Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
824 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 222 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×C5×C22⋊D5 | C2 | semidirect |
| 2. C2×C52×C22⋊C4 | C2 | semidirect |
| 3. C5×#4076 | C2 | semidirect |
| 4. C5×#4032 | C2 | semidirect |
| 5. C5×#4028 | C2 | semidirect |
| 7. C23×C5×D5 | C22 | semidirect |
| 8. C22×C4×C52 | C22 | semidirect |
| 11. C2×C5×C22⋊D5 | C22 | semidirect |
| 12. C22×C5×Dic5 | C22 | semidirect |
| 13. C2×C5×D20 | C22 | semidirect |
| 14. C52×C22⋊C4 | C22 | semidirect |
| 15. C5×#685 | C22 | semidirect |
| 16. C5×C4⋊Dic5 | C22 | semidirect |
| 18. #65827 | C5 | direct (N × H) |
| 20. C23×C52 | D4 | semidirect |
| 34. C22×C22⋊D5 | C2×C5 | semidirect |
| 39. C2×C5×C22⋊C4 | D5 | semidirect |
| 40. C2×C5×C22⋊C4 | C2×C5 | semidirect |
| 41. #4076 | C2×C5 | semidirect |
| 42. #4032 | C2×C5 | semidirect |
| 43. #4028 | C2×C5 | semidirect |
| 59. C23×D5 | C22×C5 | semidirect |
| 66. C22×C4×C5 | C2×D5 | semidirect |
| 67. C22×C4×C5 | C22×C5 | semidirect |
| 70. C2×C22⋊D5 | C22×C5 | semidirect |
| 71. C22×Dic5 | C22×C5 | semidirect |
| 72. C2×D20 | C22×C5 | semidirect |
| 76. C5×C22⋊C4 | C2×D5 | semidirect |
| 77. C5×C22⋊C4 | C22×C5 | semidirect |
| 78. #685 | C22×C5 | semidirect |
| 79. C4⋊Dic5 | C22×C5 | semidirect |
| 95. C23×C5 | D20 | semidirect |
| 96. C23×C5 | C5×D4 | semidirect |
| 124. C2×C22⋊C4 | C5×D5 | semidirect |
| 125. C52 | #534 | semidirect |
| 162. C22×C4 | C2×C5×D5 | semidirect |
| 165. C22⋊C4 | C2×C5×D5 | semidirect |
| 184. C23 | C5×D20 | semidirect |
| 195. C5 | #65827 | direct (N × H) |
| 196. C5 | C5×#534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C22⋊D5 | 2 |
| C2×C52×C22⋊C4 | 2 |
| C5×#4076 | 2 |
| C5×#4032 | 2 |
| C5×#4028 | 2 |
| C5×#534 | 5 |
| #65827 | 5 |