Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
654 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 89 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×#91184 | C2 | semidirect |
| 4. #11752113 | C2 | direct (N × H) |
| 7. C2×C5⋊GL(2,𝔽3) | C4 | semidirect |
| 10. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 11. #91184 | C22 | semidirect |
| 13. 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) | D5 | semidirect |
| 37. C4×C5×Q8 | C2×D3 | semidirect |
| 65. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 70. C4×SL(2,𝔽3) | C2×D5 | semidirect |
| 102. C2×C4×Q8 | D15 | semidirect |
| 123. C2×SL(2,𝔽3) | C4×D5 | semidirect |
| 162. C4×Q8 | C2×D15 | semidirect |
| 188. SL(2,𝔽3) | C2×C4×D5 | semidirect |
| 243. C2×C5 | #5394 | semidirect |
| 278. C5 | C2×#5394 | semidirect |
| 295. C2 | #11752113 | 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×#91184 | 2 |
| #11752113 | 2 |
| C2×#65315 | 3 |
| C2×#6714 | 4 |
| C2×#5394 | 5 |