Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 9. Q8×#170 | C5 | direct (N × H) |
| 11. C52×Q8 | C8 | semidirect |
| 16. C5×#170 | Q8 | direct (N × H) |
| 44. C5×Q8 | C5×C8 | semidirect |
| 45. C5×Q8 | #170 | direct (N × H) |
| 54. #170 | C5×Q8 | direct (N × H) |
| 60. C52 | C8×Q8 | semidirect |
| 87. Q8 | C5×#170 | direct (N × H) |
| 94. C5 | C5×C8×Q8 | semidirect |
| 95. C5 | Q8×#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×Dic5 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| Q8×#170 | 5 |
| C5×C8×Q8 | 5 |