Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 2. C3×C5×M64 | C2 | semidirect |
| 3. C3×#64719 | C2 | semidirect |
| 4. #10598093 | C3 | direct (N × H) |
| 14. C5×M64 | C2×C3 | semidirect |
| 15. #64719 | C2×C3 | semidirect |
| 26. C3×M64 | D5 | semidirect |
| 60. M64 | C3×D5 | semidirect |
| 115. C3×C5 | #1400 | semidirect |
| 136. C5 | C3×#1400 | semidirect |
| 143. C3 | #10598093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3930 | 2 |
| C3×C5×M64 | 2 |
| C3×#64719 | 2 |
| #10598093 | 3 |
| C3×#1400 | 5 |