Finite Group DatabasebetaFinite Group Databasebeta← C4×3−1+2⋊AGL(1,𝔽5) #72247365
Order 2160.
196 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. C4×C9⋊AGL(1,𝔽5) | C3 | semidirect |
| 6. 3−1+2⋊AGL(1,𝔽5) | C4 | direct (N × H) |
| 7. C4×C5×3−1+2 | C4 | semidirect |
| 8. Dic5×3−1+2 | C4 | semidirect |
| 27. C9⋊AGL(1,𝔽5) | C3×C4 | semidirect |
| 29. C4×C5×C9 | C3×C4 | semidirect |
| 31. C9×Dic5 | C3×C4 | semidirect |
| 34. C5×3−1+2 | C42 | semidirect |
| 41. C4×3−1+2 | AGL(1,𝔽5) | semidirect |
| 69. C5×C9 | C3×C42 | semidirect |
| 81. C4×C9 | C3×AGL(1,𝔽5) | semidirect |
| 87. 3−1+2 | C4×AGL(1,𝔽5) | semidirect |
| 94. C4×C5 | 3−1+2⋊C4 | semidirect |
| 95. Dic5 | 3−1+2⋊C4 | semidirect |
| 117. C9 | C3×C4×AGL(1,𝔽5) | semidirect |
| 124. C5 | C4×3−1+2⋊C4 | semidirect |
| 128. C4 | 3−1+2⋊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 |
|---|---|
| C2×3−1+2⋊AGL(1,𝔽5) | 2 |
| C4×D5×3−1+2 | 2 |
| C3×C4×ΓL(1,𝔽16) | 3 |
| C4×C9⋊AGL(1,𝔽5) | 3 |
| C4×3−1+2⋊C4 | 5 |