Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
270 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 270 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×Q8×SL(2,𝔽3) | C2 | semidirect |
| 3. C5×C8×SL(2,𝔽3) | C2 | semidirect |
| 4. C5×Q8×SD16 | C3 | semidirect |
| 9. SD16×SL(2,𝔽3) | C5 | direct (N × H) |
| 10. C5×Q82 | C2×C3 | semidirect |
| 15. C5×C8×Q8 | C2×C3 | semidirect |
| 23. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 25. C8×SL(2,𝔽3) | C2×C5 | semidirect |
| 42. Q8×SD16 | C3×C5 | semidirect |
| 50. C5×SL(2,𝔽3) | SD16 | direct (N × H) |
| 64. C5×SD16 | SL(2,𝔽3) | direct (N × H) |
| 76. Q82 | C2×C3×C5 | semidirect |
| 81. C8×Q8 | C2×C3×C5 | semidirect |
| 102. C5×Q8 | C3×SD16 | semidirect |
| 103. C5×Q8 | C2×SL(2,𝔽3) | semidirect |
| 115. C5×C8 | C2×SL(2,𝔽3) | semidirect |
| 143. SL(2,𝔽3) | C5×SD16 | direct (N × H) |
| 165. SD16 | C5×SL(2,𝔽3) | direct (N × H) |
| 195. Q8 | C3×C5×SD16 | semidirect |
| 196. Q8 | C2×C5×SL(2,𝔽3) | semidirect |
| 208. C8 | C2×C5×SL(2,𝔽3) | semidirect |
| 213. C5 | SD16×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×Q8×SL(2,𝔽3) | 2 |
| C5×D4×SL(2,𝔽3) | 2 |
| C5×C8×SL(2,𝔽3) | 2 |
| C5×Q8×SD16 | 3 |
| C2×C3×C5×SD16 | 4 |
| SD16×SL(2,𝔽3) | 5 |