Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
824 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #525 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87904 | C2 | semidirect |
| 2. C2×C4×D52 | C2 | semidirect |
| 3. C5×#4092 | C2 | semidirect |
| 4. #11717041 | C2 | semidirect |
| 5. #11717027 | C2 | semidirect |
| 6. #11717016 | C2 | semidirect |
| 7. #11716999 | C2 | semidirect |
| 8. #11716967 | C2 | semidirect |
| 10. C2×C52×Q8 | C22 | semidirect |
| 13. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 15. C2×C4×C5⋊D5 | C22 | semidirect |
| 22. C5×C4⋊Dic5 | C22 | semidirect |
| 23. C5×#683 | C22 | semidirect |
| 25. #87779 | C22 | semidirect |
| 26. Dic52 | C22 | semidirect |
| 40. C4×C5⋊D5 | D4 | semidirect |
| 51. #4092 | D5 | semidirect |
| 66. C2×C5×D5 | #41 | semidirect |
| 75. C2×C5×Q8 | C2×D5 | semidirect |
| 101. C4⋊Dic5 | C2×D5 | semidirect |
| 102. #683 | C2×D5 | semidirect |
| 154. C52 | #525 | semidirect |
| 173. C2×D5 | #713 | semidirect |
| 186. C2×Q8 | D52 | semidirect |
| 233. C5 | #65961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×C4×D52 | 2 |
| C5×#4092 | 2 |
| #11717041 | 2 |
| #11717027 | 2 |
| #11717016 | 2 |
| #11716999 | 2 |
| #11716967 | 2 |
| #65961 | 5 |