Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
485 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 94 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×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×#87825 | C2 | semidirect |
| 6. #11716849 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽5))⋊Dic5 | C2 | semidirect |
| 21. #87808 | C4 | semidirect |
| 22. C5×#685 | C4 | semidirect |
| 23. #87779 | C4 | semidirect |
| 24. #87778 | C4 | semidirect |
| 49. C2×C4×C52 | C2×C4 | semidirect |
| 50. C2×#1039 | C2×C4 | semidirect |
| 51. C2×C5×Dic5 | C2×C4 | semidirect |
| 52. C2×C5×Dic5 | C2×C4 | semidirect |
| 61. C2×C4⋊AGL(1,𝔽5) | D5 | semidirect |
| 74. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 77. C2×C5×D5 | C4⋊C4 | semidirect |
| 129. #685 | AGL(1,𝔽5) | semidirect |
| 184. C2×C4×C5 | C4×D5 | semidirect |
| 185. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 197. C2×Dic5 | C4×D5 | semidirect |
| 198. C2×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 211. C52 | #385 | semidirect |
| 243. C2×D5 | C4⋊AGL(1,𝔽5) | semidirect |
| 336. C2×C4 | D5×AGL(1,𝔽5) | semidirect |
| 338. C5 | #65278 | semidirect |
| 339. C5 | #65699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×AGL(1,𝔽5) | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×#87825 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| D5×#685 | 2 |
| #11716849 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65699 | 5 |
| #65278 | 5 |