Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
602 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 602 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 |
|---|---|---|
| 2. C2×C5×A4⋊Q8 | C2 | semidirect |
| 3. C2×C5×C8×A4 | C2 | semidirect |
| 4. C5×#5401 | C2 | direct (N × H) |
| 12. C5×A4⋊Q8 | C22 | semidirect |
| 14. C5×C8×A4 | C22 | semidirect |
| 15. C2×#5401 | C5 | direct (N × H) |
| 17. C23×C5×C8 | D3 | semidirect |
| 36. C2×A4⋊Q8 | C2×C5 | semidirect |
| 37. C2×C8×A4 | C2×C5 | semidirect |
| 38. #5401 | C2×C5 | direct (N × H) |
| 50. C22×C5×C8 | C2×D3 | semidirect |
| 69. C2×C5×A4 | SD16 | semidirect |
| 85. A4⋊Q8 | C22×C5 | semidirect |
| 87. C8×A4 | C22×C5 | semidirect |
| 122. C2×C5×C8 | S4 | semidirect |
| 134. C23×C8 | C5×D3 | semidirect |
| 145. C5×A4 | C2×SD16 | semidirect |
| 167. C23×C5 | #204 | semidirect |
| 197. C5×C8 | C2×S4 | semidirect |
| 209. C22×C8 | C2×C5×D3 | semidirect |
| 230. C2×A4 | C5×SD16 | semidirect |
| 252. C22×C5 | C2×#204 | semidirect |
| 295. C2×C8 | C5×S4 | semidirect |
| 310. A4 | C2×C5×SD16 | semidirect |
| 318. C2×C5 | #5401 | direct (N × H) |
| 328. C23 | C5×#204 | semidirect |
| 358. C8 | C2×C5×S4 | semidirect |
| 362. C5 | C2×#5401 | direct (N × H) |
| 375. C22 | C2×C5×#204 | semidirect |
| 389. C2 | C5×#5401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊S4 | 2 |
| C2×C5×A4⋊Q8 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×#5401 | 2 |
| C2×C5×#465 | 3 |
| C2×C5×#204 | 4 |
| C2×#5401 | 5 |