Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 14. C52×Q8 | C8 | semidirect |
| 59. C5×Q8 | #168 | semidirect |
| 60. C5×Q8 | #170 | semidirect |
| 80. C52 | Q8⋊C8 | semidirect |
| 118. Q8 | #6032 | semidirect |
| 127. C5 | Q8⋊#168 | semidirect |
| 128. C5 | Q8⋊#170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| Q8⋊#170 | 5 |
| Q8⋊#168 | 5 |