Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
392 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 9. #85428 | C5 | direct (N × H) |
| 85. C5×Q8 | #226 | semidirect |
| 151. Q8 | C5×#226 | semidirect |
| 163. C5 | #85428 | 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⋊#226 | 2 |
| C4×C5×#226 | 2 |
| C5×#3363 | 3 |
| C5×Q8×Dic3 | 4 |
| #85428 | 5 |