Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
658 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 84 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. C2×C5×#986 | C2 | semidirect |
| 2. C4×C5×#41⋊C3 | C2 | semidirect |
| 3. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 7. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 9. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 10. #85346 | C5 | direct (N × H) |
| 13. C4×C5×#41 | D3 | semidirect |
| 20. C5×#41⋊C3 | D4 | semidirect |
| 24. C2×#986 | C2×C5 | semidirect |
| 25. C4×#41⋊C3 | C2×C5 | semidirect |
| 26. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 50. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 53. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 55. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 58. C5×#41 | D12 | semidirect |
| 82. C4×#41 | C5×D3 | semidirect |
| 94. #41⋊C3 | C5×D4 | semidirect |
| 144. SL(2,𝔽3) | C2×C5×D4 | semidirect |
| 155. C4×C5 | #986 | semidirect |
| 158. #41 | C5×D12 | semidirect |
| 214. C5 | #85346 | direct (N × H) |
| 225. C4 | C5×#986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#3038 | 3 |
| C5×#874 | 4 |
| #85346 | 5 |