Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
744 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 125 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. C52×#100 | C2 | semidirect |
| 4. #11716700 | C2 | semidirect |
| 5. #11716690 | C2 | semidirect |
| 13. C52×M16 | C22 | semidirect |
| 14. #87804 | C22 | semidirect |
| 35. C5×#100 | D5 | semidirect |
| 57. C5×M16 | C2×D5 | semidirect |
| 67. C5⋊D5 | #100 | direct (N × H) |
| 87. #100 | C5⋊D5 | direct (N × H) |
| 88. C52 | C2×#100 | semidirect |
| 110. M16 | C2×C5⋊D5 | semidirect |
| 133. C5 | D5×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C5⋊D5 | 2 |
| M16×C5⋊D5 | 2 |
| C52×#100 | 2 |
| #11716700 | 2 |
| #11716690 | 2 |
| D5×#100 | 5 |