Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
599 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 599 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 |
|---|---|---|
| 1. C22×D5×AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×(C2×AGL(1,𝔽5))⋊D5 | C2 | semidirect |
| 4. C2×(C2×AGL(1,𝔽5))⋊D5 | C2 | semidirect |
| 5. C2×(C2×AGL(1,𝔽5))⋊D5 | C2 | semidirect |
| 6. #11716849 | C2 | semidirect |
| 7. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 17. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 18. C2×C5×D20 | C4 | semidirect |
| 20. C2×#6038 | C4 | semidirect |
| 21. C2×#6038 | C4 | semidirect |
| 30. C22×C5⋊D5 | C2×C4 | semidirect |
| 32. C22×C5×D5 | C2×C4 | semidirect |
| 51. C2×#1042 | D4 | semidirect |
| 57. C2×C5×AGL(1,𝔽5) | D4 | semidirect |
| 59. C2×C4×C52 | C2×C4 | semidirect |
| 61. C2×C5×Dic5 | C2×C4 | semidirect |
| 78. (C2×AGL(1,𝔽5))⋊C4 | D5 | semidirect |
| 87. C2×C5⋊D5 | C22⋊C4 | semidirect |
| 93. C2×C5×D5 | C22⋊C4 | semidirect |
| 142. C2×D20 | AGL(1,𝔽5) | semidirect |
| 199. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 213. C2×AGL(1,𝔽5) | D20 | semidirect |
| 225. C2×C4×C5 | C4×D5 | semidirect |
| 226. C2×C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 235. C2×Dic5 | C4×D5 | semidirect |
| 252. C52 | #386 | semidirect |
| 307. C2×D5 | C22⋊AGL(1,𝔽5) | semidirect |
| 410. C2×C4 | D5×AGL(1,𝔽5) | semidirect |
| 412. C5 | #64954 | semidirect |
| 413. C5 | #65779 | 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×D5×D20 | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| #11716849 | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65779 | 5 |
| #64954 | 5 |