Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
458 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 1. C5×#548⋊C3 | C2 | semidirect |
| 2. C5×#5427 | C2 | semidirect |
| 3. C5×#5426 | C2 | semidirect |
| 4. C5×#5421 | C2 | semidirect |
| 5. C2×C5×#859 | C2 | semidirect |
| 6. C5×#5394 | C2 | semidirect |
| 7. C5×#5391 | C2 | semidirect |
| 17. #85389 | C5 | direct (N × H) |
| 18. C5×#548 | D3 | semidirect |
| 44. #548⋊C3 | C2×C5 | semidirect |
| 45. #5427 | C2×C5 | semidirect |
| 46. #5426 | C2×C5 | semidirect |
| 47. #5421 | C2×C5 | semidirect |
| 48. C2×#859 | C2×C5 | semidirect |
| 49. #5394 | C2×C5 | semidirect |
| 50. #5391 | C2×C5 | semidirect |
| 100. C5×SL(2,𝔽3) | #41 | semidirect |
| 152. #548 | C5×D3 | semidirect |
| 277. SL(2,𝔽3) | C5×#41 | semidirect |
| 398. C5 | #85389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#548⋊C3 | 2 |
| C5×#5427 | 2 |
| C5×#5426 | 2 |
| C5×#5421 | 2 |
| C2×C5×#859 | 2 |
| C5×#5394 | 2 |
| C5×#5391 | 2 |
| C5×#3308 | 3 |
| C5×#886 | 4 |
| #85389 | 5 |