Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
472 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 4. C52×#107 | C2 | semidirect |
| 5. #11716684 | C2 | semidirect |
| 6. #11716675 | C2 | semidirect |
| 7. #11716674 | C2 | semidirect |
| 19. #87799 | C4 | semidirect |
| 31. C52×C8 | C2×C4 | semidirect |
| 32. #6029 | C2×C4 | semidirect |
| 36. C5×#107 | D5 | semidirect |
| 78. C5×C8 | C4×D5 | semidirect |
| 84. #107 | C5⋊D5 | semidirect |
| 87. C52 | #428 | semidirect |
| 126. C8 | C4×C5⋊D5 | semidirect |
| 127. C5 | #65170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| #11717212 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| C52×#107 | 2 |
| #11716684 | 2 |
| #11716675 | 2 |
| #11716674 | 2 |
| #65170 | 5 |