Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 2. C5×#4700 | C2 | semidirect |
| 3. C3×C5×#346 | C2 | semidirect |
| 4. C5×#4510 | C2 | semidirect |
| 5. C5×#4506 | C2 | semidirect |
| 14. C5×Dic24 | C4 | semidirect |
| 15. C5×#800 | C4 | semidirect |
| 16. C5×D48 | C4 | semidirect |
| 17. #69085 | C5 | direct (N × H) |
| 22. C5×#346 | D3 | semidirect |
| 37. #4700 | C2×C5 | semidirect |
| 38. C3×#346 | C2×C5 | semidirect |
| 39. #4510 | C2×C5 | semidirect |
| 40. #4506 | C2×C5 | semidirect |
| 69. Dic24 | C4×C5 | semidirect |
| 70. #800 | C4×C5 | semidirect |
| 71. D48 | C4×C5 | semidirect |
| 89. #346 | C5×D3 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #69085 | direct (N × H) |
| 191. C3 | C5×#2179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4904 | 2 |
| C5×#4700 | 2 |
| C3×C5×#346 | 2 |
| C5×#4510 | 2 |
| C5×#4506 | 2 |
| C5×#2179 | 3 |
| #69085 | 5 |