Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
234 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×#2971 | C3 | semidirect |
| 8. #2971⋊C3 | C5 | direct (N × H) |
| 19. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 33. #2971 | C3×C5 | semidirect |
| 37. C5×SL(2,𝔽3) | M16 | semidirect |
| 89. C5×C8 | #41⋊C3 | semidirect |
| 109. SL(2,𝔽3) | C5×M16 | semidirect |
| 164. C8 | C5×#41⋊C3 | semidirect |
| 168. C5 | #2971⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×#41⋊C3 | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#2971 | 3 |
| C3×C5×#97 | 4 |
| #2971⋊C3 | 5 |