Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
542 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 76 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×C5×#984 | C2 | semidirect |
| 3. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. C5×#5395 | C2 | semidirect |
| 10. C2×C5×#226 | C22 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. #85347 | C5 | direct (N × H) |
| 17. C4×C5×#41 | D3 | semidirect |
| 32. C2×#984 | C2×C5 | semidirect |
| 33. C4×#41⋊C3 | C2×C5 | semidirect |
| 34. #5395 | C2×C5 | semidirect |
| 71. C2×#226 | C22×C5 | semidirect |
| 73. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 110. C4×#41 | C5×D3 | semidirect |
| 273. C5 | #85347 | 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 |
| C2×C5×#984 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#5395 | 2 |
| C5×#3040 | 3 |
| C5×#875 | 4 |
| #85347 | 5 |