Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
464 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. C3×C5×#358 | C2 | semidirect |
| 5. #11746385 | C2 | semidirect |
| 6. #11746324 | C2 | semidirect |
| 7. #11746313 | C2 | semidirect |
| 13. Q16×D15 | C4 | semidirect |
| 27. C5×#358 | D3 | semidirect |
| 40. C3×C5×Q16 | C2×C4 | semidirect |
| 48. Dic60 | C2×C4 | semidirect |
| 56. C3×#358 | D5 | semidirect |
| 117. C5×Q16 | C4×D3 | semidirect |
| 136. #358 | D15 | direct (N × H) |
| 157. C3×Q16 | C4×D5 | semidirect |
| 206. D15 | #358 | direct (N × H) |
| 249. Q16 | C4×D15 | semidirect |
| 259. C3×C5 | C2×#358 | semidirect |
| 298. C5 | D3×#358 | semidirect |
| 310. C3 | D5×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D15 | 2 |
| C2×C16×D15 | 2 |
| D15×#107 | 2 |
| C3×C5×#358 | 2 |
| #11746385 | 2 |
| #11746324 | 2 |
| #11746313 | 2 |
| D5×#358 | 3 |
| D3×#358 | 5 |