Finite Group DatabasebetaFinite Group DatabasebetaOrder 5400.
276 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C5×D5×3−1+2 | C2 | semidirect |
| 3. C2×C52×AGL(1,ℤ/9) | C2 | semidirect |
| 5. C5×#67082 | C3 | semidirect |
| 10. #67082⋊C3 | C5 | direct (N × H) |
| 14. C2×C52×D9 | C2×C3 | semidirect |
| 16. C2×C5×C9×D5 | C2×C3 | semidirect |
| 17. C5×Dic45 | C2×C3 | semidirect |
| 18. C52×3−1+2 | D4 | semidirect |
| 23. C2×C5×AGL(1,ℤ/9) | D5 | semidirect |
| 24. C2×C5×AGL(1,ℤ/9) | C2×C5 | semidirect |
| 25. C2×D5×3−1+2 | C2×C5 | semidirect |
| 26. 3−1+2⋊Dic5 | C2×C5 | semidirect |
| 39. #67082 | C3×C5 | semidirect |
| 56. C52×C9 | C3×D4 | semidirect |
| 69. C2×C5×D9 | C3×D5 | semidirect |
| 70. C2×C5×D9 | C2×C3×C5 | semidirect |
| 72. C2×C9×D5 | C2×C3×C5 | semidirect |
| 73. Dic45 | C2×C3×C5 | semidirect |
| 82. C5×3−1+2 | C22⋊D5 | semidirect |
| 83. C5×3−1+2 | C5×D4 | semidirect |
| 89. C2×AGL(1,ℤ/9) | C5×D5 | semidirect |
| 92. C2×C5×D5 | AGL(1,ℤ/9) | semidirect |
| 146. C5×C9 | C3×C22⋊D5 | semidirect |
| 147. C5×C9 | C3×C5×D4 | semidirect |
| 155. C2×D9 | C3×C5×D5 | semidirect |
| 173. 3−1+2 | C5×C22⋊D5 | semidirect |
| 174. C52 | #611⋊C3 | semidirect |
| 181. C2×D5 | C5×AGL(1,ℤ/9) | semidirect |
| 214. C9 | C3×C5×C22⋊D5 | semidirect |
| 223. C5 | #67082⋊C3 | direct (N × H) |
| 224. C5 | C5×#611⋊C3 | 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 |
| C2×C5×D5×3−1+2 | 2 |
| C2×C52×AGL(1,ℤ/9) | 2 |
| C3×C5×#1201 | 3 |
| C5×#67082 | 3 |
| C5×#611⋊C3 | 5 |
| #67082⋊C3 | 5 |