Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
390 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 88 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. Q8×#226 | C5 | direct (N × H) |
| 19. C5×#226 | Q8 | direct (N × H) |
| 78. #226 | C5×Q8 | direct (N × H) |
| 86. C5×Q8 | #226 | direct (N × H) |
| 153. Q8 | C5×#226 | direct (N × H) |
| 165. C5 | Q8×#226 | 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×#5391 | 2 |
| C4×C5×#226 | 2 |
| C5×Q8×Q16 | 3 |
| C5×Q8×Dic3 | 4 |
| Q8×#226 | 5 |