Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C5×#4016 | C2 | semidirect |
| 3. C52×#97 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 12. #65002 | C5 | direct (N × H) |
| 23. #4016 | C2×C5 | semidirect |
| 26. C5×#97 | D5 | semidirect |
| 27. C5×#97 | C2×C5 | semidirect |
| 28. #3953 | C2×C5 | semidirect |
| 73. #97 | C5×D5 | semidirect |
| 74. C52 | #490 | semidirect |
| 112. C5 | #65002 | direct (N × H) |
| 113. C5 | C5×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4020 | 2 |
| C5×#4016 | 2 |
| C52×#97 | 2 |
| C5×#3953 | 2 |
| C5×#490 | 5 |
| #65002 | 5 |