Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
112 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 48 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 | C2×D5×D7 |
| commutator, socle, prime radical, cosocle | C22×C5×C7 | C23 |
| Fitting | C2×C4×C5×C7 | C22 |
| hypercenter | C2×C4 | D5×D7 |
| hypocenter | C5×C7 | #125 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 56. C5×C7 | #125 | semidirect |
| 94. C7 | #4036 | semidirect |
| 95. C5 | #6452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Dic35 | 2 |
| C7×#683 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587858 | 2 |
| Dic7⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| #6452 | 5 |
| #4036 | 7 |