Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
298 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 298 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. C5×D4×SL(2,𝔽3) | C2 | semidirect |
| 2. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×Q8×D8 | C3 | semidirect |
| 7. D8×SL(2,𝔽3) | C5 | direct (N × H) |
| 8. C5×D4×Q8 | C2×C3 | semidirect |
| 11. C5×C8×Q8 | C2×C3 | semidirect |
| 18. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 19. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 31. Q8×D8 | C3×C5 | semidirect |
| 36. C5×SL(2,𝔽3) | D8 | direct (N × H) |
| 47. C5×D8 | SL(2,𝔽3) | direct (N × H) |
| 55. D4×Q8 | C2×C3×C5 | semidirect |
| 58. C8×Q8 | C2×C3×C5 | semidirect |
| 75. C5×Q8 | C3×D8 | semidirect |
| 77. C5×D4 | C2×SL(2,𝔽3) | semidirect |
| 85. C5×C8 | C2×SL(2,𝔽3) | semidirect |
| 105. SL(2,𝔽3) | C5×D8 | direct (N × H) |
| 123. D8 | C5×SL(2,𝔽3) | direct (N × H) |
| 146. Q8 | C3×C5×D8 | semidirect |
| 148. D4 | C2×C5×SL(2,𝔽3) | semidirect |
| 156. C8 | C2×C5×SL(2,𝔽3) | semidirect |
| 161. C5 | D8×SL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×SL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×Q8×D8 | 3 |
| C2×C3×C5×D8 | 4 |
| D8×SL(2,𝔽3) | 5 |