Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 210 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×C22⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. #3999 | C2 | direct (N × H) |
| 4. C23×D5 | C4 | semidirect |
| 7. C22×C4×C5 | C4 | semidirect |
| 10. C2×D20 | C4 | semidirect |
| 13. C22⋊AGL(1,𝔽5) | C22 | semidirect |
| 21. C22×D5 | C2×C4 | semidirect |
| 29. C2×C4×C5 | C2×C4 | semidirect |
| 58. C22×C4 | AGL(1,𝔽5) | semidirect |
| 63. C2×C5 | #99 | semidirect |
| 84. C2×C4 | C2×AGL(1,𝔽5) | semidirect |
| 85. C5 | C2×#99 | semidirect |
| 107. C2 | #3999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| C2×C22⋊AGL(1,𝔽5) | 2 |
| #3999 | 2 |
| C2×#99 | 5 |