Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 122 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×#5080 | C2 | semidirect |
| 3. C5×#5079 | C2 | semidirect |
| 6. C5×#4681 | C2 | semidirect |
| 7. C5×C8×C3⋊C8 | C2 | semidirect |
| 22. #71181 | C5 | direct (N × H) |
| 48. #5080 | C2×C5 | semidirect |
| 49. #5079 | C2×C5 | semidirect |
| 52. #4681 | C2×C5 | semidirect |
| 53. C8×C3⋊C8 | C2×C5 | semidirect |
| 224. C3×C5 | #1708 | semidirect |
| 259. C5 | #71181 | direct (N × H) |
| 270. C3 | C5×#1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#486 | 2 |
| C5×#5080 | 2 |
| C5×#5079 | 2 |
| C5×#5076 | 2 |
| C5×#5070 | 2 |
| C5×#4681 | 2 |
| C5×C8×C3⋊C8 | 2 |
| C5×#1708 | 3 |
| #71181 | 5 |