Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
654 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 654 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 |
|---|---|---|
| 2. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 3. C2×C5×#859 | C2 | semidirect |
| 4. C5×#5394 | C2 | direct (N × H) |
| 7. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 10. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 11. C5×#859 | C22 | semidirect |
| 12. C2×#5394 | C5 | direct (N × H) |
| 14. C2×C4×C5×Q8 | D3 | semidirect |
| 25. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 27. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 30. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 31. C2×#859 | C2×C5 | semidirect |
| 32. #5394 | C2×C5 | direct (N × H) |
| 43. C4×C5×Q8 | C2×D3 | semidirect |
| 65. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 67. C2×GL(2,𝔽3) | C4×C5 | semidirect |
| 70. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 71. #859 | C22×C5 | semidirect |
| 102. C2×C4×Q8 | C5×D3 | semidirect |
| 123. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 125. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 162. C4×Q8 | C2×C5×D3 | semidirect |
| 188. SL(2,𝔽3) | C22×C4×C5 | semidirect |
| 244. C2×C5 | #5394 | direct (N × H) |
| 278. C5 | C2×#5394 | direct (N × H) |
| 295. C2 | C5×#5394 | 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 |
| C2×C5×#859 | 2 |
| C5×#5394 | 2 |
| C2×C5×#440 | 3 |
| C2×C5×(C2×D3)⋊C4 | 4 |
| C2×#5394 | 5 |