Finite Group Databasebeta

← C3×C72×(C5⋊D5)⋊C3 #36347947

Subgroups — C3×C72×(C5⋊D5)⋊C3 #36347947

Order 22050.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C72×C52⋊C3C211yesmaximal, characteristic, complemented, Hall
2C3×C72×C5⋊D5C311yesmaximal, characteristic, complemented
3C72×(C5⋊D5)⋊C3C313yesmaximal, direct product factor
4C72×C52⋊C3C2×C313yescomplemented
5C3×C52×C72C2×C311yescharacteristic, complemented
6C3×C7×(C5⋊D5)⋊C3C718yesmaximal, direct product factor
7C72×C5⋊D5C3211yescharacteristic, complemented, Hall
8C3×C7×C52⋊C3C2×C718yescomplemented
9C3×C72×D5—152no—
10C52×C72C2×C3211yescharacteristic, complemented, Hall
11C3×C7×C5⋊D5C3×C718yescomplemented
12C7×(C5⋊D5)⋊C3C3×C7124yesdirect product factor
13C2×C32×C72—251nomaximal, Hall
14C3×C5×C72—32no—
15C3×C52×C7C2×C3×C718yescomplemented
16C7×C52⋊C3C2×C3×C7124yescomplemented
17C72×D5—152no—
18C3×(C5⋊D5)⋊C3C7211yescharacteristic, direct product factor, Hall
19C32×C72—251noHall
20C7×C5⋊D5C32×C718yescomplemented
21C2×C3×C72—253no—
22C2×C3×C72—251no—
23C5×C72—32no—
24C3×C52⋊C3C2×C7211yescharacteristic, complemented, Hall
25C3×C7×D5—1516no—
26C52×C7C2×C32×C718yescomplemented
27C3×C5⋊D5C3×C7211yescharacteristic, complemented
28(C5⋊D5)⋊C3C3×C7213yesdirect product factor
29C3×C72—253no—
30C3×C72(C5⋊D5)⋊C311yescharacteristic, direct product factor
31C2×C32×C7—258no—
32C3×C5×C7—316no—
33C2×C72—251noHall
34C3×C52C2×C3×C7211yescharacteristic, complemented
35C52⋊C3C2×C3×C7213yescomplemented
36C7×D5—1516no—
37C32×C7—258no—
38C5⋊D5C32×C7211yescharacteristic, complemented, Hall
39C72C3×(C5⋊D5)⋊C311yescharacteristic, direct product factor, Sylow
40C2×C3×C7—2524no—
41C2×C3×C7—258no—
42C5×C7—316no—
43C3×D5—152no—
44C52C2×C32×C7211yescharacteristic, complemented, Sylow
45C3×C7—2524no—
46C3×C7C7×(C5⋊D5)⋊C318yesdirect product factor
47C2×C32—251noHall
48C3×C5—32no—
49C2×C7—258no—
50D5—152no—
51C32—251noSylow
52C7C3×C7×(C5⋊D5)⋊C318yesdirect product factor
53C2×C3—253no—
54C2×C3—251no—
55C5—32no—
56C3—253no—
57C3C72×(C5⋊D5)⋊C311yescharacteristic, direct product factor
58C2—251noSylow
subgroupG/H
center, hypercenterC3×C72(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C2×C32×C72
FrattiniC1G
Fitting, socleC3×C52×C72C2×C3
LCSG ▷ C52
UCSC1 ◁ C3×C72

Complements

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

NH ≅ G/Ntype
1. C3×C72×C52⋊C3C2semidirect
2. C3×C72×C5⋊D5C3semidirect
3. C72×(C5⋊D5)⋊C3C3direct (N × H)
4. C72×C52⋊C3C2×C3semidirect
5. C3×C52×C72C2×C3semidirect
6. C3×C7×(C5⋊D5)⋊C3C7direct (N × H)
7. C72×C5⋊D5C32semidirect
8. C3×C7×C52⋊C3C2×C7semidirect
10. C52×C72C2×C32semidirect
11. C3×C7×C5⋊D5C3×C7semidirect
12. C7×(C5⋊D5)⋊C3C3×C7direct (N × H)
15. C3×C52×C7C2×C3×C7semidirect
16. C7×C52⋊C3C2×C3×C7semidirect
18. C3×(C5⋊D5)⋊C3C72direct (N × H)
20. C7×C5⋊D5C32×C7semidirect
24. C3×C52⋊C3C2×C72semidirect
26. C52×C7C2×C32×C7semidirect
27. C3×C5⋊D5C3×C72semidirect
28. (C5⋊D5)⋊C3C3×C72direct (N × H)
30. C3×C72(C5⋊D5)⋊C3direct (N × H)
34. C3×C52C2×C3×C72semidirect
35. C52⋊C3C2×C3×C72semidirect
38. C5⋊D5C32×C72semidirect
39. C72C3×(C5⋊D5)⋊C3direct (N × H)
44. C52C2×C32×C72semidirect
46. C3×C7C7×(C5⋊D5)⋊C3direct (N × H)
52. C7C3×C7×(C5⋊D5)⋊C3direct (N × H)
57. C3C72×(C5⋊D5)⋊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
C3×C72×C5⋊D53
C72×(C5⋊D5)⋊C33
C3×C7×(C5⋊D5)⋊C37
C2×C32×C7225