Finite Group DatabasebetaFinite Group DatabasebetaOrder 2880.
1116 conjugacy classes of subgroups; only the 480 normal subgroups are shown.
This group has 1116 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 |
|---|---|---|
| 3. C3×#65688 | C3 | direct (N × H) |
| 7. C32×C42×C5 | C4 | semidirect |
| 8. C32×C4×Dic5 | C4 | semidirect |
| 18. #65688 | C32 | direct (N × H) |
| 24. C3×C42×C5 | C3×C4 | semidirect |
| 25. C3×C4×Dic5 | C3×C4 | semidirect |
| 31. C32×C4×C5 | C4⋊C4 | semidirect |
| 32. C32×Dic5 | C4⋊C4 | semidirect |
| 39. C32×C42 | AGL(1,𝔽5) | semidirect |
| 54. C42×C5 | C32×C4 | semidirect |
| 55. C4×Dic5 | C32×C4 | semidirect |
| 67. C3×C4×C5 | C3×C4⋊C4 | semidirect |
| 68. C3×Dic5 | C3×C4⋊C4 | semidirect |
| 73. C3×C42 | C3×AGL(1,𝔽5) | semidirect |
| 74. C32×C5 | #384 | semidirect |
| 86. C32×C4 | C4⋊AGL(1,𝔽5) | semidirect |
| 102. C4×C5 | C32×C4⋊C4 | semidirect |
| 103. Dic5 | C32×C4⋊C4 | semidirect |
| 111. C42 | C32×AGL(1,𝔽5) | semidirect |
| 112. C3×C5 | C3×#384 | semidirect |
| 118. C3×C4 | C3×C4⋊AGL(1,𝔽5) | semidirect |
| 122. C32 | #65688 | direct (N × H) |
| 132. C5 | C32×#384 | semidirect |
| 138. C4 | C32×C4⋊AGL(1,𝔽5) | semidirect |
| 139. C3 | C3×#65688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊AGL(1,𝔽5) | 2 |
| C32×C42×D5 | 2 |
| C3×#65688 | 3 |
| C32×#384 | 5 |