Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 3. C5×#3994 | C2 | direct (N × H) |
| 8. C2×C52×C8 | C4 | semidirect |
| 9. C2×C5×#168 | C4 | semidirect |
| 10. C5×C8×D5 | C4 | semidirect |
| 12. C2×#3994 | C5 | direct (N × H) |
| 23. C52×C8 | C2×C4 | semidirect |
| 24. C5×#168 | C2×C4 | semidirect |
| 29. #3994 | C2×C5 | direct (N × H) |
| 51. C2×C5×C8 | C4×C5 | semidirect |
| 52. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 55. C2×#168 | C4×C5 | semidirect |
| 56. C8×D5 | C4×C5 | semidirect |
| 59. C2×C52 | #107 | semidirect |
| 61. C5×D5 | #107 | semidirect |
| 85. C5×C8 | C2×C4×C5 | semidirect |
| 86. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 87. #168 | C2×C4×C5 | semidirect |
| 91. C52 | C2×#107 | semidirect |
| 120. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 128. C2×C5 | C5×#107 | semidirect |
| 129. C2×C5 | #3994 | direct (N × H) |
| 132. D5 | C5×#107 | semidirect |
| 145. C8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 147. C5 | C2×C5×#107 | semidirect |
| 148. C5 | C2×#3994 | direct (N × H) |
| 162. C2 | C5×#3994 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×C8×D5 | 2 |
| C5×#3994 | 2 |
| C2×#3994 | 5 |
| C2×C5×#107 | 5 |