Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. C5×#557⋊C3 | C2 | semidirect |
| 3. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 4. C5×#3359 | C3 | semidirect |
| 9. #3359⋊C3 | C5 | direct (N × H) |
| 10. C5×#557 | C2×C3 | semidirect |
| 15. C5×C8×Q8 | C2×C3 | semidirect |
| 22. #557⋊C3 | C2×C5 | semidirect |
| 24. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 41. #3359 | C3×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | SD16 | semidirect |
| 73. #557 | C2×C3×C5 | semidirect |
| 78. C8×Q8 | C2×C3×C5 | semidirect |
| 136. SL(2,𝔽3) | C5×SD16 | semidirect |
| 205. C5 | #3359⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557⋊C3 | 2 |
| C5×D4×SL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#3359 | 3 |
| C3×C5×#102 | 4 |
| #3359⋊C3 | 5 |