Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
183 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 13. C2×C4×C52 | C8 | semidirect |
| 62. C2×C4×C5 | #168 | semidirect |
| 63. C2×C4×C5 | #170 | semidirect |
| 72. C52 | #324 | semidirect |
| 122. C2×C4 | #6032 | semidirect |
| 125. C5 | #64748 | semidirect |
| 126. C5 | #64913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊Dic5 | 2 |
| C22⋊#6032 | 2 |
| #64913 | 5 |
| #64748 | 5 |