Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C4⋊#674 | C2 | direct (N × H) |
| 29. C2×C4×C5 | C16 | semidirect |
| 53. C4×C5 | C2×C16 | semidirect |
| 68. C2×C5 | C4⋊C16 | semidirect |
| 74. C2×C4 | #674 | semidirect |
| 85. C5 | C2×C4⋊C16 | semidirect |
| 91. C4 | C2×#674 | semidirect |
| 95. C2 | C4⋊#674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#674 | 2 |
| C2×C4×#168 | 2 |
| C4⋊#674 | 2 |
| C2×C4⋊C16 | 5 |