Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
234 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 56 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×C8×SL(2,𝔽3) | C2 | semidirect |
| 4. C5×#3362 | C3 | semidirect |
| 9. #3362⋊C3 | C5 | direct (N × H) |
| 22. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 24. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 41. #3362 | C3×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | SD16 | semidirect |
| 95. C5×Q8 | #41⋊C3 | semidirect |
| 135. SL(2,𝔽3) | C5×SD16 | semidirect |
| 184. Q8 | C5×#41⋊C3 | semidirect |
| 203. C5 | #3362⋊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×C4⋊(#41⋊C3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#3362 | 3 |
| C3×C5×#103 | 4 |
| #3362⋊C3 | 5 |