Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. C5×#3961 | C2 | direct (N × H) |
| 14. C2×#3961 | C5 | direct (N × H) |
| 31. #3961 | C2×C5 | direct (N × H) |
| 59. C2×C52 | Q32 | semidirect |
| 89. C52 | C2×Q32 | semidirect |
| 114. C2×C5 | #3961 | direct (N × H) |
| 115. C2×C5 | C5×Q32 | semidirect |
| 128. C5 | C2×#3961 | direct (N × H) |
| 129. C5 | C2×C5×Q32 | semidirect |
| 135. C2 | C5×#3961 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#3961 | 2 |
| C2×C5×#672 | 2 |
| C2×C5×Q32 | 5 |
| C2×#3961 | 5 |