Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
530 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 530 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. C2×C5×#985 | C2 | semidirect |
| 2. C2×C5×#983 | C2 | semidirect |
| 3. C5×#548⋊C3 | C2 | semidirect |
| 4. C5×#5425 | C2 | semidirect |
| 5. C5×#5419 | C2 | semidirect |
| 6. C5×#5394 | C2 | semidirect |
| 7. C5×C4⋊#226 | C2 | semidirect |
| 19. #85383 | C5 | direct (N × H) |
| 22. C5×#548 | D3 | semidirect |
| 40. C5×GL(2,𝔽3) | D4 | semidirect |
| 48. C2×#985 | C2×C5 | semidirect |
| 49. C2×#983 | C2×C5 | semidirect |
| 50. #548⋊C3 | C2×C5 | semidirect |
| 51. #5425 | C2×C5 | semidirect |
| 52. #5419 | C2×C5 | semidirect |
| 53. #5394 | C2×C5 | semidirect |
| 54. C4⋊#226 | C2×C5 | semidirect |
| 175. #548 | C5×D3 | semidirect |
| 205. GL(2,𝔽3) | C5×D4 | semidirect |
| 442. C5 | #85383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#985 | 2 |
| C2×C5×#983 | 2 |
| C5×#548⋊C3 | 2 |
| C5×#5425 | 2 |
| C5×#5419 | 2 |
| C5×#5394 | 2 |
| C5×C4⋊#226 | 2 |
| C5×#3269 | 3 |
| C5×#883 | 4 |
| #85383 | 5 |