Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 84 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×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#5421 | C2 | semidirect |
| 3. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 4. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 5. C5×#5386 | C2 | semidirect |
| 13. #85325 | C5 | direct (N × H) |
| 15. C2×C4×C5×Q8 | D3 | semidirect |
| 34. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 35. #5421 | C2×C5 | semidirect |
| 36. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 37. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 38. #5386 | C2×C5 | semidirect |
| 77. C5×SL(2,𝔽3) | #41 | semidirect |
| 115. C2×C4×Q8 | C5×D3 | semidirect |
| 150. C5×Q8 | #235 | semidirect |
| 165. C2×C4×C5 | GL(2,𝔽3) | semidirect |
| 212. SL(2,𝔽3) | C5×#41 | semidirect |
| 280. Q8 | C5×#235 | semidirect |
| 295. C2×C4 | C5×GL(2,𝔽3) | semidirect |
| 305. C5 | #85325 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×#5421 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5386 | 2 |
| C5×#3103 | 3 |
| C2×C5×#235 | 4 |
| #85325 | 5 |