Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
996 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 421 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. C2×C4×ΓL(1,𝔽16) | C2 | direct (N × H) |
| 6. C22×ΓL(1,𝔽16) | C4 | direct (N × H) |
| 8. C22×C3×C4×C5 | C4 | semidirect |
| 9. C22×C3×Dic5 | C4 | semidirect |
| 10. C2×C3×C4×D5 | C4 | semidirect |
| 12. C4×ΓL(1,𝔽16) | C22 | direct (N × H) |
| 21. C2×ΓL(1,𝔽16) | C2×C4 | direct (N × H) |
| 23. C2×C3×C4×C5 | C2×C4 | semidirect |
| 24. C2×C3×Dic5 | C2×C4 | semidirect |
| 25. C3×C4×D5 | C2×C4 | semidirect |
| 33. C22×C4×C5 | Dic3 | semidirect |
| 34. C22×Dic5 | Dic3 | semidirect |
| 35. C2×C4×D5 | Dic3 | semidirect |
| 39. C22×C3×C5 | C42 | semidirect |
| 41. C2×C3×D5 | C42 | semidirect |
| 45. ΓL(1,𝔽16) | C22×C4 | direct (N × H) |
| 46. C3×C4×C5 | C22×C4 | semidirect |
| 47. C3×Dic5 | C22×C4 | semidirect |
| 52. C22×C3×C4 | AGL(1,𝔽5) | semidirect |
| 62. C2×C4×C5 | C2×Dic3 | semidirect |
| 63. C2×Dic5 | C2×Dic3 | semidirect |
| 64. C4×D5 | C2×Dic3 | semidirect |
| 69. C2×C3×C5 | C2×C42 | semidirect |
| 71. C3×D5 | C2×C42 | semidirect |
| 80. C2×C3×C4 | C2×AGL(1,𝔽5) | semidirect |
| 83. C22×C5 | C4×Dic3 | semidirect |
| 85. C2×D5 | C4×Dic3 | semidirect |
| 90. C4×C5 | C22×Dic3 | semidirect |
| 91. Dic5 | C22×Dic3 | semidirect |
| 98. C22×C4 | ΓL(1,𝔽16) | direct (N × H) |
| 100. C3×C5 | C22×C42 | semidirect |
| 105. C22×C3 | C4×AGL(1,𝔽5) | semidirect |
| 108. C3×C4 | C22×AGL(1,𝔽5) | semidirect |
| 110. C2×C5 | C2×C4×Dic3 | semidirect |
| 112. D5 | C2×C4×Dic3 | semidirect |
| 123. C2×C4 | C2×ΓL(1,𝔽16) | direct (N × H) |
| 126. C2×C3 | C2×C4×AGL(1,𝔽5) | semidirect |
| 128. C5 | C22×C4×Dic3 | semidirect |
| 133. C22 | C4×ΓL(1,𝔽16) | direct (N × H) |
| 137. C4 | C22×ΓL(1,𝔽16) | direct (N × H) |
| 138. C3 | C22×C4×AGL(1,𝔽5) | semidirect |
| 141. C2 | C2×C4×ΓL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×ΓL(1,𝔽16) | 2 |
| C22×C3×C4×D5 | 2 |
| C2×C4×ΓL(1,𝔽16) | 2 |
| C22×C4×AGL(1,𝔽5) | 3 |
| C22×C4×Dic3 | 5 |