Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
602 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 602 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×#983 | C2 | semidirect |
| 2. C22×C5×GL(2,𝔽3) | C2 | semidirect |
| 3. C5×#519⋊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. #85355 | C5 | direct (N × H) |
| 19. C5×#519 | D3 | semidirect |
| 30. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 37. C2×#983 | C2×C5 | semidirect |
| 38. C22×GL(2,𝔽3) | C2×C5 | semidirect |
| 39. #519⋊C3 | C2×C5 | semidirect |
| 40. #5395 | C2×C5 | semidirect |
| 41. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 63. C4×C5×Q8 | C2×D3 | semidirect |
| 87. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 88. C2×#226 | C22×C5 | semidirect |
| 90. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 97. C2×C5×Q8 | D12 | semidirect |
| 134. #519 | C5×D3 | semidirect |
| 156. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 214. C4×Q8 | C2×C5×D3 | semidirect |
| 259. C2×Q8 | C5×D12 | semidirect |
| 345. C5 | #85355 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#983 | 2 |
| C22×C5×GL(2,𝔽3) | 2 |
| C5×#519⋊C3 | 2 |
| C5×#5395 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#3043 | 3 |
| C5×#882 | 4 |
| #85355 | 5 |