Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11716889 | C2 | semidirect |
| 4. #11716888 | C2 | semidirect |
| 62. C5⋊D5 | #108 | semidirect |
| 90. C52 | C2×#108 | semidirect |
| 138. C5 | D5⋊#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717448 | 2 |
| C2×C8×C5⋊D5 | 2 |
| #11716889 | 2 |
| #11716888 | 2 |
| D5⋊#108 | 5 |