Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
380 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 56 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×#5423 | C2 | semidirect |
| 6. C22×C5×SL(2,𝔽3) | C4 | semidirect |
| 9. #73154 | C5 | direct (N × H) |
| 21. #5423 | C2×C5 | semidirect |
| 45. C22×SL(2,𝔽3) | C4×C5 | semidirect |
| 199. C5 | #73154 | 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 |
| C5×#5423 | 2 |
| C5×#1796 | 3 |
| C5×#833 | 4 |
| #73154 | 5 |