Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 3. C4×#6045 | C2 | semidirect |
| 4. C4×C52×C8 | C2 | semidirect |
| 6. #11716684 | C2 | semidirect |
| 7. #11716683 | C2 | semidirect |
| 19. #87800 | C4 | direct (N × H) |
| 32. #6045 | C2×C4 | semidirect |
| 34. C52×C8 | C2×C4 | semidirect |
| 38. C4×C5×C8 | D5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 83. C5×C8 | C4×D5 | semidirect |
| 90. C4×C8 | C5⋊D5 | semidirect |
| 91. C52 | C4×SD16 | semidirect |
| 97. C4×C5 | #677 | semidirect |
| 132. C8 | C4×C5⋊D5 | semidirect |
| 133. C5 | C4×#677 | semidirect |
| 142. C4 | #87800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C4×#6045 | 2 |
| C4×C52×C8 | 2 |
| #11716688 | 2 |
| #11716684 | 2 |
| #11716683 | 2 |
| C4×#677 | 5 |