Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
536 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
| 4. C5×Q8×#41 | C3 | semidirect |
| 9. Q8×#41⋊C3 | C5 | direct (N × H) |
| 18. C5×#41⋊C3 | Q8 | direct (N × H) |
| 22. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 23. #557⋊C3 | C2×C5 | semidirect |
| 44. Q8×#41 | C3×C5 | semidirect |
| 49. C5×SL(2,𝔽3) | C2×Q8 | semidirect |
| 55. C5×#41 | C3×Q8 | semidirect |
| 88. #41⋊C3 | C5×Q8 | direct (N × H) |
| 96. C5×Q8 | #41⋊C3 | direct (N × H) |
| 136. SL(2,𝔽3) | C2×C5×Q8 | semidirect |
| 149. #41 | C3×C5×Q8 | semidirect |
| 183. Q8 | C5×#41⋊C3 | direct (N × H) |
| 200. C5 | Q8×#41⋊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 |
| C4×C5×#41⋊C3 | 2 |
| C5×Q8×#41 | 3 |
| C3×C4×C5×Q8 | 4 |
| Q8×#41⋊C3 | 5 |