Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C5×#683 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 15. #87779 | C4 | semidirect |
| 31. C2×C5×Dic5 | C2×C4 | semidirect |
| 39. C2×#683 | D5 | semidirect |
| 51. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 115. C2×Dic5 | C4×D5 | semidirect |
| 123. C52 | #385 | semidirect |
| 198. C5 | #65278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6036 | 2 |
| C2×#87808 | 2 |
| C2×C5×#683 | 2 |
| C2×#87779 | 2 |
| #11716620 | 2 |
| #65278 | 5 |