Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
191 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11716841 | C2 | semidirect |
| 3. C5×#3998 | C2 | semidirect |
| 4. #11716748 | C2 | semidirect |
| 5. D5×#674 | C2 | semidirect |
| 13. #87763 | C22 | semidirect |
| 14. C5×#674 | C22 | semidirect |
| 32. #3998 | D5 | direct (N × H) |
| 62. #674 | C2×D5 | semidirect |
| 69. C5×D5 | M32 | semidirect |
| 100. C52 | C2×M32 | semidirect |
| 138. D5 | #3998 | direct (N × H) |
| 151. C5 | D5×M32 | semidirect |
| 152. C5 | C2×#3998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#168 | 2 |
| #11716841 | 2 |
| C5×#3998 | 2 |
| #11716748 | 2 |
| D5×#674 | 2 |
| C2×#3998 | 5 |
| D5×M32 | 5 |