Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. C2×C4×#1039 | C2 | semidirect |
| 3. C2×C5×#683 | C2 | semidirect |
| 6. #11716620 | C2 | semidirect |
| 7. #11716620 | C2 | semidirect |
| 19. #87778 | C4 | semidirect |
| 55. C2×#683 | D5 | semidirect |
| 189. C52 | #388 | semidirect |
| 302. C5 | #65234 | semidirect |
| 303. C5 | #65279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C2×#87778 | 2 |
| #11716620 | 2 |
| #65279 | 5 |
| #65234 | 5 |