Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
396 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 130 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×#5093 | C2 | semidirect |
| 3. C5×#5080 | C2 | semidirect |
| 6. C5×#4682 | C2 | semidirect |
| 7. C5×#4455 | C2 | semidirect |
| 22. #71258 | C5 | direct (N × H) |
| 49. #5093 | C2×C5 | semidirect |
| 50. #5080 | C2×C5 | semidirect |
| 53. #4682 | C2×C5 | semidirect |
| 54. #4455 | C2×C5 | semidirect |
| 82. C3×C5×C8 | SD16 | semidirect |
| 166. C5×C8 | #214 | semidirect |
| 197. C3×C8 | C5×SD16 | semidirect |
| 228. C3×C5 | #1714 | semidirect |
| 258. C8 | C5×#214 | semidirect |
| 263. C5 | #71258 | direct (N × H) |
| 274. C3 | C5×#1714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#492 | 2 |
| C5×#5093 | 2 |
| C5×#5080 | 2 |
| C5×#5076 | 2 |
| C5×#5070 | 2 |
| C5×#4682 | 2 |
| C5×#4455 | 2 |
| C5×#1714 | 3 |
| #71258 | 5 |