Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 328 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. C2×C5×#700 | C2 | semidirect |
| 4. C5×#4010 | C2 | semidirect |
| 5. C5×#4008 | C2 | semidirect |
| 6. C52×#41 | C4 | semidirect |
| 8. C5×Q8×D5 | C4 | semidirect |
| 12. C5×D4×D5 | C4 | semidirect |
| 14. C5×#709 | C4 | semidirect |
| 20. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 22. C5×#700 | C22 | semidirect |
| 23. #65795 | C5 | direct (N × H) |
| 52. #4130 | C2×C5 | semidirect |
| 53. C2×#700 | C2×C5 | semidirect |
| 56. #4010 | C2×C5 | semidirect |
| 57. #4008 | C2×C5 | semidirect |
| 80. C5×#41 | C4×C5 | semidirect |
| 81. C5×#41 | AGL(1,𝔽5) | semidirect |
| 88. Q8×D5 | C4×C5 | semidirect |
| 92. D4×D5 | C4×C5 | semidirect |
| 94. #709 | C4×C5 | semidirect |
| 100. C4×AGL(1,𝔽5) | C22×C5 | semidirect |
| 102. #700 | C22×C5 | semidirect |
| 176. C52 | #421 | semidirect |
| 215. #41 | C5×AGL(1,𝔽5) | semidirect |
| 268. C5 | C5×#421 | semidirect |
| 269. C5 | #65795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#41 | 2 |
| C5×#4130 | 2 |
| C2×C5×#700 | 2 |
| C5×#4010 | 2 |
| C5×#4008 | 2 |
| #65795 | 5 |
| C5×#421 | 5 |