Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
570 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 92 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. C5×#520⋊C3 | C2 | semidirect |
| 3. C5×#5424 | C2 | semidirect |
| 4. C5×#5394 | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 8. C5×#986 | C4 | semidirect |
| 11. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 12. C5×#859 | C22 | semidirect |
| 13. C5×#859 | C22 | semidirect |
| 14. #85366 | C5 | direct (N × H) |
| 16. C5×#520 | D3 | semidirect |
| 28. C5×#41⋊C3 | C2×C4 | semidirect |
| 30. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 35. #520⋊C3 | C2×C5 | semidirect |
| 36. #5424 | C2×C5 | semidirect |
| 37. #5394 | C2×C5 | semidirect |
| 38. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 77. #986 | C4×C5 | semidirect |
| 80. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 81. #859 | C22×C5 | semidirect |
| 82. #859 | C22×C5 | semidirect |
| 85. C5×#41 | C4×D3 | semidirect |
| 116. #520 | C5×D3 | semidirect |
| 136. #41⋊C3 | C2×C4×C5 | semidirect |
| 138. GL(2,𝔽3) | C2×C4×C5 | semidirect |
| 225. #41 | C4×C5×D3 | semidirect |
| 299. C5 | #85366 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C5×#520⋊C3 | 2 |
| C5×#5424 | 2 |
| C5×#5394 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#2946 | 3 |
| C5×#893 | 4 |
| #85366 | 5 |