Finite Group DatabasebetaFinite Group DatabasebetaOrder 5400.
268 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. C5×Dic5×3−1+2 | C2 | semidirect |
| 2. C2×C5×C5⋊AGL(1,ℤ/9) | C2 | semidirect |
| 3. C2×C5⋊(C5⋊AGL(1,ℤ/9)) | C2 | semidirect |
| 5. #14267979 | C3 | semidirect |
| 14. C2×C5⋊D45 | C2×C3 | semidirect |
| 15. C2×C5×D45 | C2×C3 | semidirect |
| 17. C5×C9×Dic5 | C2×C3 | semidirect |
| 18. C52×3−1+2 | D4 | semidirect |
| 24. C2×C5⋊AGL(1,ℤ/9) | D5 | semidirect |
| 27. Dic5×3−1+2 | D5 | semidirect |
| 55. C52×C9 | C3×D4 | semidirect |
| 68. C2×D45 | C3×D5 | semidirect |
| 73. C9×Dic5 | C3×D5 | semidirect |
| 81. C5×3−1+2 | D20 | semidirect |
| 82. C5×3−1+2 | C22⋊D5 | semidirect |
| 92. C5×Dic5 | AGL(1,ℤ/9) | semidirect |
| 143. C5×C9 | C3×D20 | semidirect |
| 144. C5×C9 | C3×C22⋊D5 | semidirect |
| 170. 3−1+2 | #6038 | semidirect |
| 171. C52 | C4⋊AGL(1,ℤ/9) | semidirect |
| 180. Dic5 | C5⋊AGL(1,ℤ/9) | semidirect |
| 210. C9 | C3×#6038 | semidirect |
| 219. C5 | #67080⋊C3 | semidirect |
| 220. C5 | C4⋊(C5⋊AGL(1,ℤ/9)) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Dic5×3−1+2 | 2 |
| C2×C5×C5⋊AGL(1,ℤ/9) | 2 |
| C2×C5⋊(C5⋊AGL(1,ℤ/9)) | 2 |
| C3×#10597122 | 3 |
| #14267979 | 3 |
| C4⋊(C5⋊AGL(1,ℤ/9)) | 5 |
| #67080⋊C3 | 5 |