Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
694 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 232 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 | direct (N × H) |
| 3. C2×C5×Q82 | C3 | semidirect |
| 7. C2×Q8×SL(2,𝔽3) | C5 | direct (N × H) |
| 9. C5×Q82 | C2×C3 | semidirect |
| 16. C2×C5×SL(2,𝔽3) | Q8 | direct (N × H) |
| 18. Q8×SL(2,𝔽3) | C2×C5 | direct (N × H) |
| 32. C2×Q82 | C3×C5 | semidirect |
| 37. C5×SL(2,𝔽3) | C2×Q8 | direct (N × H) |
| 45. C2×C5×Q8 | SL(2,𝔽3) | direct (N × H) |
| 46. C2×C5×Q8 | C3×Q8 | semidirect |
| 58. Q82 | C2×C3×C5 | semidirect |
| 70. C2×SL(2,𝔽3) | C5×Q8 | direct (N × H) |
| 77. C5×Q8 | C2×SL(2,𝔽3) | direct (N × H) |
| 78. C5×Q8 | C2×C3×Q8 | semidirect |
| 107. SL(2,𝔽3) | C2×C5×Q8 | direct (N × H) |
| 121. C2×Q8 | C5×SL(2,𝔽3) | direct (N × H) |
| 122. C2×Q8 | C3×C5×Q8 | semidirect |
| 139. C2×C5 | Q8×SL(2,𝔽3) | direct (N × H) |
| 148. Q8 | C2×C5×SL(2,𝔽3) | direct (N × H) |
| 149. Q8 | C2×C3×C5×Q8 | semidirect |
| 162. C5 | C2×Q8×SL(2,𝔽3) | direct (N × H) |
| 173. C2 | C5×Q8×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 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C2×C5×Q82 | 3 |
| C22×C3×C5×Q8 | 4 |
| C2×Q8×SL(2,𝔽3) | 5 |