Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
338 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 102 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×D5×M16 | C2 | semidirect |
| 3. C52×#101 | C2 | semidirect |
| 4. C5×#3968 | C2 | semidirect |
| 5. C5×#3955 | C2 | semidirect |
| 18. #65040 | C5 | direct (N × H) |
| 36. D5×M16 | C2×C5 | semidirect |
| 39. C5×#101 | D5 | semidirect |
| 40. C5×#101 | C2×C5 | semidirect |
| 42. #3968 | C2×C5 | semidirect |
| 43. #3955 | C2×C5 | semidirect |
| 117. #101 | C5×D5 | semidirect |
| 119. C52 | #413 | semidirect |
| 177. C5 | #65040 | direct (N × H) |
| 178. C5 | C5×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C5×D5×M16 | 2 |
| C52×#101 | 2 |
| C5×#3968 | 2 |
| C5×#3955 | 2 |
| C5×#413 | 5 |
| #65040 | 5 |