Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
312 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 13. #65381 | C5 | direct (N × H) |
| 32. C4×C52 | Q16 | semidirect |
| 77. C52 | #494 | semidirect |
| 87. C4×C5 | #689 | semidirect |
| 88. C4×C5 | C5×Q16 | semidirect |
| 113. C5 | #65381 | direct (N × H) |
| 114. C5 | C5×#494 | semidirect |
| 118. C4 | C5×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C2×C5×#689 | 2 |
| C5×#4015 | 2 |
| C4×C5×#168 | 2 |
| C5×#494 | 5 |
| #65381 | 5 |