Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 102 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. #65367 | C5 | direct (N × H) |
| 22. C5×#168 | Q8 | semidirect |
| 82. #168 | C5×Q8 | semidirect |
| 87. C52 | #500 | semidirect |
| 131. C5 | #65367 | direct (N × H) |
| 132. C5 | C5×#500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C5×#4015 | 2 |
| C5×#3939 | 2 |
| C4×C5×#168 | 2 |
| C5×#500 | 5 |
| #65367 | 5 |