Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
568 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 568 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×#986 | C2 | semidirect |
| 2. C2×C5×#985 | C2 | semidirect |
| 3. C5×#520⋊C3 | C2 | semidirect |
| 4. C5×#5395 | C2 | semidirect |
| 5. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 11. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 12. C2×C5×#226 | C22 | semidirect |
| 14. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 15. #85368 | C5 | direct (N × H) |
| 19. C5×#520 | D3 | semidirect |
| 30. C5×#41⋊C3 | D4 | semidirect |
| 37. C2×#986 | C2×C5 | semidirect |
| 38. C2×#985 | C2×C5 | semidirect |
| 39. #520⋊C3 | C2×C5 | semidirect |
| 40. #5395 | C2×C5 | semidirect |
| 41. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 86. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 87. C2×#226 | C22×C5 | semidirect |
| 89. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 94. C5×#41 | D12 | semidirect |
| 133. #520 | C5×D3 | semidirect |
| 154. #41⋊C3 | C5×D4 | semidirect |
| 258. #41 | C5×D12 | semidirect |
| 348. C5 | #85368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C2×C5×#985 | 2 |
| C5×#520⋊C3 | 2 |
| C5×#5395 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#3045 | 3 |
| C5×#895 | 4 |
| #85368 | 5 |