Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
242 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 3. C5×Q8×Q16 | C3 | semidirect |
| 7. Q16×SL(2,𝔽3) | C5 | direct (N × H) |
| 30. Q8×Q16 | C3×C5 | semidirect |
| 35. C5×SL(2,𝔽3) | Q16 | direct (N × H) |
| 43. C5×Q16 | SL(2,𝔽3) | direct (N × H) |
| 68. C5×Q8 | C3×Q16 | semidirect |
| 95. SL(2,𝔽3) | C5×Q16 | direct (N × H) |
| 108. Q16 | C5×SL(2,𝔽3) | direct (N × H) |
| 128. Q8 | C3×C5×Q16 | semidirect |
| 140. C5 | Q16×SL(2,𝔽3) | 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×C8×SL(2,𝔽3) | 2 |
| C5×Q8×Q16 | 3 |
| C2×C3×C5×Q16 | 4 |
| Q16×SL(2,𝔽3) | 5 |