Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
398 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
| 4. C5×C4⋊#226 | C2 | semidirect |
| 5. C5×#5388 | C2 | semidirect |
| 13. #85432 | C5 | direct (N × H) |
| 14. C5×Q82 | D3 | semidirect |
| 33. Q8×SL(2,𝔽3) | C2×C5 | semidirect |
| 36. C4⋊#226 | C2×C5 | semidirect |
| 37. #5388 | C2×C5 | semidirect |
| 106. Q82 | C5×D3 | semidirect |
| 267. C5 | #85432 | 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×#5395 | 2 |
| C4×C5×GL(2,𝔽3) | 2 |
| C5×C4⋊#226 | 2 |
| C5×#5388 | 2 |
| C5×#3369 | 3 |
| C5×#946 | 4 |
| #85432 | 5 |