Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 223 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 |
|---|---|---|
| 4. #11716745 | C2 | semidirect |
| 5. #11716744 | C2 | semidirect |
| 83. C5×D5 | #108 | semidirect |
| 118. C52 | C2×#108 | semidirect |
| 160. D5 | #3954 | semidirect |
| 175. C5 | C2×#3954 | semidirect |
| 176. C5 | D5⋊#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#681 | 2 |
| C5×D5⋊M16 | 2 |
| C2×D5×#168 | 2 |
| #11716745 | 2 |
| #11716744 | 2 |
| D5⋊#108 | 5 |
| C2×#3954 | 5 |