Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
564 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 128 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. C5×#557⋊C3 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 3. C5×#548⋊C3 | C2 | semidirect |
| 4. C4×C5×#41⋊C3 | C2 | semidirect |
| 5. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 6. C5×#3480 | C3 | semidirect |
| 13. #3480⋊C3 | C5 | direct (N × H) |
| 15. C5×#557 | C2×C3 | semidirect |
| 18. C5×#550 | C2×C3 | semidirect |
| 23. C4×C5×#41 | C2×C3 | semidirect |
| 33. #557⋊C3 | C2×C5 | semidirect |
| 34. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 35. #548⋊C3 | C2×C5 | semidirect |
| 36. C4×#41⋊C3 | C2×C5 | semidirect |
| 37. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 72. #3480 | C3×C5 | semidirect |
| 79. C5×SL(2,𝔽3) | #41 | semidirect |
| 126. #557 | C2×C3×C5 | semidirect |
| 129. #550 | C2×C3×C5 | semidirect |
| 134. C4×#41 | C2×C3×C5 | semidirect |
| 176. C2×C4×C5 | #41⋊C3 | semidirect |
| 225. SL(2,𝔽3) | C5×#41 | semidirect |
| 320. C2×C4 | C5×#41⋊C3 | semidirect |
| 329. C5 | #3480⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#548⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×#3480 | 3 |
| C3×C5×#117 | 4 |
| #3480⋊C3 | 5 |