Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
284 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
| 4. C5×#3940 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 16. #65373 | C5 | direct (N × H) |
| 25. C5×D20 | Q8 | semidirect |
| 29. C5×C4⋊Q8 | D5 | semidirect |
| 30. C5×C4⋊Q8 | C2×C5 | semidirect |
| 37. #3940 | C2×C5 | semidirect |
| 38. C4⋊#168 | C2×C5 | semidirect |
| 99. D20 | C5×Q8 | semidirect |
| 103. C4⋊Q8 | C5×D5 | semidirect |
| 108. C52 | #476 | semidirect |
| 167. C5 | #65373 | direct (N × H) |
| 168. C5 | C5×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C4×C5×D20 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#476 | 5 |
| #65373 | 5 |