Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4858 | C2 | semidirect |
| 5. C5×#4513 | C2 | semidirect |
| 6. C5×#4511 | C2 | semidirect |
| 7. C5×#4487 | C2 | semidirect |
| 20. #69247 | C5 | direct (N × H) |
| 45. #4858 | C2×C5 | semidirect |
| 48. #4513 | C2×C5 | semidirect |
| 49. #4511 | C2×C5 | semidirect |
| 50. #4487 | C2×C5 | semidirect |
| 198. C3×C5 | #2231 | semidirect |
| 226. C5 | #69247 | direct (N × H) |
| 235. C3 | C5×#2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5196 | 2 |
| C5×#4858 | 2 |
| C3×C5×#360 | 2 |
| C5×#4566 | 2 |
| C5×#4513 | 2 |
| C5×#4511 | 2 |
| C5×#4487 | 2 |
| C5×#2231 | 3 |
| #69247 | 5 |