Finite Group Databasebeta

← C22×C5×C7×C73⋊C3 #44501455

Subgroups — C22×C5×C7×C73⋊C3 #44501455

Order 30660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C7×C73⋊C3C213yesmaximal, direct product factor
2C22×C5×C7×C73C311yesmaximal, characteristic, complemented, Hall
3C5×C7×C73⋊C3C2211yescharacteristic, direct product factor, Hall
4C22×C7×C73⋊C3C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C7×C73C2×C313yescomplemented
6C22×C5×C73⋊C3C711yesmaximal, characteristic, direct product factor, Hall
7C2×C7×C73⋊C3C2×C513yesdirect product factor
8C5×C7×C73C22×C311yescharacteristic, complemented, Hall
9C2×C5×C73⋊C3C2×C713yesdirect product factor
10C22×C7×C73C3×C511yescharacteristic, complemented, Hall
11C7×C73⋊C3C22×C511yescharacteristic, direct product factor, Hall
12C22×C5×C73C3×C711yescharacteristic, complemented, Hall
13C5×C73⋊C3C22×C711yescharacteristic, direct product factor, Hall
14C2×C7×C73C2×C3×C513yescomplemented
15C22×C73⋊C3C5×C711yescharacteristic, direct product factor, Hall
16C2×C5×C73C2×C3×C713yescomplemented
17C7×C73C22×C3×C511yescharacteristic, complemented, Hall
18C2×C73⋊C3C2×C5×C713yesdirect product factor
19C22×C3×C5×C7—731nomaximal, Hall
20C5×C73C22×C3×C711yescharacteristic, complemented, Hall
21C22×C73C3×C5×C711yescharacteristic, complemented, Hall
22C73⋊C3C22×C5×C711yescharacteristic, direct product factor, Hall
23C2×C3×C5×C7—733no—
24C2×C73C2×C3×C5×C713yescomplemented
25C22×C5×C7C73⋊C311yescharacteristic, direct product factor, Hall
26C3×C5×C7—731noHall
27C22×C3×C7—731noHall
28C73C22×C3×C5×C711yescharacteristic, complemented, Sylow
29C2×C5×C7C2×C73⋊C313yesdirect product factor
30C22×C3×C5—731noHall
31C2×C3×C7—733no—
32C5×C7C22×C73⋊C311yescharacteristic, direct product factor, Hall
33C2×C3×C5—733no—
34C22×C7C5×C73⋊C311yescharacteristic, direct product factor, Hall
35C3×C7—731noHall
36C22×C5C7×C73⋊C311yescharacteristic, direct product factor, Hall
37C3×C5—731noHall
38C2×C7C2×C5×C73⋊C313yesdirect product factor
39C22×C3—731noHall
40C2×C5C2×C7×C73⋊C313yesdirect product factor
41C7C22×C5×C73⋊C311yescharacteristic, direct product factor, Sylow
42C2×C3—733no—
43C5C22×C7×C73⋊C311yescharacteristic, direct product factor, Sylow
44C22C5×C7×C73⋊C311yescharacteristic, direct product factor, Sylow
45C3—731noSylow
46C2C2×C5×C7×C73⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C5×C7C73⋊C3
commutator, cosocle, hypocenterC73C22×C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C73
UCSC1 ◁ C22×C5×C7

Complements

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

NH ≅ G/Ntype
1. C2×C5×C7×C73⋊C3C2direct (N × H)
2. C22×C5×C7×C73C3semidirect
3. C5×C7×C73⋊C3C22direct (N × H)
4. C22×C7×C73⋊C3C5direct (N × H)
5. C2×C5×C7×C73C2×C3semidirect
6. C22×C5×C73⋊C3C7direct (N × H)
7. C2×C7×C73⋊C3C2×C5direct (N × H)
8. C5×C7×C73C22×C3semidirect
9. C2×C5×C73⋊C3C2×C7direct (N × H)
10. C22×C7×C73C3×C5semidirect
11. C7×C73⋊C3C22×C5direct (N × H)
12. C22×C5×C73C3×C7semidirect
13. C5×C73⋊C3C22×C7direct (N × H)
14. C2×C7×C73C2×C3×C5semidirect
15. C22×C73⋊C3C5×C7direct (N × H)
16. C2×C5×C73C2×C3×C7semidirect
17. C7×C73C22×C3×C5semidirect
18. C2×C73⋊C3C2×C5×C7direct (N × H)
20. C5×C73C22×C3×C7semidirect
21. C22×C73C3×C5×C7semidirect
22. C73⋊C3C22×C5×C7direct (N × H)
24. C2×C73C2×C3×C5×C7semidirect
25. C22×C5×C7C73⋊C3direct (N × H)
28. C73C22×C3×C5×C7semidirect
29. C2×C5×C7C2×C73⋊C3direct (N × H)
32. C5×C7C22×C73⋊C3direct (N × H)
34. C22×C7C5×C73⋊C3direct (N × H)
36. C22×C5C7×C73⋊C3direct (N × H)
38. C2×C7C2×C5×C73⋊C3direct (N × H)
40. C2×C5C2×C7×C73⋊C3direct (N × H)
41. C7C22×C5×C73⋊C3direct (N × H)
43. C5C22×C7×C73⋊C3direct (N × H)
44. C22C5×C7×C73⋊C3direct (N × H)
46. C2C2×C5×C7×C73⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C7×C73⋊C32
C22×C5×C7×C733
C22×C7×C73⋊C35
C22×C5×C73⋊C37
C22×C3×C5×C773