Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
112 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #6452 | C5 | direct (N × H) |
| 56. C5×C7 | #125 | semidirect |
| 94. C7 | C5×#125 | semidirect |
| 95. C5 | #6452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×C4⋊C4 | 2 |
| C5×C4⋊Dic7 | 2 |
| C5×Dic7⋊C4 | 2 |
| C4×C5×Dic7 | 2 |
| #6452 | 5 |
| C5×#125 | 7 |