Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 222 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. C2×C42×C52 | C2 | semidirect |
| 3. C2×C5×#683 | C2 | semidirect |
| 4. C5×#4022 | C2 | direct (N × H) |
| 8. C42×C52 | C22 | semidirect |
| 10. C5×#683 | C22 | semidirect |
| 12. C2×#4022 | C5 | direct (N × H) |
| 24. C2×C42×C5 | D5 | semidirect |
| 25. C2×C42×C5 | C2×C5 | semidirect |
| 27. C2×#683 | C2×C5 | semidirect |
| 28. #4022 | C2×C5 | direct (N × H) |
| 45. C42×C5 | C2×D5 | semidirect |
| 46. C42×C5 | C22×C5 | semidirect |
| 48. #683 | C22×C5 | semidirect |
| 50. C2×C52 | #126 | semidirect |
| 73. C2×C42 | C5×D5 | semidirect |
| 74. C52 | C2×#126 | semidirect |
| 95. C42 | C2×C5×D5 | semidirect |
| 99. C2×C5 | #4022 | direct (N × H) |
| 100. C2×C5 | C5×#126 | semidirect |
| 112. C5 | C2×#4022 | direct (N × H) |
| 113. C5 | C2×C5×#126 | semidirect |
| 121. C2 | C5×#4022 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C52 | 2 |
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C5×#4022 | 2 |
| C2×C5×#126 | 5 |
| C2×#4022 | 5 |