| 81. C2×C5 | C3×C22⋊C4 | semidirect |
| 84. D5 | C3×C22⋊C4 | semidirect |
| 91. C23 | C3×AGL(1,𝔽5) | semidirect |
| 98. C2×C3 | C22⋊AGL(1,𝔽5) | direct (N × H) |
| 100. C5 | C2×C3×C22⋊C4 | semidirect |
| 110. C22 | C2×C3×AGL(1,𝔽5) | semidirect |
| 112. C3 | C2×C22⋊AGL(1,𝔽5) | direct (N × H) |
| 117. C2 | C3×C22⋊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 |
|---|---|
| C23×C3×D5 | 2 |
| C22×C3×AGL(1,𝔽5) | 2 |
| C3×C22⋊AGL(1,𝔽5) | 2 |
| C2×C22⋊AGL(1,𝔽5) | 3 |
| C2×C3×C22⋊C4 | 5 |