Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 102 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. C52×C4⋊Q8 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 13. #65374 | C5 | direct (N × H) |
| 21. C5×#168 | D4 | semidirect |
| 24. C5×C4⋊Q8 | D5 | semidirect |
| 25. C5×C4⋊Q8 | C2×C5 | semidirect |
| 27. C2×#688 | C2×C5 | semidirect |
| 30. C4×#168 | C2×C5 | semidirect |
| 35. C4×C52 | SD16 | semidirect |
| 77. #168 | C5×D4 | semidirect |
| 79. C4⋊Q8 | C5×D5 | semidirect |
| 82. C52 | #492 | semidirect |
| 95. C4×C5 | #688 | semidirect |
| 96. C4×C5 | C5×SD16 | semidirect |
| 123. C5 | #65374 | direct (N × H) |
| 124. C5 | C5×#492 | semidirect |
| 129. C4 | C5×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C2×C5×#688 | 2 |
| C5×#4020 | 2 |
| C4×C5×#168 | 2 |
| C5×#492 | 5 |
| #65374 | 5 |