Finite Group DatabasebetaFinite Group Databasebeta← C5×(C2×AGL(1,𝔽5))⋊Q8 #13104550
Order 1600.
391 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 7. C2×C52×Q8 | C4 | semidirect |
| 12. C2×C5×Dic10 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 16. (C2×AGL(1,𝔽5))⋊Q8 | C5 | direct (N × H) |
| 23. C2×C5×AGL(1,𝔽5) | Q8 | semidirect |
| 61. C2×C5×Q8 | C4×C5 | semidirect |
| 62. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 71. C2×Dic10 | C4×C5 | semidirect |
| 72. C2×Dic10 | C4×C5 | semidirect |
| 89. C2×AGL(1,𝔽5) | C5×Q8 | semidirect |
| 124. C52 | #391 | semidirect |
| 154. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 191. C5 | C5×#391 | semidirect |
| 192. C5 | (C2×AGL(1,𝔽5))⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| (C2×AGL(1,𝔽5))⋊Q8 | 5 |
| C5×#391 | 5 |