Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
264 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 81 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×ΓL(1,𝔽16) | C2 | semidirect |
| 3. #6763 | C2 | direct (N × H) |
| 5. C23×C3×C5 | C4 | semidirect |
| 7. C22×C3×D5 | C4 | semidirect |
| 8. C22×C3×D5 | C4 | semidirect |
| 12. C2×ΓL(1,𝔽16) | C22 | semidirect |
| 19. C22×C3×C5 | C2×C4 | semidirect |
| 24. C2×C3×D5 | C2×C4 | semidirect |
| 31. C23×C5 | Dic3 | semidirect |
| 33. C22×D5 | Dic3 | semidirect |
| 34. C22×D5 | Dic3 | 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×Dic3 | semidirect |
| 61. C2×D5 | C2×Dic3 | semidirect |
| 68. C3×C5 | C2×C22⋊C4 | semidirect |
| 78. C22×C3 | C2×AGL(1,𝔽5) | semidirect |
| 81. C2×C5 | #217 | semidirect |
| 84. D5 | #217 | semidirect |
| 91. C23 | ΓL(1,𝔽16) | semidirect |
| 98. C2×C3 | C22⋊AGL(1,𝔽5) | semidirect |
| 100. C5 | C2×#217 | semidirect |
| 110. C22 | C2×ΓL(1,𝔽16) | semidirect |
| 112. C3 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 117. C2 | #6763 | 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×ΓL(1,𝔽16) | 2 |
| #6763 | 2 |
| C2×C22⋊AGL(1,𝔽5) | 3 |
| C2×#217 | 5 |