Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
534 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. C5×#5398 | C2 | direct (N × H) |
| 11. C2×#5398 | C5 | direct (N × H) |
| 28. #5398 | C2×C5 | direct (N × H) |
| 49. C2×C5×A4 | Q16 | semidirect |
| 99. C5×A4 | C2×Q16 | semidirect |
| 113. C23×C5 | Dic12 | semidirect |
| 156. C2×A4 | C5×Q16 | semidirect |
| 170. C22×C5 | C2×Dic12 | semidirect |
| 209. A4 | C2×C5×Q16 | semidirect |
| 216. C2×C5 | #5398 | direct (N × H) |
| 221. C23 | C5×Dic12 | semidirect |
| 245. C5 | C2×#5398 | direct (N × H) |
| 253. C22 | C2×C5×Dic12 | semidirect |
| 265. C2 | C5×#5398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×A4⋊Q8 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×#5398 | 2 |
| C2×C5×#467 | 3 |
| C2×C5×Dic12 | 4 |
| C2×#5398 | 5 |