Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
178 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 96 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. C5×#3998 | C2 | semidirect |
| 3. C2×C5×#674 | C2 | semidirect |
| 4. C5×#3990 | C2 | semidirect |
| 5. C5×D5⋊C16 | C2 | semidirect |
| 14. #65725 | C5 | direct (N × H) |
| 26. #3998 | C2×C5 | semidirect |
| 27. C2×#674 | C2×C5 | semidirect |
| 28. #3990 | C2×C5 | semidirect |
| 29. D5⋊C16 | C2×C5 | semidirect |
| 83. C52 | #504 | semidirect |
| 122. C5 | C5×#504 | semidirect |
| 123. C5 | #65725 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4053 | 2 |
| C5×#3998 | 2 |
| C2×C5×#674 | 2 |
| C5×#3990 | 2 |
| C5×D5⋊C16 | 2 |
| #65725 | 5 |
| C5×#504 | 5 |