Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C5×#3996 | C2 | semidirect |
| 4. C5×#3995 | C2 | semidirect |
| 15. D5⋊#108 | C5 | direct (N × H) |
| 33. #3996 | C2×C5 | semidirect |
| 34. #3995 | C2×C5 | semidirect |
| 70. C5×D5 | #108 | semidirect |
| 102. C52 | C2×#108 | semidirect |
| 141. D5 | C5×#108 | semidirect |
| 155. C5 | C2×C5×#108 | semidirect |
| 156. C5 | D5⋊#108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5⋊M16 | 2 |
| C2×C5×C8×D5 | 2 |
| C5×#3996 | 2 |
| C5×#3995 | 2 |
| D5⋊#108 | 5 |
| C2×C5×#108 | 5 |