Finite Group Databasebeta

← C2×C3×C72×C52⋊C3 #36348053

Subgroups — C2×C3×C72×C52⋊C3 #36348053

Order 22050.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×C52⋊C3C211yesmaximal, characteristic, direct product factor, Hall
2C2×C72×C52⋊C3C313yesmaximal, direct product factor
3C2×C3×C52×C72C311yesmaximal, characteristic, complemented
4C72×C52⋊C3C2×C313yesdirect product factor
5C3×C52×C72C2×C311yescharacteristic, complemented
6C2×C3×C7×C52⋊C3C718yesmaximal, direct product factor
7C2×C52×C72C3211yescharacteristic, complemented, Hall
8C3×C7×C52⋊C3C2×C718yesdirect product factor
9C2×C3×C5×C72—32no—
10C52×C72C2×C3211yescharacteristic, complemented, Hall
11C2×C3×C52×C7C3×C718yescomplemented
12C2×C7×C52⋊C3C3×C7124yesdirect product factor
13C2×C32×C72—251nomaximal, Hall
14C3×C5×C72—32no—
15C3×C52×C7C2×C3×C718yescomplemented
16C7×C52⋊C3C2×C3×C7124yesdirect product factor
17C2×C5×C72—32no—
18C2×C3×C52⋊C3C7211yescharacteristic, direct product factor, Hall
19C32×C72—251noHall
20C2×C52×C7C32×C718yescomplemented
21C2×C3×C72—253no—
22C2×C3×C72C52⋊C311yescharacteristic, direct product factor
23C5×C72—32no—
24C3×C52⋊C3C2×C7211yescharacteristic, direct product factor, Hall
25C2×C3×C5×C7—316no—
26C52×C7C2×C32×C718yescomplemented
27C2×C3×C52C3×C7211yescharacteristic, complemented
28C2×C52⋊C3C3×C7213yesdirect product factor
29C3×C72—253no—
30C3×C72C2×C52⋊C311yescharacteristic, direct product factor
31C2×C32×C7—258no—
32C3×C5×C7—316no—
33C2×C72C3×C52⋊C311yescharacteristic, direct product factor, Hall
34C3×C52C2×C3×C7211yescharacteristic, complemented
35C52⋊C3C2×C3×C7213yesdirect product factor
36C2×C5×C7—316no—
37C32×C7—258no—
38C2×C52C32×C7211yescharacteristic, complemented, Hall
39C72C2×C3×C52⋊C311yescharacteristic, direct product factor, Sylow
40C2×C3×C7—2524no—
41C2×C3×C7C7×C52⋊C318yesdirect product factor
42C5×C7—316no—
43C2×C3×C5—32no—
44C52C2×C32×C7211yescharacteristic, complemented, Sylow
45C3×C7—2524no—
46C3×C7C2×C7×C52⋊C318yesdirect product factor
47C2×C32—251noHall
48C3×C5—32no—
49C2×C7C3×C7×C52⋊C318yesdirect product factor
50C2×C5—32no—
51C32—251noSylow
52C7C2×C3×C7×C52⋊C318yesdirect product factor
53C2×C3—253no—
54C2×C3C72×C52⋊C311yescharacteristic, direct product factor
55C5—32no—
56C3—253no—
57C3C2×C72×C52⋊C311yescharacteristic, direct product factor
58C2C3×C72×C52⋊C311yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3×C72C52⋊C3
commutator, cosocle, hypocenterC52C2×C32×C72
FrattiniC1G
Fitting, socleC2×C3×C52×C72C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C72

Complements

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

NH ≅ G/Ntype
1. C3×C72×C52⋊C3C2direct (N × H)
2. C2×C72×C52⋊C3C3direct (N × H)
3. C2×C3×C52×C72C3semidirect
4. C72×C52⋊C3C2×C3direct (N × H)
5. C3×C52×C72C2×C3semidirect
6. C2×C3×C7×C52⋊C3C7direct (N × H)
7. C2×C52×C72C32semidirect
8. C3×C7×C52⋊C3C2×C7direct (N × H)
10. C52×C72C2×C32semidirect
11. C2×C3×C52×C7C3×C7semidirect
12. C2×C7×C52⋊C3C3×C7direct (N × H)
15. C3×C52×C7C2×C3×C7semidirect
16. C7×C52⋊C3C2×C3×C7direct (N × H)
18. C2×C3×C52⋊C3C72direct (N × H)
20. C2×C52×C7C32×C7semidirect
22. C2×C3×C72C52⋊C3direct (N × H)
24. C3×C52⋊C3C2×C72direct (N × H)
26. C52×C7C2×C32×C7semidirect
27. C2×C3×C52C3×C72semidirect
28. C2×C52⋊C3C3×C72direct (N × H)
30. C3×C72C2×C52⋊C3direct (N × H)
33. C2×C72C3×C52⋊C3direct (N × H)
34. C3×C52C2×C3×C72semidirect
35. C52⋊C3C2×C3×C72direct (N × H)
38. C2×C52C32×C72semidirect
39. C72C2×C3×C52⋊C3direct (N × H)
41. C2×C3×C7C7×C52⋊C3direct (N × H)
44. C52C2×C32×C72semidirect
46. C3×C7C2×C7×C52⋊C3direct (N × H)
49. C2×C7C3×C7×C52⋊C3direct (N × H)
52. C7C2×C3×C7×C52⋊C3direct (N × H)
54. C2×C3C72×C52⋊C3direct (N × H)
57. C3C2×C72×C52⋊C3direct (N × H)
58. C2C3×C72×C52⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C72×C52⋊C32
C2×C72×C52⋊C33
C2×C3×C52×C723
C2×C3×C7×C52⋊C37
C2×C32×C7225