Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
330 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 1. C5×#4147 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C5×#4054 | C2 | semidirect |
| 4. C52×#101 | C2 | semidirect |
| 5. C5×#3957 | C2 | semidirect |
| 18. #65042 | C5 | direct (N × H) |
| 34. #4147 | C2×C5 | semidirect |
| 37. #4093 | C2×C5 | semidirect |
| 38. #4054 | C2×C5 | semidirect |
| 41. C5×#101 | D5 | semidirect |
| 42. C5×#101 | C2×C5 | semidirect |
| 43. #3957 | C2×C5 | semidirect |
| 117. #101 | C5×D5 | semidirect |
| 118. C52 | #454 | semidirect |
| 174. C5 | #65042 | direct (N × H) |
| 175. C5 | C5×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4147 | 2 |
| C5×#4093 | 2 |
| C5×#4054 | 2 |
| C52×#101 | 2 |
| C5×#3957 | 2 |
| C5×#454 | 5 |
| #65042 | 5 |