Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
530 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 128 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×Q8×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×#557⋊C3 | C2 | semidirect |
| 5. C5×#3503 | C3 | semidirect |
| 11. #3503⋊C3 | C5 | direct (N × H) |
| 22. C5×#41⋊C3 | Q8 | semidirect |
| 27. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 28. #557⋊C3 | C2×C5 | semidirect |
| 57. #3503 | C3×C5 | semidirect |
| 63. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 70. C5×#41 | C3×Q8 | semidirect |
| 113. #41⋊C3 | C5×Q8 | semidirect |
| 173. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 188. #41 | C3×C5×Q8 | semidirect |
| 250. C5 | #3503⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×SL(2,𝔽3) | 2 |
| C5×#557⋊C3 | 2 |
| C5×#520⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3503 | 3 |
| C3×C5×C4⋊Q8 | 4 |
| #3503⋊C3 | 5 |