Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
472 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C5 | C2×C4 |
| prime radical | C22×D3×D5 | C2 |
| cosocle | C3×D5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C22×C3×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×D3×AGL(1,𝔽5) | C2 | direct (N × H) |
| 6. C22×D15 | C4 | semidirect |
| 7. C22×C5×D3 | C4 | semidirect |
| 9. C2×D3×D5 | C4 | semidirect |
| 11. C2×ΓL(1,𝔽16) | C22 | semidirect |
| 12. C2×C3×AGL(1,𝔽5) | C22 | semidirect |
| 13. D3×AGL(1,𝔽5) | C22 | direct (N × H) |
| 18. C22×AGL(1,𝔽5) | D3 | direct (N × H) |
| 19. C22×C3×C5 | C2×C4 | semidirect |
| 20. C2×D15 | C2×C4 | semidirect |
| 21. C2×C5×D3 | C2×C4 | semidirect |
| 22. C2×C3×D5 | C2×C4 | semidirect |
| 24. D3×D5 | C2×C4 | semidirect |
| 26. ΓL(1,𝔽16) | C23 | semidirect |
| 27. C3×AGL(1,𝔽5) | C23 | semidirect |
| 39. C2×AGL(1,𝔽5) | C2×D3 | direct (N × H) |
| 41. C2×C3×C5 | C22×C4 | semidirect |
| 42. D15 | C22×C4 | semidirect |
| 43. C3×D5 | C22×C4 | semidirect |
| 45. C5×D3 | C22×C4 | semidirect |
| 50. C22×D3 | AGL(1,𝔽5) | direct (N × H) |
| 55. C22×C5 | C4×D3 | semidirect |
| 59. C2×D5 | C4×D3 | semidirect |
| 62. AGL(1,𝔽5) | C22×D3 | direct (N × H) |
| 67. C3×C5 | C23×C4 | semidirect |
| 70. C22×C3 | C2×AGL(1,𝔽5) | semidirect |
| 74. C2×D3 | C2×AGL(1,𝔽5) | direct (N × H) |
| 78. C2×C5 | C2×C4×D3 | semidirect |
| 80. D5 | C2×C4×D3 | semidirect |
| 92. C2×C3 | C22×AGL(1,𝔽5) | semidirect |
| 94. D3 | C22×AGL(1,𝔽5) | direct (N × H) |
| 95. C5 | C22×C4×D3 | semidirect |
| 102. C22 | D3×AGL(1,𝔽5) | direct (N × H) |
| 105. C3 | C23×AGL(1,𝔽5) | semidirect |
| 110. C2 | C2×D3×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×D3×D5 | 2 |
| C22×ΓL(1,𝔽16) | 2 |
| C22×C3×AGL(1,𝔽5) | 2 |
| C2×D3×AGL(1,𝔽5) | 2 |
| C23×AGL(1,𝔽5) | 3 |
| C22×C4×D3 | 5 |