Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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×D5⋊C8 | C2 | semidirect |
| 4. #4007 | C2 | direct (N × H) |
| 7. C2×C5×D4 | C4 | semidirect |
| 11. D4×D5 | C4 | semidirect |
| 13. C2×D20 | C4 | semidirect |
| 17. C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 19. D5⋊C8 | C22 | semidirect |
| 31. C5×D4 | C2×C4 | semidirect |
| 37. D20 | C2×C4 | semidirect |
| 71. C2×D4 | AGL(1,𝔽5) | semidirect |
| 80. C2×C5 | #102 | semidirect |
| 83. D5 | #102 | semidirect |
| 98. D4 | C2×AGL(1,𝔽5) | semidirect |
| 108. C5 | C2×#102 | semidirect |
| 131. C2 | #4007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| C2×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5⋊C8 | 2 |
| #4007 | 2 |
| C2×#102 | 5 |