Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 1. C2×C5×#677 | C2 | semidirect |
| 3. C5×#4015 | C2 | semidirect |
| 4. C4×C52×C8 | C2 | semidirect |
| 13. #64982 | C5 | direct (N × H) |
| 21. C52×C8 | D4 | semidirect |
| 25. C2×#677 | C2×C5 | semidirect |
| 27. #4015 | C2×C5 | semidirect |
| 29. C4×C5×C8 | D5 | semidirect |
| 30. C4×C5×C8 | C2×C5 | semidirect |
| 34. C4×C52 | SD16 | semidirect |
| 74. C5×C8 | D20 | semidirect |
| 75. C5×C8 | C5×D4 | semidirect |
| 79. C4×C8 | C5×D5 | semidirect |
| 80. C52 | #492 | semidirect |
| 91. C4×C5 | #677 | semidirect |
| 92. C4×C5 | C5×SD16 | semidirect |
| 118. C8 | C5×D20 | semidirect |
| 120. C5 | #64982 | direct (N × H) |
| 121. C5 | C5×#492 | semidirect |
| 126. C4 | C5×#677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#677 | 2 |
| C5×#4020 | 2 |
| C5×#4015 | 2 |
| C4×C52×C8 | 2 |
| C5×#492 | 5 |
| #64982 | 5 |