Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
610 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 81 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. C22×C5⋊#226 | C2 | semidirect |
| 3. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 4. #11752114 | C2 | direct (N × H) |
| 10. C2×C5⋊#226 | C22 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 14. C2×C4×C5×Q8 | D3 | semidirect |
| 33. C2×C4×SL(2,𝔽3) | D5 | semidirect |
| 39. C4×C5×Q8 | C2×D3 | semidirect |
| 76. C4×SL(2,𝔽3) | C2×D5 | semidirect |
| 113. C2×C4×Q8 | D15 | semidirect |
| 180. C4×Q8 | C2×D15 | semidirect |
| 261. C2×C5 | #5395 | semidirect |
| 298. C5 | C2×#5395 | semidirect |
| 315. C2 | #11752114 | 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 |
| C22×C5⋊#226 | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| #11752114 | 2 |
| C2×#65317 | 3 |
| C2×#6714 | 4 |
| C2×#5395 | 5 |