Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 312 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. C5×#3940 | C2 | semidirect |
| 5. #11716616 | C2 | semidirect |
| 15. #87769 | C4 | semidirect |
| 26. C5×#168 | C2×C4 | semidirect |
| 33. #3940 | D5 | semidirect |
| 85. #168 | C4×D5 | semidirect |
| 91. C52 | #428 | semidirect |
| 141. C5 | #65150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717212 | 2 |
| #11717018 | 2 |
| C2×#87769 | 2 |
| C5×#3940 | 2 |
| #11716616 | 2 |
| #65150 | 5 |