Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 2. M16×C5⋊D5 | C2 | semidirect |
| 3. #11716936 | C2 | semidirect |
| 4. C5×#3955 | C2 | semidirect |
| 5. #11716599 | C2 | semidirect |
| 14. C52×M16 | C22 | semidirect |
| 15. #87804 | C22 | semidirect |
| 18. C5×#681 | C22 | semidirect |
| 47. #3955 | D5 | semidirect |
| 72. C5×M16 | C2×D5 | semidirect |
| 75. #681 | C2×D5 | semidirect |
| 86. C5⋊D5 | #100 | semidirect |
| 124. C52 | C2×#100 | semidirect |
| 159. M16 | D52 | semidirect |
| 191. C5 | D5×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87877 | 2 |
| M16×C5⋊D5 | 2 |
| #11716936 | 2 |
| C5×#3955 | 2 |
| #11716599 | 2 |
| D5×#100 | 5 |