Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
614 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C2×C5×#986 | C2 | semidirect |
| 2. C5×C4⋊(#41⋊C3) | C2 | semidirect |
| 3. C5×#5427 | C2 | semidirect |
| 4. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 5. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 7. C2×C5×#41⋊C3 | C22 | semidirect |
| 10. C2×C5×GL(2,𝔽3) | C22 | semidirect |
| 12. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 13. C5×#859 | C22 | semidirect |
| 14. #85410 | C5 | direct (N × H) |
| 16. C5×#550 | D3 | semidirect |
| 32. C5×GL(2,𝔽3) | D4 | semidirect |
| 35. C2×#986 | C2×C5 | semidirect |
| 36. C4⋊(#41⋊C3) | C2×C5 | semidirect |
| 37. #5427 | C2×C5 | semidirect |
| 38. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 39. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 77. C5×SL(2,𝔽3) | C2×D4 | semidirect |
| 78. C2×#41⋊C3 | C22×C5 | semidirect |
| 81. C2×GL(2,𝔽3) | C22×C5 | semidirect |
| 83. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 84. #859 | C22×C5 | semidirect |
| 122. #550 | C5×D3 | semidirect |
| 148. GL(2,𝔽3) | C5×D4 | semidirect |
| 223. SL(2,𝔽3) | C2×C5×D4 | semidirect |
| 240. C4×C5 | #986 | semidirect |
| 330. C5 | #85410 | direct (N × H) |
| 347. C4 | C5×#986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#986 | 2 |
| C5×C4⋊(#41⋊C3) | 2 |
| C5×#5427 | 2 |
| C5×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#3274 | 3 |
| C5×#895 | 4 |
| #85410 | 5 |