Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 88 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×#87849 | C2 | semidirect |
| 3. C2×C5×#700 | C2 | semidirect |
| 4. #11716754 | C2 | semidirect |
| 5. #11716753 | C2 | semidirect |
| 15. C2×#6032 | C22 | semidirect |
| 17. C2×C5×#170 | C22 | semidirect |
| 45. C2×#700 | D5 | semidirect |
| 55. C2×C5⋊D5 | M16 | semidirect |
| 61. C2×C5×D5 | M16 | semidirect |
| 88. C2×#170 | C2×D5 | semidirect |
| 153. C52 | #407 | semidirect |
| 179. C2×D5 | #700 | semidirect |
| 243. C5 | #65415 | semidirect |
| 244. C5 | #65756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×#87849 | 2 |
| C2×C5×#700 | 2 |
| #11716754 | 2 |
| #11716753 | 2 |
| #65756 | 5 |
| #65415 | 5 |