Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C4⋊Q8 |
| 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 |
|---|---|---|
| 24. C5×Dic7 | Q8 | semidirect |
| 26. C7×Dic5 | Q8 | semidirect |
| 62. C5×C7 | C4⋊Q8 | semidirect |
| 71. Dic7 | Dic10 | semidirect |
| 79. Dic5 | Dic14 | semidirect |
| 102. C7 | #4034 | semidirect |
| 103. C5 | #6451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic70 | 2 |
| C2×#63308 | 2 |
| C7×#683 | 2 |
| C5×Dic7⋊C4 | 2 |
| #10587859 | 2 |
| Dic7⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| #6451 | 5 |
| #4034 | 7 |