Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
798 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 108 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×GL(2,𝔽3) | C2 | semidirect |
| 2. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×C4⋊GL(2,𝔽3) | C2 | direct (N × H) |
| 8. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. C2×C4⋊GL(2,𝔽3) | C5 | direct (N × H) |
| 13. C2×C4×C5×Q8 | D3 | semidirect |
| 22. C2×C5×SL(2,𝔽3) | D4 | semidirect |
| 25. C22×GL(2,𝔽3) | C2×C5 | semidirect |
| 26. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 27. C4⋊GL(2,𝔽3) | C2×C5 | direct (N × H) |
| 40. C4×C5×Q8 | C2×D3 | semidirect |
| 54. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 58. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 59. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 63. C2×C5×Q8 | D12 | semidirect |
| 87. C2×C4×Q8 | C5×D3 | semidirect |
| 105. C2×SL(2,𝔽3) | C5×D4 | semidirect |
| 116. C5×Q8 | C2×D12 | semidirect |
| 128. C2×C4×C5 | GL(2,𝔽3) | semidirect |
| 143. C4×Q8 | C2×C5×D3 | semidirect |
| 161. SL(2,𝔽3) | C2×C5×D4 | semidirect |
| 174. C4×C5 | C2×GL(2,𝔽3) | semidirect |
| 178. C2×Q8 | C5×D12 | semidirect |
| 211. C2×C5 | C4⋊GL(2,𝔽3) | direct (N × H) |
| 223. Q8 | C2×C5×D12 | semidirect |
| 235. C2×C4 | C5×GL(2,𝔽3) | semidirect |
| 243. C5 | C2×C4⋊GL(2,𝔽3) | direct (N × H) |
| 256. C4 | C2×C5×GL(2,𝔽3) | semidirect |
| 259. C2 | C5×C4⋊GL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×GL(2,𝔽3) | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C2×C5×#460 | 3 |
| C22×C5×D12 | 4 |
| C2×C4⋊GL(2,𝔽3) | 5 |