Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4130 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. C5×#4010 | C2 | semidirect |
| 5. C2×C52×Q8 | C4 | semidirect |
| 8. C5×#713 | C4 | semidirect |
| 11. C2×C5×D20 | C4 | semidirect |
| 17. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 18. C5×#700 | C22 | semidirect |
| 20. #65784 | C5 | direct (N × H) |
| 43. #4130 | C2×C5 | semidirect |
| 44. D5⋊M16 | C2×C5 | semidirect |
| 47. #4010 | C2×C5 | semidirect |
| 66. C2×C5×Q8 | C4×C5 | semidirect |
| 67. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 74. #713 | C4×C5 | semidirect |
| 77. C2×D20 | C4×C5 | semidirect |
| 83. C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 84. #700 | C22×C5 | semidirect |
| 144. C52 | #421 | semidirect |
| 177. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 220. C5 | C5×#421 | semidirect |
| 221. C5 | #65784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4010 | 2 |
| #65784 | 5 |
| C5×#421 | 5 |