Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 2. C22⋊#6034 | C2 | semidirect |
| 13. C23×C52 | C8 | semidirect |
| 61. C23×C5 | #170 | semidirect |
| 74. C52 | #323 | semidirect |
| 120. C23 | #6034 | semidirect |
| 128. C5 | #64933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1039 | 2 |
| C22⋊#6034 | 2 |
| #64933 | 5 |