Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
196 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 9. #226⋊C8 | C5 | direct (N × H) |
| 18. C5×#226 | C8 | semidirect |
| 77. #226 | C5×C8 | semidirect |
| 168. C5 | #226⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#226 | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×SL(2,𝔽3)⋊C8 | 2 |
| C5×#1579 | 3 |
| C5×Dic3⋊C8 | 4 |
| #226⋊C8 | 5 |