Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×D7 |
| commutator, socle | C2×C5×C7 | C22×C4 |
| Frattini | C4 | C2×D5×D7 |
| Fitting | C5×C7×C8 | C22 |
| prime radical | #10587944 | C2 |
| cosocle | C4×C5×C7 | C23 |
| hypocenter | C5×C7 | #131 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×D35 | C2 | semidirect |
| 3. C7×C8×D5 | C2 | semidirect |
| 4. C5×C8×D7 | C2 | semidirect |
| 5. #10587840 | C2 | semidirect |
| 6. #10587839 | C2 | semidirect |
| 7. #10587838 | C2 | semidirect |
| 34. C8×D7 | D5 | semidirect |
| 41. C8×D5 | D7 | semidirect |
| 68. C5×C7 | #131 | semidirect |
| 110. C7 | #4047 | semidirect |
| 111. C5 | #6464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587944 | 2 |
| C8×D35 | 2 |
| C7×C8×D5 | 2 |
| C5×C8×D7 | 2 |
| #10587840 | 2 |
| #10587839 | 2 |
| #10587838 | 2 |
| #6464 | 5 |
| #4047 | 7 |