Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
766 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 99 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×Dic5×SL(2,𝔽3) | C2 | semidirect |
| 3. C2×#91184 | C2 | semidirect |
| 4. Dic5×GL(2,𝔽3) | C2 | direct (N × H) |
| 8. C2×C5×GL(2,𝔽3) | C4 | semidirect |
| 10. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 11. #91184 | C22 | semidirect |
| 14. C2×Q8×Dic5 | D3 | semidirect |
| 25. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5×GL(2,𝔽3) | C2×C4 | semidirect |
| 44. Q8×Dic5 | C2×D3 | semidirect |
| 66. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 70. C2×GL(2,𝔽3) | Dic5 | direct (N × H) |
| 77. C2×C5×Q8 | C4×D3 | semidirect |
| 127. C2×SL(2,𝔽3) | C2×Dic5 | semidirect |
| 129. GL(2,𝔽3) | C2×Dic5 | direct (N × H) |
| 138. C5×Q8 | C2×C4×D3 | semidirect |
| 151. C2×Dic5 | GL(2,𝔽3) | direct (N × H) |
| 192. SL(2,𝔽3) | C22×Dic5 | semidirect |
| 206. Dic5 | C2×GL(2,𝔽3) | direct (N × H) |
| 210. C2×Q8 | D3×Dic5 | semidirect |
| 248. C2×C5 | C4×GL(2,𝔽3) | semidirect |
| 260. Q8 | C2×D3×Dic5 | semidirect |
| 282. C5 | C2×C4×GL(2,𝔽3) | semidirect |
| 299. C2 | Dic5×GL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×GL(2,𝔽3) | 2 |
| C2×Dic5×SL(2,𝔽3) | 2 |
| C2×#91184 | 2 |
| Dic5×GL(2,𝔽3) | 2 |
| C2×SD16×Dic5 | 3 |
| C22×D3×Dic5 | 4 |
| C2×C4×GL(2,𝔽3) | 5 |