Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
196 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 96 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 | #102 |
| commutator | C2×C8 | C2×C3×C4×C5 |
| Frattini, cosocle | C4×C8 | C22×C3×C5 |
| LCS | G ▷ C2×C8 ▷ C2×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×#1362 | C3 | direct (N × H) |
| 11. C3×#1362 | C5 | direct (N × H) |
| 35. #1362 | C3×C5 | direct (N × H) |
| 131. C3×C5 | #1362 | direct (N × H) |
| 155. C5 | C3×#1362 | direct (N × H) |
| 163. C3 | C5×#1362 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#494 | 2 |
| C3×C5×C4⋊C16 | 2 |
| C3×C5×#335 | 2 |
| C5×#1362 | 3 |
| C3×#1362 | 5 |