Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
350 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 6. C4×C5×SL(2,𝔽3) | C4 | semidirect |
| 8. C4⋊#859 | C5 | direct (N × H) |
| 25. C4×C5×Q8 | Dic3 | semidirect |
| 42. C5×SL(2,𝔽3) | C4⋊C4 | semidirect |
| 45. C4×SL(2,𝔽3) | C4×C5 | semidirect |
| 93. C5×Q8 | C4⋊Dic3 | semidirect |
| 113. C4×Q8 | C5×Dic3 | semidirect |
| 136. SL(2,𝔽3) | C5×C4⋊C4 | semidirect |
| 150. C4×C5 | #859 | semidirect |
| 194. Q8 | C5×C4⋊Dic3 | semidirect |
| 218. C5 | C4⋊#859 | direct (N × H) |
| 232. C4 | C5×#859 | semidirect |
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×#1803 | 3 |
| C2×C5×C4⋊Dic3 | 4 |
| C4⋊#859 | 5 |