Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 8. C5×#859 | C4 | semidirect |
| 10. #73062 | C5 | direct (N × H) |
| 54. C5×SL(2,𝔽3) | C4⋊C4 | semidirect |
| 58. #859 | C4×C5 | semidirect |
| 168. SL(2,𝔽3) | C5×C4⋊C4 | semidirect |
| 261. C5 | #73062 | 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×#1863 | 3 |
| C5×C3⋊#95 | 4 |
| #73062 | 5 |