Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 3. C52×C22⋊C8 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3950 | C2 | semidirect |
| 16. #65025 | C5 | direct (N × H) |
| 31. C2×C4⋊Dic5 | C2×C5 | semidirect |
| 35. C5×C22⋊C8 | D5 | semidirect |
| 36. C5×C22⋊C8 | C2×C5 | semidirect |
| 37. #3953 | C2×C5 | semidirect |
| 38. #3950 | C2×C5 | semidirect |
| 107. C22⋊C8 | C5×D5 | semidirect |
| 108. C52 | #480 | semidirect |
| 172. C5 | #65025 | direct (N × H) |
| 173. C5 | C5×#480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4076 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3950 | 2 |
| C5×#480 | 5 |
| #65025 | 5 |