Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
542 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 84 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×C4⋊GL(2,𝔽3) | C2 | semidirect |
| 3. C4×C5×GL(2,𝔽3) | C2 | semidirect |
| 9. #85430 | C5 | direct (N × H) |
| 10. C5×Q82 | D3 | semidirect |
| 23. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 24. C4⋊GL(2,𝔽3) | C2×C5 | semidirect |
| 25. C4×GL(2,𝔽3) | C2×C5 | semidirect |
| 47. C5×SL(2,𝔽3) | #41 | semidirect |
| 69. Q82 | C5×D3 | semidirect |
| 91. C5×Q8 | GL(2,𝔽3) | semidirect |
| 92. C5×Q8 | #239 | semidirect |
| 128. SL(2,𝔽3) | C5×#41 | semidirect |
| 169. Q8 | C5×GL(2,𝔽3) | semidirect |
| 170. Q8 | C5×#239 | semidirect |
| 186. C5 | #85430 | 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×C4⋊GL(2,𝔽3) | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×#3362 | 3 |
| C2×C5×#239 | 4 |
| #85430 | 5 |