Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
214 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 1. C22×#3928 | C2 | semidirect |
| 3. C22⋊#3928 | C2 | semidirect |
| 4. C4⋊#3928 | C2 | semidirect |
| 5. C4×#3928 | C2 | semidirect |
| 28. #3928 | D4 | direct (N × H) |
| 58. C5×D4 | C32 | semidirect |
| 84. C22×C5 | C2×C32 | semidirect |
| 88. C4×C5 | C2×C32 | semidirect |
| 110. D4 | #3928 | direct (N × H) |
| 121. C5 | D4×C32 | semidirect |
| 124. C22 | C2×#3928 | semidirect |
| 128. C4 | C2×#3928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3928 | 2 |
| D4×#672 | 2 |
| C22⋊#3928 | 2 |
| C4⋊#3928 | 2 |
| C4×#3928 | 2 |
| D4×C32 | 5 |