Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 79. C3×C5×C8 | Q16 | semidirect |
| 155. C5×C8 | #216 | semidirect |
| 185. C3×C8 | #689 | semidirect |
| 213. C3×C5 | #1723 | semidirect |
| 238. C8 | #6718 | semidirect |
| 242. C5 | #71367 | semidirect |
| 251. C3 | #10602160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| #11751194 | 2 |
| #11751193 | 2 |
| #11751180 | 2 |
| #11751179 | 2 |
| #11750781 | 2 |
| #11746276 | 2 |
| #10602160 | 3 |
| #71367 | 5 |