Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×C4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×#700 | C2 | semidirect |
| 4. #4010 | C2 | direct (N × H) |
| 6. C2×C5×Q8 | C4 | semidirect |
| 9. #713 | C4 | semidirect |
| 12. C2×D20 | C4 | semidirect |
| 17. C4×AGL(1,𝔽5) | C22 | semidirect |
| 19. #700 | C22 | semidirect |
| 26. C5×Q8 | C2×C4 | semidirect |
| 33. D20 | C2×C4 | semidirect |
| 61. C2×Q8 | AGL(1,𝔽5) | semidirect |
| 72. C2×C5 | #104 | semidirect |
| 80. Q8 | C2×AGL(1,𝔽5) | semidirect |
| 97. C5 | C2×#104 | semidirect |
| 113. C2 | #4010 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#713 | 2 |
| C2×C4×AGL(1,𝔽5) | 2 |
| C2×#700 | 2 |
| #4010 | 2 |
| C2×#104 | 5 |