Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
262 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 44 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. C5×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 2. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 7. #73022 | C5 | direct (N × H) |
| 10. C5×C8×Q8 | D3 | semidirect |
| 18. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 19. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 34. C5×SL(2,𝔽3) | D8 | semidirect |
| 54. C8×Q8 | C5×D3 | semidirect |
| 70. C5×Q8 | D24 | semidirect |
| 81. C5×C8 | GL(2,𝔽3) | semidirect |
| 99. SL(2,𝔽3) | C5×D8 | semidirect |
| 136. Q8 | C5×D24 | semidirect |
| 147. C8 | C5×GL(2,𝔽3) | semidirect |
| 152. C5 | #73022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C4⋊GL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×#1668 | 3 |
| C2×C5×D24 | 4 |
| #73022 | 5 |