Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
676 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 174 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. #91989 | C2 | semidirect |
| 3. C3×#4130 | C2 | semidirect |
| 4. D3×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. #91921 | C2 | semidirect |
| 6. AGL(1,𝔽5)×D12 | C2 | semidirect |
| 9. C2×D3×AGL(1,𝔽5) | C22 | semidirect |
| 10. C2×D60 | C4 | semidirect |
| 11. C2×C5×D12 | C4 | semidirect |
| 13. C2×#1203 | C4 | semidirect |
| 14. D5×D12 | C4 | semidirect |
| 15. D5×D12 | C4 | semidirect |
| 19. C4⋊ΓL(1,𝔽16) | C22 | semidirect |
| 20. C4×ΓL(1,𝔽16) | C22 | semidirect |
| 22. C3×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 23. C3×C4×AGL(1,𝔽5) | C22 | semidirect |
| 24. (C2×D3)⋊AGL(1,𝔽5) | C22 | semidirect |
| 31. #4130 | D3 | semidirect |
| 32. C22×D15 | C2×C4 | semidirect |
| 33. C22×C5×D3 | C2×C4 | semidirect |
| 36. C2×D3×D5 | C2×C4 | semidirect |
| 41. C2×C3×C4×C5 | C2×C4 | semidirect |
| 42. D60 | C2×C4 | semidirect |
| 43. D60 | C2×C4 | semidirect |
| 44. C5×D12 | C2×C4 | semidirect |
| 45. C5×D12 | C2×C4 | semidirect |
| 46. C2×C3×Dic5 | C2×C4 | semidirect |
| 47. C3×C4×D5 | C2×C4 | semidirect |
| 48. C3×C4×D5 | C2×C4 | semidirect |
| 51. #1203 | C2×C4 | semidirect |
| 52. #1203 | C2×C4 | semidirect |
| 73. C4⋊AGL(1,𝔽5) | C2×D3 | semidirect |
| 75. C4×AGL(1,𝔽5) | C2×D3 | semidirect |
| 101. C2×D12 | AGL(1,𝔽5) | semidirect |
| 121. C2×C4×C5 | C4×D3 | semidirect |
| 124. C2×Dic5 | C4×D3 | semidirect |
| 127. C4×D5 | C4×D3 | semidirect |
| 128. C4×D5 | C4×D3 | semidirect |
| 148. C22×D3 | C2×AGL(1,𝔽5) | semidirect |
| 155. C2×C3×C4 | C2×AGL(1,𝔽5) | semidirect |
| 161. D12 | C2×AGL(1,𝔽5) | semidirect |
| 162. D12 | C2×AGL(1,𝔽5) | semidirect |
| 197. C3×C5 | #518 | semidirect |
| 240. C2×C4 | D3×AGL(1,𝔽5) | semidirect |
| 247. C5 | #5521 | semidirect |
| 264. C3 | #66258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D12 | 2 |
| #91989 | 2 |
| C3×#4130 | 2 |
| D3×C22⋊AGL(1,𝔽5) | 2 |
| #91921 | 2 |
| AGL(1,𝔽5)×D12 | 2 |
| #66258 | 3 |
| #5521 | 5 |