Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
280 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 72 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 | semidirect |
| 5. #11716618 | C2 | semidirect |
| 35. #3954 | D5 | semidirect |
| 67. C5⋊D5 | #108 | semidirect |
| 95. C52 | C2×#108 | semidirect |
| 143. C5 | D5×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×C5⋊D5 | 2 |
| #11716936 | 2 |
| C2×#87767 | 2 |
| C5×#3954 | 2 |
| #11716618 | 2 |
| D5×#108 | 5 |