Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
2582 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 2582 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C5 | C2×S4 |
| commutator, cosocle | C2×A4 | C24×C5 |
| Frattini | C2 | C23×C5×S4 |
| Fitting | C24×C4×C5 | D3 |
| socle | C25×C5 | C2×D3 |
| hypercenter | C22×C4×C5 | S4 |
| hypocenter | A4 | C22×C5×D4 |
| LCS | G ▷ C2×A4 ▷ A4 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C5×S4 | C2 | semidirect |
| 2. C22×C4×C5×A4 | C2 | semidirect |
| 3. C2×C5×C4⋊S4 | C2 | direct (N × H) |
| 7. C22×C5×S4 | C22 | semidirect |
| 9. C2×C4×C5×A4 | C22 | semidirect |
| 10. C5×C4⋊S4 | C22 | direct (N × H) |
| 11. C22×C4⋊S4 | C5 | direct (N × H) |
| 14. C24×C4×C5 | D3 | semidirect |
| 20. C22×C5×A4 | D4 | semidirect |
| 23. C2×C5×S4 | C23 | semidirect |
| 26. C4×C5×A4 | C23 | semidirect |
| 27. C23×S4 | C2×C5 | semidirect |
| 28. C22×C4×A4 | C2×C5 | semidirect |
| 29. C2×C4⋊S4 | C2×C5 | direct (N × H) |
| 44. C23×C4×C5 | C2×D3 | semidirect |
| 53. C2×C5×A4 | C2×D4 | semidirect |
| 60. C22×S4 | C22×C5 | semidirect |
| 62. C2×C4×A4 | C22×C5 | semidirect |
| 63. C4⋊S4 | C22×C5 | direct (N × H) |
| 72. C24×C5 | D12 | semidirect |
| 92. C22×C4×C5 | S4 | semidirect |
| 93. C22×C4×C5 | C22×D3 | semidirect |
| 98. C24×C4 | C5×D3 | semidirect |
| 107. C5×A4 | C22×D4 | semidirect |
| 110. C22×A4 | C5×D4 | semidirect |
| 113. C2×S4 | C23×C5 | semidirect |
| 116. C4×A4 | C23×C5 | semidirect |
| 133. C23×C5 | C2×D12 | semidirect |
| 148. C2×C4×C5 | C2×S4 | semidirect |
| 163. C23×C4 | C2×C5×D3 | semidirect |
| 174. C2×A4 | C2×C5×D4 | semidirect |
| 193. C22×C5 | C4⋊S4 | direct (N × H) |
| 194. C22×C5 | C22×D12 | semidirect |
| 198. C4×C5 | C22×S4 | semidirect |
| 207. C24 | C5×D12 | semidirect |
| 227. C22×C4 | C5×S4 | semidirect |
| 228. C22×C4 | C22×C5×D3 | semidirect |
| 236. A4 | C22×C5×D4 | semidirect |
| 242. C2×C5 | C2×C4⋊S4 | direct (N × H) |
| 260. C23 | C2×C5×D12 | semidirect |
| 275. C2×C4 | C2×C5×S4 | semidirect |
| 279. C5 | C22×C4⋊S4 | direct (N × H) |
| 294. C22 | C5×C4⋊S4 | direct (N × H) |
| 295. C22 | C22×C5×D12 | semidirect |
| 299. C4 | C22×C5×S4 | semidirect |
| 305. C2 | C2×C5×C4⋊S4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×S4 | 2 |
| C22×C4×C5×A4 | 2 |
| C2×C5×C4⋊S4 | 2 |
| C22×C5×#121 | 3 |
| C22×C5×D12 | 4 |
| C22×C4⋊S4 | 5 |