Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
260 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 68 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. C5×SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 8. #73055 | C5 | direct (N × H) |
| 20. SL(2,𝔽3)⋊C8 | C2×C5 | semidirect |
| 40. C5×SL(2,𝔽3) | M16 | semidirect |
| 84. C5×Q8 | #208 | semidirect |
| 120. SL(2,𝔽3) | C5×M16 | semidirect |
| 167. Q8 | C5×#208 | semidirect |
| 185. C5 | #73055 | 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 |
| C5×SL(2,𝔽3)⋊C8 | 2 |
| C5×#1487 | 3 |
| C2×C5×#208 | 4 |
| #73055 | 5 |