Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 304 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 304 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 | C23 | C22×C3×C4×C5 |
| Frattini, cosocle | C22×C4 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C22×C4 |
| LCS | G ▷ C23 ▷ 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×#1843 | C3 | direct (N × H) |
| 8. C3×#1843 | C5 | direct (N × H) |
| 22. #1843 | C3×C5 | direct (N × H) |
| 78. C3×C5 | #1843 | direct (N × H) |
| 94. C5 | C3×#1843 | direct (N × H) |
| 100. C3 | C5×#1843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×C4⋊C8 | 2 |
| C3×C5×#376 | 2 |
| C5×#1843 | 3 |
| C3×#1843 | 5 |