Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
384 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 16. #71362 | C5 | direct (N × H) |
| 55. C3×C5×C8 | Q16 | semidirect |
| 57. C5×C3⋊C8 | Q16 | semidirect |
| 109. C5×C8 | #216 | semidirect |
| 129. C3×C8 | C5×Q16 | semidirect |
| 131. C3⋊C8 | C5×Q16 | semidirect |
| 149. C3×C5 | #1713 | semidirect |
| 168. C8 | C5×#216 | semidirect |
| 172. C5 | #71362 | direct (N × H) |
| 179. C3 | C5×#1713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C5×#5092 | 2 |
| C5×#5078 | 2 |
| C5×#4682 | 2 |
| C5×C8×C3⋊C8 | 2 |
| C5×#1713 | 3 |
| #71362 | 5 |