Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
696 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
| 2. C5×D4×SL(2,𝔽3) | C2 | semidirect |
| 3. C2×C4×C5×SL(2,𝔽3) | C2 | semidirect |
| 4. C5×Q8×#41 | C3 | semidirect |
| 9. #41×SL(2,𝔽3) | C5 | direct (N × H) |
| 10. C5×Q82 | C2×C3 | semidirect |
| 13. C5×D4×Q8 | C2×C3 | semidirect |
| 16. C2×C4×C5×Q8 | C2×C3 | semidirect |
| 23. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 24. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 25. C2×C4×SL(2,𝔽3) | C2×C5 | semidirect |
| 45. Q8×#41 | C3×C5 | semidirect |
| 52. C5×SL(2,𝔽3) | #41 | direct (N × H) |
| 57. C5×#41 | SL(2,𝔽3) | direct (N × H) |
| 79. Q82 | C2×C3×C5 | semidirect |
| 82. D4×Q8 | C2×C3×C5 | semidirect |
| 85. C2×C4×Q8 | C2×C3×C5 | semidirect |
| 103. C5×Q8 | C2×SL(2,𝔽3) | semidirect |
| 104. C5×Q8 | C3×#41 | semidirect |
| 105. C5×D4 | C2×SL(2,𝔽3) | semidirect |
| 113. C2×C4×C5 | C2×SL(2,𝔽3) | semidirect |
| 145. SL(2,𝔽3) | C5×#41 | direct (N × H) |
| 157. #41 | C5×SL(2,𝔽3) | direct (N × H) |
| 195. Q8 | C2×C5×SL(2,𝔽3) | semidirect |
| 196. Q8 | C3×C5×#41 | semidirect |
| 197. D4 | C2×C5×SL(2,𝔽3) | semidirect |
| 205. C2×C4 | C2×C5×SL(2,𝔽3) | semidirect |
| 212. C5 | #41×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 |
| C2×C4×C5×SL(2,𝔽3) | 2 |
| C5×Q8×#41 | 3 |
| C2×C3×C5×#41 | 4 |
| #41×SL(2,𝔽3) | 5 |