Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
280 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C5×#3954 | C2 | direct (N × H) |
| 16. C2×#3954 | C5 | direct (N × H) |
| 35. #3954 | C2×C5 | direct (N × H) |
| 71. C2×C52 | #108 | semidirect |
| 105. C52 | C2×#108 | semidirect |
| 148. C2×C5 | #3954 | direct (N × H) |
| 149. C2×C5 | C5×#108 | semidirect |
| 163. C5 | C2×#3954 | direct (N × H) |
| 164. C5 | C2×C5×#108 | semidirect |
| 175. C2 | C5×#3954 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C2×C5×#681 | 2 |
| C22×C5×#168 | 2 |
| C5×#3954 | 2 |
| C2×C5×#108 | 5 |
| C2×#3954 | 5 |