Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
206 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 40 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×#5391 | C2 | semidirect |
| 3. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 9. #73023 | C5 | direct (N × H) |
| 13. C5×C8×Q8 | D3 | semidirect |
| 23. #5391 | C2×C5 | semidirect |
| 24. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 68. C8×Q8 | C5×D3 | semidirect |
| 183. C5 | #73023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×#5391 | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#1678 | 3 |
| C5×#821 | 4 |
| #73023 | 5 |