Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
346 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 6. C5×A4⋊C8 | C4 | semidirect |
| 8. #73044 | C5 | direct (N × H) |
| 41. A4⋊C8 | C4×C5 | semidirect |
| 68. C5×A4 | #97 | semidirect |
| 121. C22×C5 | #803 | semidirect |
| 148. A4 | C5×#97 | semidirect |
| 177. C5 | #73044 | direct (N × H) |
| 185. C22 | C5×#803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×A4 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C5×#1749 | 3 |
| C5×#803 | 4 |
| #73044 | 5 |