Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11716691 | C2 | semidirect |
| 34. C5×#100 | D5 | semidirect |
| 80. #100 | C5⋊D5 | semidirect |
| 81. C52 | #413 | semidirect |
| 120. C5 | #65034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| M16×C5⋊D5 | 2 |
| C52×#100 | 2 |
| #11716700 | 2 |
| #11716691 | 2 |
| #65034 | 5 |