Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
718 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 718 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 |
|---|---|---|
| 2. D5⋊GU(2,𝔽3) | C2 | direct (N × H) |
| 3. C2×#91885 | C2 | semidirect |
| 5. C2×C5×#41⋊C3 | C4 | semidirect |
| 7. D5×#41⋊C3 | C4 | semidirect |
| 9. C2×D5×SL(2,𝔽3) | C4 | semidirect |
| 11. #91885 | C22 | semidirect |
| 21. C5×#41⋊C3 | C2×C4 | semidirect |
| 22. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. D5×SL(2,𝔽3) | C2×C4 | semidirect |
| 26. C5⋊(#41⋊C3) | C2×C4 | semidirect |
| 61. C5×SL(2,𝔽3) | C22×C4 | semidirect |
| 66. C2×#41⋊C3 | AGL(1,𝔽5) | semidirect |
| 131. #41⋊C3 | C2×AGL(1,𝔽5) | semidirect |
| 133. C2×SL(2,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 207. SL(2,𝔽3) | C22×AGL(1,𝔽5) | semidirect |
| 217. C2×D5 | GU(2,𝔽3) | semidirect |
| 279. C2×C5 | C2×GU(2,𝔽3) | semidirect |
| 283. D5 | C2×GU(2,𝔽3) | semidirect |
| 326. C5 | C22×GU(2,𝔽3) | semidirect |
| 349. C2 | D5⋊GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#41⋊C3 | 2 |
| D5⋊GU(2,𝔽3) | 2 |
| C2×#91885 | 2 |
| C2×D5⋊#104 | 3 |
| C2×D5⋊(C3⋊C8) | 4 |
| C22×GU(2,𝔽3) | 5 |