Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
| 3. C5×#5386 | C2 | semidirect |
| 9. Q8×GL(2,𝔽3) | C5 | direct (N × H) |
| 10. C5×Q82 | D3 | semidirect |
| 22. C5×GL(2,𝔽3) | Q8 | direct (N × H) |
| 23. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 25. #5386 | C2×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 69. Q82 | C5×D3 | semidirect |
| 87. GL(2,𝔽3) | C5×Q8 | direct (N × H) |
| 92. C5×Q8 | GL(2,𝔽3) | direct (N × H) |
| 93. C5×Q8 | D3×Q8 | semidirect |
| 127. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 169. Q8 | C5×GL(2,𝔽3) | direct (N × H) |
| 170. Q8 | C5×D3×Q8 | semidirect |
| 184. C5 | Q8×GL(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 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5386 | 2 |
| C5×Q8×SD16 | 3 |
| C2×C5×D3×Q8 | 4 |
| Q8×GL(2,𝔽3) | 5 |