Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×#5420 | C2 | semidirect |
| 4. C5×#5394 | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 6. C5×#5388 | C2 | semidirect |
| 7. C4×C5×#226 | C2 | semidirect |
| 10. C5×#983 | C4 | direct (N × H) |
| 18. C4×#983 | C5 | direct (N × H) |
| 21. C2×C4×C5×Q8 | D3 | semidirect |
| 37. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 39. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 40. C5×#226 | C2×C4 | semidirect |
| 46. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 47. #5420 | C2×C5 | semidirect |
| 48. #5394 | C2×C5 | semidirect |
| 49. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 50. #5388 | C2×C5 | semidirect |
| 51. C4×#226 | C2×C5 | semidirect |
| 106. #983 | C4×C5 | direct (N × H) |
| 119. C2×C5×Q8 | C4×D3 | semidirect |
| 160. C2×C4×Q8 | C5×D3 | semidirect |
| 188. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 190. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 191. #226 | C2×C4×C5 | semidirect |
| 300. C4×C5 | #983 | direct (N × H) |
| 306. C2×Q8 | C4×C5×D3 | semidirect |
| 399. C5 | C4×#983 | direct (N × H) |
| 416. C4 | C5×#983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#983 | 2 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×#5420 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#5388 | 2 |
| C4×C5×#226 | 2 |
| C4×C5×#137 | 3 |
| C4×C5×#67 | 4 |
| C4×#983 | 5 |