Finite Group DatabasebetaFinite Group Databasebeta← C2×(C2×D7)⋊AGL(1,𝔽5) #11765327
Order 1120.
264 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 70 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. C22×C7⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C22×C7×AGL(1,𝔽5) | C2 | semidirect |
| 4. (C2×D7)⋊AGL(1,𝔽5) | C2 | direct (N × H) |
| 5. C22×D35 | C4 | semidirect |
| 7. C22×C5×D7 | C4 | semidirect |
| 10. C2×D5×D7 | C4 | semidirect |
| 13. C2×C7⋊AGL(1,𝔽5) | C22 | semidirect |
| 15. C2×C7×AGL(1,𝔽5) | C22 | semidirect |
| 20. C2×D35 | C2×C4 | semidirect |
| 26. C2×C5×D7 | C2×C4 | semidirect |
| 38. C22×AGL(1,𝔽5) | D7 | semidirect |
| 40. C2×C5×C7 | C22⋊C4 | semidirect |
| 44. C7×D5 | C22⋊C4 | semidirect |
| 53. C22×D7 | AGL(1,𝔽5) | semidirect |
| 68. C2×AGL(1,𝔽5) | C2×D7 | semidirect |
| 69. C5×C7 | C2×C22⋊C4 | semidirect |
| 82. C2×D7 | C2×AGL(1,𝔽5) | semidirect |
| 106. C2×C7 | C22⋊AGL(1,𝔽5) | semidirect |
| 111. C2×C5 | (C2×D7)⋊C4 | semidirect |
| 114. D5 | (C2×D7)⋊C4 | semidirect |
| 128. C7 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 129. C5 | C2×(C2×D7)⋊C4 | semidirect |
| 149. C2 | (C2×D7)⋊AGL(1,𝔽5) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D7 | 2 |
| C22×C7⋊AGL(1,𝔽5) | 2 |
| C22×C7×AGL(1,𝔽5) | 2 |
| (C2×D7)⋊AGL(1,𝔽5) | 2 |
| C2×(C2×D7)⋊C4 | 5 |
| C2×C22⋊AGL(1,𝔽5) | 7 |