Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1556 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 1556 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C5 |
| Frattini, cosocle | C22×D4 | C23×C5 |
| prime radical | C2×C5×D42 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#353 | C2 | semidirect |
| 3. C2×C5×AΣL(1,𝔽16) | C2 | semidirect |
| 4. C5×#1889 | C2 | semidirect |
| 5. C5×#1887 | C2 | semidirect |
| 9. C5×D42 | C4 | semidirect |
| 14. C5×#518 | C22 | semidirect |
| 17. C2×C5×#100 | C22 | semidirect |
| 18. C2×C5×#99 | C22 | semidirect |
| 24. #12759 | C5 | direct (N × H) |
| 66. C2×#353 | C2×C5 | semidirect |
| 67. C2×AΣL(1,𝔽16) | C2×C5 | semidirect |
| 68. #1889 | C2×C5 | semidirect |
| 69. #1887 | C2×C5 | semidirect |
| 80. C24×C5 | C22⋊C4 | semidirect |
| 99. C2×C5×D4 | C22⋊C4 | semidirect |
| 124. C5×C22⋊C4 | C22⋊C4 | semidirect |
| 127. C42×C5 | C22⋊C4 | semidirect |
| 131. D42 | C4×C5 | semidirect |
| 136. #518 | C22×C5 | semidirect |
| 139. C2×#100 | C22×C5 | semidirect |
| 140. C2×#99 | C22×C5 | semidirect |
| 276. C24 | C5×C22⋊C4 | semidirect |
| 295. C2×D4 | C5×C22⋊C4 | semidirect |
| 320. C22⋊C4 | C5×C22⋊C4 | semidirect |
| 323. C42 | C5×C22⋊C4 | semidirect |
| 383. C5 | #12759 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D42 | 2 |
| C2×C5×#353 | 2 |
| C2×C5×AΣL(1,𝔽16) | 2 |
| C5×#1889 | 2 |
| C5×#1887 | 2 |
| #12759 | 5 |