Finite Group DatabasebetaFinite Group Databasebeta← C2×C4⋊(C9⋊AGL(1,𝔽5)) #13085243
Order 1440.
276 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 116 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. C4⋊(C9⋊AGL(1,𝔽5)) | C2 | direct (N × H) |
| 8. C2×C4×C5×C9 | C4 | semidirect |
| 9. C2×C9×Dic5 | C4 | semidirect |
| 10. C4×C9×D5 | C4 | semidirect |
| 22. C4×C5×C9 | C2×C4 | semidirect |
| 23. C9×Dic5 | C2×C4 | semidirect |
| 36. C2×C5×C9 | C4⋊C4 | semidirect |
| 38. C9×D5 | C4⋊C4 | semidirect |
| 48. C2×C4×C9 | AGL(1,𝔽5) | semidirect |
| 62. C5×C9 | C2×C4⋊C4 | semidirect |
| 66. C2×C4×C5 | Dic9 | semidirect |
| 67. C2×Dic5 | Dic9 | semidirect |
| 68. C4×D5 | Dic9 | semidirect |
| 76. C4×C9 | C2×AGL(1,𝔽5) | semidirect |
| 97. C4×C5 | C2×Dic9 | semidirect |
| 98. Dic5 | C2×Dic9 | semidirect |
| 102. C2×C9 | C4⋊AGL(1,𝔽5) | semidirect |
| 116. C2×C5 | C4⋊Dic9 | semidirect |
| 118. D5 | C4⋊Dic9 | semidirect |
| 121. C9 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 128. C2×C4 | C9⋊AGL(1,𝔽5) | semidirect |
| 134. C5 | C2×C4⋊Dic9 | semidirect |
| 142. C4 | C2×C9⋊AGL(1,𝔽5) | semidirect |
| 147. C2 | C4⋊(C9⋊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 |
|---|---|
| C22×C9⋊AGL(1,𝔽5) | 2 |
| C2×C4×C9×D5 | 2 |
| C4⋊(C9⋊AGL(1,𝔽5)) | 2 |
| C2×C4⋊ΓL(1,𝔽16) | 3 |
| C2×C4⋊Dic9 | 5 |