Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
342 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 342 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. C2×C5×#681 | C2 | semidirect |
| 3. C2×#87767 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 5. #11716613 | C2 | semidirect |
| 6. #11716598 | C2 | semidirect |
| 7. #11716596 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 43. C2×#681 | D5 | semidirect |
| 47. C22⋊#168 | D5 | semidirect |
| 60. C2×C5⋊D5 | M16 | semidirect |
| 149. #168 | C22⋊D5 | semidirect |
| 157. C52 | #435 | semidirect |
| 242. C5 | #65017 | semidirect |
| 243. C5 | #65416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊(C5⋊D5) | 2 |
| C2×C5×#681 | 2 |
| C2×#87767 | 2 |
| C5×C22⋊#168 | 2 |
| #11716613 | 2 |
| #11716598 | 2 |
| #11716596 | 2 |
| #65416 | 5 |
| #65017 | 5 |