Finite Group DatabasebetaFinite Group DatabasebetaOrder 5400.
268 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 62 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. C5×3−1+2⋊Dic5 | C2 | semidirect |
| 2. C5×Dic5×3−1+2 | C2 | semidirect |
| 5. #14267978 | C3 | semidirect |
| 7. C5⋊(C5⋊AGL(1,ℤ/9)) | C4 | semidirect |
| 14. C5×Dic45 | C2×C3 | semidirect |
| 16. C5×C9×Dic5 | C2×C3 | semidirect |
| 17. C52×3−1+2 | C2×C4 | semidirect |
| 24. 3−1+2⋊Dic5 | D5 | semidirect |
| 26. Dic5×3−1+2 | D5 | semidirect |
| 31. C5⋊D45 | C3×C4 | semidirect |
| 50. C52×C9 | C2×C3×C4 | semidirect |
| 65. Dic45 | C3×D5 | semidirect |
| 67. C9×Dic5 | C3×D5 | semidirect |
| 74. C5×3−1+2 | C4×D5 | semidirect |
| 75. C5×3−1+2 | C4×D5 | semidirect |
| 85. C5×Dic5 | AGL(1,ℤ/9) | semidirect |
| 130. C5×C9 | C3×C4×D5 | semidirect |
| 131. C5×C9 | C3×C4×D5 | semidirect |
| 153. 3−1+2 | #6036 | semidirect |
| 154. C52 | C4×AGL(1,ℤ/9) | semidirect |
| 163. Dic5 | C5⋊AGL(1,ℤ/9) | semidirect |
| 189. C9 | C3×#6036 | semidirect |
| 196. C5 | #67079⋊C3 | semidirect |
| 197. 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 |
|---|---|
| C5×3−1+2⋊Dic5 | 2 |
| C5×Dic5×3−1+2 | 2 |
| C2×C5⋊(C5⋊AGL(1,ℤ/9)) | 2 |
| C3×#10597120 | 3 |
| #14267978 | 3 |
| C4×C5⋊AGL(1,ℤ/9) | 5 |
| #67079⋊C3 | 5 |