Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
658 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 1. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. C2×C5×#986 | C2 | semidirect |
| 3. C5×#5424 | C2 | semidirect |
| 4. C5×#5421 | C2 | semidirect |
| 8. C22×C5×SL(2,𝔽3) | C22 | semidirect |
| 12. C5×#859 | C22 | semidirect |
| 13. #85540 | C5 | direct (N × H) |
| 14. C2×C5×2−1+4 | D3 | semidirect |
| 26. C5×#41⋊C3 | D4 | semidirect |
| 31. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 32. C2×#986 | C2×C5 | semidirect |
| 33. #5424 | C2×C5 | semidirect |
| 34. #5421 | C2×C5 | semidirect |
| 71. C22×SL(2,𝔽3) | C22×C5 | semidirect |
| 75. #859 | C22×C5 | semidirect |
| 82. C5×#41 | #67 | semidirect |
| 113. C2×2−1+4 | C5×D3 | semidirect |
| 132. #41⋊C3 | C5×D4 | semidirect |
| 222. #41 | C5×#67 | semidirect |
| 299. C5 | #85540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| C2×C5×#986 | 2 |
| C5×#5424 | 2 |
| C5×#5421 | 2 |
| C5×#3010 | 3 |
| C5×#940 | 4 |
| #85540 | 5 |