Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C3×C4×C5 | C23 |
| commutator | C22 | C22×C3×C5×C8 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1839 | C3 | direct (N × H) |
| 8. C3×#1839 | C5 | direct (N × H) |
| 17. C3×C42×C5 | C8 | semidirect |
| 24. #1839 | C3×C5 | direct (N × H) |
| 44. C42×C5 | C3×C8 | semidirect |
| 59. C3×C42 | C5×C8 | semidirect |
| 97. C42 | C3×C5×C8 | semidirect |
| 98. C3×C5 | #1839 | direct (N × H) |
| 120. C5 | C3×#1839 | direct (N × H) |
| 127. C3 | C5×#1839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×C5 | 2 |
| C3×C5×#336 | 2 |
| C5×#1839 | 3 |
| C3×#1839 | 5 |