Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4895 | C2 | semidirect |
| 3. C3×C5×#368 | C2 | semidirect |
| 4. C5×#4502 | C2 | semidirect |
| 5. C5×#4497 | C2 | semidirect |
| 14. C5×Dic24 | C4 | semidirect |
| 15. C5×#800 | C4 | semidirect |
| 16. C5×D48 | C4 | semidirect |
| 17. #69358 | C5 | direct (N × H) |
| 20. C5×#368 | D3 | semidirect |
| 37. #4895 | C2×C5 | semidirect |
| 38. C3×#368 | C2×C5 | semidirect |
| 39. #4502 | C2×C5 | semidirect |
| 40. #4497 | C2×C5 | semidirect |
| 69. Dic24 | C4×C5 | semidirect |
| 70. #800 | C4×C5 | semidirect |
| 71. D48 | C4×C5 | semidirect |
| 87. #368 | C5×D3 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #69358 | 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×#4895 | 2 |
| C3×C5×#368 | 2 |
| C5×#4502 | 2 |
| C5×#4497 | 2 |
| C5×#2179 | 3 |
| #69358 | 5 |