Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
3036 conjugacy classes of subgroups; only the 480 normal subgroups are shown.
This group has 3036 conjugacy classes of subgroups — too many to draw. Only its 480 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. C2×C32×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×#65800 | C3 | direct (N × H) |
| 4. C24×C32×C5 | C4 | semidirect |
| 6. C23×C32×D5 | C4 | semidirect |
| 8. C22×C32×AGL(1,𝔽5) | C22 | semidirect |
| 12. C2×C3×C22⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 23. #65800 | C32 | direct (N × H) |
| 26. C24×C3×C5 | C3×C4 | semidirect |
| 28. C23×C3×D5 | C3×C4 | semidirect |
| 30. C22×C3×AGL(1,𝔽5) | C22×C3 | semidirect |
| 35. C22×C32×C5 | C22⋊C4 | semidirect |
| 40. C2×C32×D5 | C22⋊C4 | semidirect |
| 44. C2×C22⋊AGL(1,𝔽5) | C2×C32 | semidirect |
| 48. C24×C32 | AGL(1,𝔽5) | semidirect |
| 67. C24×C5 | C32×C4 | semidirect |
| 69. C23×D5 | C32×C4 | semidirect |
| 71. C22×AGL(1,𝔽5) | C22×C32 | semidirect |
| 86. C22×C3×C5 | C3×C22⋊C4 | semidirect |
| 91. C2×C3×D5 | C3×C22⋊C4 | semidirect |
| 97. C24×C3 | C3×AGL(1,𝔽5) | semidirect |
| 100. C32×C5 | #379 | semidirect |
| 118. C22×C32 | C22⋊AGL(1,𝔽5) | semidirect |
| 139. C22×C5 | C32×C22⋊C4 | semidirect |
| 144. C2×D5 | C32×C22⋊C4 | semidirect |
| 154. C24 | C32×AGL(1,𝔽5) | semidirect |
| 157. C3×C5 | C3×#379 | semidirect |
| 165. C22×C3 | C3×C22⋊AGL(1,𝔽5) | semidirect |
| 172. C32 | #65800 | direct (N × H) |
| 187. C5 | C32×#379 | semidirect |
| 195. C22 | C32×C22⋊AGL(1,𝔽5) | semidirect |
| 198. C3 | C3×#65800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×D5 | 2 |
| C2×C32×C22⋊AGL(1,𝔽5) | 2 |
| C3×#65800 | 3 |
| C32×#379 | 5 |