Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
254 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 254 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. #73068 | C5 | direct (N × H) |
| 14. C5×#41⋊C3 | C8 | semidirect |
| 19. SL(2,𝔽3)⋊C8 | C2×C5 | semidirect |
| 37. C5×SL(2,𝔽3) | C2×C8 | semidirect |
| 44. C5×#41 | C3⋊C8 | semidirect |
| 69. #41⋊C3 | C5×C8 | semidirect |
| 109. SL(2,𝔽3) | C2×C5×C8 | semidirect |
| 123. #41 | C5×C3⋊C8 | semidirect |
| 168. C5 | #73068 | 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×SL(2,𝔽3)⋊C8 | 2 |
| C5×#1476 | 3 |
| C4×C5×C3⋊C8 | 4 |
| #73068 | 5 |