Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
624 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. C2×C5×#983 | C2 | semidirect |
| 3. C5×#5427 | C2 | semidirect |
| 4. C5×#5425 | C2 | semidirect |
| 5. C5×#5421 | C2 | semidirect |
| 6. C5×#5419 | C2 | semidirect |
| 7. C2×C5×#859 | C2 | semidirect |
| 19. #85539 | C5 | direct (N × H) |
| 20. C2×C5×2−1+4 | D3 | semidirect |
| 41. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 48. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 49. C2×#983 | C2×C5 | semidirect |
| 50. #5427 | C2×C5 | semidirect |
| 51. #5425 | C2×C5 | semidirect |
| 52. #5421 | C2×C5 | semidirect |
| 53. #5419 | C2×C5 | semidirect |
| 54. C2×#859 | C2×C5 | semidirect |
| 141. C2×C5×Q8 | #67 | semidirect |
| 182. C2×2−1+4 | C5×D3 | semidirect |
| 217. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 369. C2×Q8 | C5×#67 | semidirect |
| 481. C5 | #85539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| C2×C5×#983 | 2 |
| C5×#5427 | 2 |
| C5×#5425 | 2 |
| C5×#5421 | 2 |
| C5×#5419 | 2 |
| C2×C5×#859 | 2 |
| C5×#3013 | 3 |
| C5×#939 | 4 |
| #85539 | 5 |