Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
840 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 125 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. C22⋊C4×C5⋊D5 | C2 | semidirect |
| 3. C52×#99 | C2 | semidirect |
| 4. #11716701 | C2 | semidirect |
| 5. #11716673 | C2 | semidirect |
| 6. C23×C5⋊D5 | C4 | semidirect |
| 9. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 13. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 15. C2×C4×C5⋊D5 | C4 | semidirect |
| 16. C52×C22⋊C4 | C22 | semidirect |
| 17. C22⋊#1039 | C22 | semidirect |
| 20. C23×C52 | C2×C4 | semidirect |
| 28. C22×C5⋊D5 | C2×C4 | semidirect |
| 33. C2×C4×C52 | C2×C4 | semidirect |
| 37. C2×#1039 | C2×C4 | semidirect |
| 44. C5×#99 | D5 | semidirect |
| 77. C5×C22⋊C4 | C2×D5 | semidirect |
| 88. C5⋊D5 | #99 | direct (N × H) |
| 89. C23×C5 | C4×D5 | semidirect |
| 102. C2×C4×C5 | C4×D5 | semidirect |
| 115. #99 | C5⋊D5 | direct (N × H) |
| 116. C52 | C2×#99 | semidirect |
| 149. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 167. C23 | C4×C5⋊D5 | semidirect |
| 179. C2×C4 | C4×C5⋊D5 | semidirect |
| 180. C5 | D5×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C5⋊D5 | 2 |
| C22⋊C4×C5⋊D5 | 2 |
| C52×#99 | 2 |
| #11716701 | 2 |
| #11716673 | 2 |
| D5×#99 | 5 |