Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 98 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×#5155 | C2 | semidirect |
| 3. C5×Dic3×D8 | C2 | semidirect |
| 4. C2×C5×#827 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. C5×#4503 | C2 | semidirect |
| 7. C5×Dic3⋊C16 | C2 | semidirect |
| 22. #71463 | C5 | direct (N × H) |
| 51. #5155 | C2×C5 | semidirect |
| 52. Dic3×D8 | C2×C5 | semidirect |
| 53. C2×#827 | C2×C5 | semidirect |
| 54. #4562 | C2×C5 | semidirect |
| 55. #4503 | C2×C5 | semidirect |
| 56. Dic3⋊C16 | C2×C5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #71463 | direct (N × H) |
| 301. C3 | C5×#2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D16 | 2 |
| C5×#5155 | 2 |
| C5×Dic3×D8 | 2 |
| C2×C5×#827 | 2 |
| C5×#4562 | 2 |
| C5×#4503 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#2210 | 3 |
| #71463 | 5 |