Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
766 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 91 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×C5×#859 | C2 | semidirect |
| 4. #11751610 | C2 | direct (N × H) |
| 8. C2×C5⋊GL(2,𝔽3) | C4 | semidirect |
| 10. Dic5×SL(2,𝔽3) | C22 | semidirect |
| 11. C5×#859 | C22 | semidirect |
| 13. C2×Q8×Dic5 | D3 | semidirect |
| 25. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. C5⋊GL(2,𝔽3) | C2×C4 | semidirect |
| 32. C2×#859 | D5 | semidirect |
| 40. Q8×Dic5 | C2×D3 | semidirect |
| 66. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 73. #859 | C2×D5 | semidirect |
| 77. C2×C5×Q8 | C4×D3 | semidirect |
| 127. C2×SL(2,𝔽3) | C4×D5 | semidirect |
| 138. C5×Q8 | C2×C4×D3 | semidirect |
| 147. C2×Dic5 | GL(2,𝔽3) | semidirect |
| 192. SL(2,𝔽3) | C2×C4×D5 | semidirect |
| 206. Dic5 | C2×GL(2,𝔽3) | semidirect |
| 210. C2×Q8 | #1200 | semidirect |
| 247. C2×C5 | C4×GL(2,𝔽3) | semidirect |
| 260. Q8 | C2×#1200 | semidirect |
| 282. C5 | C2×C4×GL(2,𝔽3) | semidirect |
| 299. C2 | #11751610 | 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×C5×#859 | 2 |
| #11751610 | 2 |
| C2×#65077 | 3 |
| C22×#1200 | 4 |
| C2×C4×GL(2,𝔽3) | 5 |