Finite Group Databasebeta

← C22×C3×C13⋊(C52⋊C3) #26043864

Subgroups — C22×C3×C13⋊(C52⋊C3) #26043864

Order 11700.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13⋊(C52⋊C3)C213yesmaximal, direct product factor
2C22×C13⋊(C52⋊C3)C313yesmaximal, direct product factor
3C22×C3×C52×C13C311yesmaximal, characteristic, complemented
4C3×C13⋊(C52⋊C3)C2211yescharacteristic, direct product factor, Hall
5C2×C3×C52×C13C2×C313yescomplemented
6C2×C13⋊(C52⋊C3)C2×C319yesdirect product factor
7C22×C52×C13C3211yescharacteristic, complemented, Hall
8C3×C52×C13C22×C311yescharacteristic, complemented
9C13⋊(C52⋊C3)C22×C313yesdirect product factor
10C22×C3×C52⋊C3—131nomaximal, Hall
11C22×C3×C5×C13—32no—
12C2×C52×C13C2×C3213yescomplemented
13C22×C3×C13⋊C3—251nomaximal, Hall
14C2×C3×C52⋊C3—133no—
15C2×C3×C5×C13—36no—
16C52×C13C22×C3211yescharacteristic, complemented, Hall
17C22×C3×C52C13⋊C311yescharacteristic, complemented
18C22×C52⋊C3—133no—
19C22×C5×C13—32no—
20C2×C3×C13⋊C3—253no—
21C3×C52⋊C3—131noHall
22C3×C5×C13—32no—
23C22×C3×C13C52⋊C311yescharacteristic, complemented
24C22×C13⋊C3—253no—
25C2×C3×C52C2×C13⋊C313yescomplemented
26C2×C52⋊C3—139no—
27C2×C5×C13—36no—
28C3×C13⋊C3—251noHall
29C22×C52C3×C13⋊C311yescharacteristic, complemented, Hall
30C2×C3×C13C2×C52⋊C313yescomplemented
31C2×C13⋊C3—259no—
32C3×C52C22×C13⋊C311yescharacteristic, complemented
33C52⋊C3—133no—
34C5×C13—32no—
35C22×C3×C5—32no—
36C22×C13C3×C52⋊C311yescharacteristic, complemented, Hall
37C2×C52C2×C3×C13⋊C313yescomplemented
38C3×C13C22×C52⋊C311yescharacteristic, complemented
39C13⋊C3—253no—
40C22×C32—3251noHall
41C2×C3×C5—36no—
42C2×C13C2×C3×C52⋊C313yescomplemented
43C52C22×C3×C13⋊C311yescharacteristic, complemented, Sylow
44C22×C5—32no—
45C2×C32—3253no—
46C3×C5—32no—
47C13C22×C3×C52⋊C311yescharacteristic, complemented, Sylow
48C22×C3—3253no—
49C22×C3C13⋊(C52⋊C3)11yescharacteristic, direct product factor
50C2×C5—36no—
51C32—3251noSylow
52C2×C3—3259no—
53C2×C3C2×C13⋊(C52⋊C3)13yesdirect product factor
54C5—32no—
55C22C3×C13⋊(C52⋊C3)11yescharacteristic, direct product factor, Sylow
56C3—3253no—
57C3C22×C13⋊(C52⋊C3)11yescharacteristic, direct product factor
58C2C2×C3×C13⋊(C52⋊C3)13yesdirect product factor
subgroupG/H
center, hypercenterC22×C3C13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C22×C32
FrattiniC1G
Fitting, socleC22×C3×C52×C13C3
LCSG ▷ C52×C13
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C13⋊(C52⋊C3)C2direct (N × H)
2. C22×C13⋊(C52⋊C3)C3direct (N × H)
3. C22×C3×C52×C13C3semidirect
4. C3×C13⋊(C52⋊C3)C22direct (N × H)
5. C2×C3×C52×C13C2×C3semidirect
6. C2×C13⋊(C52⋊C3)C2×C3direct (N × H)
7. C22×C52×C13C32semidirect
8. C3×C52×C13C22×C3semidirect
9. C13⋊(C52⋊C3)C22×C3direct (N × H)
12. C2×C52×C13C2×C32semidirect
16. C52×C13C22×C32semidirect
17. C22×C3×C52C13⋊C3semidirect
23. C22×C3×C13C52⋊C3semidirect
25. C2×C3×C52C2×C13⋊C3semidirect
29. C22×C52C3×C13⋊C3semidirect
30. C2×C3×C13C2×C52⋊C3semidirect
32. C3×C52C22×C13⋊C3semidirect
36. C22×C13C3×C52⋊C3semidirect
37. C2×C52C2×C3×C13⋊C3semidirect
38. C3×C13C22×C52⋊C3semidirect
42. C2×C13C2×C3×C52⋊C3semidirect
43. C52C22×C3×C13⋊C3semidirect
47. C13C22×C3×C52⋊C3semidirect
49. C22×C3C13⋊(C52⋊C3)direct (N × H)
53. C2×C3C2×C13⋊(C52⋊C3)direct (N × H)
55. C22C3×C13⋊(C52⋊C3)direct (N × H)
57. C3C22×C13⋊(C52⋊C3)direct (N × H)
58. C2C2×C3×C13⋊(C52⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C13⋊(C52⋊C3)2
C22×C13⋊(C52⋊C3)3
C22×C3×C52×C133
C22×C3×C52⋊C313
C22×C3×C13⋊C325