Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
470 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 3. C5×#5391 | C2 | direct (N × H) |
| 9. C2×#5391 | C5 | direct (N × H) |
| 19. C2×C5×SL(2,𝔽3) | Q8 | semidirect |
| 24. #5391 | C2×C5 | direct (N × H) |
| 46. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 85. C2×SL(2,𝔽3) | C5×Q8 | semidirect |
| 129. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 166. C2×C5 | #5391 | direct (N × H) |
| 191. C5 | C2×#5391 | direct (N × H) |
| 203. C2 | C5×#5391 | 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 |
| C2×C5×#859 | 2 |
| C5×#5391 | 2 |
| C2×C5×#477 | 3 |
| C2×C5×C4⋊Dic3 | 4 |
| C2×#5391 | 5 |