Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11716619 | C2 | direct (N × H) |
| 51. C2×C52 | #108 | semidirect |
| 74. C52 | C2×#108 | semidirect |
| 104. C2×C5 | #3954 | semidirect |
| 116. C5 | C2×#3954 | semidirect |
| 127. C2 | #11716619 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6029 | 2 |
| C2×C5×#681 | 2 |
| #11716619 | 2 |
| C2×#3954 | 5 |