Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C5×#674 | C2 | semidirect |
| 3. C5×#3990 | C2 | direct (N × H) |
| 9. C5×#674 | C22 | semidirect |
| 10. C2×#3990 | C5 | direct (N × H) |
| 22. C2×#674 | C2×C5 | semidirect |
| 23. #3990 | C2×C5 | direct (N × H) |
| 43. #674 | C22×C5 | semidirect |
| 46. C2×C52 | M32 | semidirect |
| 70. C52 | C2×M32 | semidirect |
| 95. C2×C5 | C5×M32 | semidirect |
| 96. C2×C5 | #3990 | direct (N × H) |
| 109. C5 | C2×C5×M32 | semidirect |
| 110. C5 | C2×#3990 | direct (N × H) |
| 118. C2 | C5×#3990 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| C2×C5×#674 | 2 |
| C5×#3990 | 2 |
| C2×#3990 | 5 |
| C2×C5×M32 | 5 |