Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊#1042 | C2 | semidirect |
| 3. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. (C2×AGL(1,𝔽5))⋊Dic5 | C2 | semidirect |
| 9. C2×C4×C5⋊D5 | C4 | semidirect |
| 10. C2×C4×C5×D5 | C4 | semidirect |
| 12. C2×#6036 | C4 | semidirect |
| 13. C2×D5×Dic5 | C4 | semidirect |
| 53. C2×C4⋊AGL(1,𝔽5) | D5 | semidirect |
| 62. C2×C5⋊D5 | C4⋊C4 | semidirect |
| 65. C2×C5×D5 | C4⋊C4 | semidirect |
| 78. C4×C52 | C22⋊C4 | semidirect |
| 81. C5×Dic5 | C22⋊C4 | semidirect |
| 103. C2×C4×D5 | AGL(1,𝔽5) | semidirect |
| 184. C52 | #380 | semidirect |
| 216. C2×D5 | C4⋊AGL(1,𝔽5) | semidirect |
| 229. C4×C5 | #685 | semidirect |
| 230. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 236. Dic5 | #685 | semidirect |
| 301. C5 | #65276 | semidirect |
| 302. C5 | #65765 | semidirect |
| 325. C4 | (C2×AGL(1,𝔽5))⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D52 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| (C2×AGL(1,𝔽5))⋊Dic5 | 2 |
| #65765 | 5 |
| #65276 | 5 |