Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D35 |
| commutator, socle, cosocle | C22×C5×C7 | C23 |
| Fitting, prime radical | C2×C5×C7×D4 | C2 |
| hypercenter | C2×D4 | D35 |
| hypocenter | C5×C7 | #123 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic35 | C2 | semidirect |
| 3. C22⋊Dic35 | C2 | semidirect |
| 4. C22⋊Dic35 | C2 | semidirect |
| 5. #10587900 | C2 | semidirect |
| 51. C5×C7 | #123 | semidirect |
| 89. C7 | #4081 | semidirect |
| 90. C5 | #6498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C7×D4 | 2 |
| C22×Dic35 | 2 |
| C22⋊Dic35 | 2 |
| #10587900 | 2 |
| #6498 | 5 |
| #4081 | 7 |