Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
308 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 308 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×#3967 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 17. #65372 | C5 | direct (N × H) |
| 32. C5×C4⋊Q8 | D5 | semidirect |
| 33. C5×C4⋊Q8 | C2×C5 | semidirect |
| 39. #3967 | C2×C5 | semidirect |
| 40. C4⋊#168 | C2×C5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 111. C4⋊Q8 | C5×D5 | semidirect |
| 115. C52 | #461 | semidirect |
| 135. C4×C5 | #688 | semidirect |
| 136. C4×C5 | C5×SD16 | semidirect |
| 176. C5 | #65372 | direct (N × H) |
| 177. C5 | C5×#461 | semidirect |
| 185. 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 |
| C4×C5×D20 | 2 |
| C5×#3967 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#461 | 5 |
| #65372 | 5 |