Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
352 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C3×C5 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C5 ◁ C3×C42×C5 ◁ C3×C4×C5×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C5×#2247 | C3 | direct (N × H) |
| 11. C3×#2247 | C5 | direct (N × H) |
| 32. #2247 | C3×C5 | direct (N × H) |
| 59. C3×C4×C5 | Q32 | semidirect |
| 94. C4×C5 | C3×Q32 | semidirect |
| 105. C3×C5 | #2247 | direct (N × H) |
| 108. C3×C4 | C5×Q32 | semidirect |
| 122. C5 | C3×#2247 | direct (N × H) |
| 125. C4 | C3×C5×Q32 | semidirect |
| 128. C3 | C5×#2247 | 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×Q32 | 2 |
| C3×C5×#494 | 2 |
| C3×C4×C5×C16 | 2 |
| C5×#2247 | 3 |
| C3×#2247 | 5 |