Finite Group Databasebeta

← C22×C53×C72 #72201767

Subgroups — C22×C53×C72 #72201767

Order 24500.

3200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×C72C213yesmaximal, direct product factor
2C53×C72C2211yescharacteristic, direct product factor, Hall
3C22×C53×C7C718yesmaximal, direct product factor
4C22×C52×C72C5131yesmaximal, direct product factor
5C2×C52×C72C2×C5193yesdirect product factor
6C2×C53×C7C2×C7124yesdirect product factor
7C52×C72C22×C5131yesdirect product factor
8C22×C5×C72C52131yesdirect product factor
9C53×C7C22×C718yesdirect product factor
10C22×C52×C7C5×C71248yesdirect product factor
11C22×C53C7211yescharacteristic, direct product factor, Hall
12C2×C5×C72C2×C52193yesdirect product factor
13C2×C52×C7C2×C5×C71744yesdirect product factor
14C2×C53C2×C7213yesdirect product factor
15C5×C72C22×C52131yesdirect product factor
16C22×C72C5311yescharacteristic, direct product factor, Hall
17C52×C7C22×C5×C71248yesdirect product factor
18C22×C5×C7C52×C71248yesdirect product factor
19C53C22×C7211yescharacteristic, direct product factor, Sylow
20C22×C52C5×C72131yesdirect product factor
21C2×C72C2×C5313yesdirect product factor
22C2×C5×C7C2×C52×C71744yesdirect product factor
23C2×C52C2×C5×C72193yesdirect product factor
24C72C22×C5311yescharacteristic, direct product factor, Sylow
25C5×C7C22×C52×C71248yesdirect product factor
26C22×C7C53×C718yesdirect product factor
27C52C22×C5×C72131yesdirect product factor
28C22×C5C52×C72131yesdirect product factor
29C2×C7C2×C53×C7124yesdirect product factor
30C2×C5C2×C52×C72193yesdirect product factor
31C7C22×C53×C718yesdirect product factor
32C5C22×C52×C72131yesdirect product factor
33C22C53×C7211yescharacteristic, direct product factor, Sylow
34C2C2×C53×C7213yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C53×C72C2direct (N × H)
2. C53×C72C22direct (N × H)
3. C22×C53×C7C7direct (N × H)
4. C22×C52×C72C5direct (N × H)
5. C2×C52×C72C2×C5direct (N × H)
6. C2×C53×C7C2×C7direct (N × H)
7. C52×C72C22×C5direct (N × H)
8. C22×C5×C72C52direct (N × H)
9. C53×C7C22×C7direct (N × H)
10. C22×C52×C7C5×C7direct (N × H)
11. C22×C53C72direct (N × H)
12. C2×C5×C72C2×C52direct (N × H)
13. C2×C52×C7C2×C5×C7direct (N × H)
14. C2×C53C2×C72direct (N × H)
15. C5×C72C22×C52direct (N × H)
16. C22×C72C53direct (N × H)
17. C52×C7C22×C5×C7direct (N × H)
18. C22×C5×C7C52×C7direct (N × H)
19. C53C22×C72direct (N × H)
20. C22×C52C5×C72direct (N × H)
21. C2×C72C2×C53direct (N × H)
22. C2×C5×C7C2×C52×C7direct (N × H)
23. C2×C52C2×C5×C72direct (N × H)
24. C72C22×C53direct (N × H)
25. C5×C7C22×C52×C7direct (N × H)
26. C22×C7C53×C7direct (N × H)
27. C52C22×C5×C72direct (N × H)
28. C22×C5C52×C72direct (N × H)
29. C2×C7C2×C53×C7direct (N × H)
30. C2×C5C2×C52×C72direct (N × H)
31. C7C22×C53×C7direct (N × H)
32. C5C22×C52×C72direct (N × H)
33. C22C53×C72direct (N × H)
34. C2C2×C53×C72direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C53×C722
C22×C53×C77
C22×C52×C725