Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
454 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 454 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×#859 | C2 | semidirect |
| 5. C2×C5×#41⋊C3 | C4 | semidirect |
| 9. #73151 | C5 | direct (N × H) |
| 21. C2×#859 | C2×C5 | semidirect |
| 25. C2×C5×#41 | Dic3 | semidirect |
| 44. C5×SL(2,𝔽3) | C22⋊C4 | semidirect |
| 46. C2×#41⋊C3 | C4×C5 | semidirect |
| 122. C2×#41 | C5×Dic3 | semidirect |
| 145. SL(2,𝔽3) | C5×C22⋊C4 | semidirect |
| 232. C5 | #73151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C2×C5×#859 | 2 |
| C5×#1788 | 3 |
| C5×C3⋊#95 | 4 |
| #73151 | 5 |