Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
822 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 152 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. C22×C5×#41⋊C3 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | direct (N × H) |
| 3. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 4. C2×C5×#550 | C3 | semidirect |
| 6. C2×C5×#41⋊C3 | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C2×C4⋊(#41⋊C3) | C5 | direct (N × H) |
| 13. C5×#550 | C2×C3 | semidirect |
| 21. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 24. C22×#41⋊C3 | C2×C5 | semidirect |
| 25. C4⋊(#41⋊C3) | C2×C5 | direct (N × H) |
| 26. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 48. C2×#550 | C3×C5 | semidirect |
| 54. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 56. C2×#41⋊C3 | C22×C5 | semidirect |
| 59. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 93. #550 | C2×C3×C5 | semidirect |
| 107. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 134. C2×C4×C5 | #41⋊C3 | semidirect |
| 167. SL(2,𝔽3) | C2×C5×D4 | semidirect |
| 181. C4×C5 | C2×#41⋊C3 | semidirect |
| 221. C2×C5 | C4⋊(#41⋊C3) | direct (N × H) |
| 249. C2×C4 | C5×#41⋊C3 | semidirect |
| 256. C5 | C2×C4⋊(#41⋊C3) | direct (N × H) |
| 270. C4 | C2×C5×#41⋊C3 | semidirect |
| 273. C2 | C5×C4⋊(#41⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C2×C5×#550 | 3 |
| C2×C3×C5×C4⋊C4 | 4 |
| C2×C4⋊(#41⋊C3) | 5 |