Finite Group Databasebeta

← C22×C3×C52⋊(C31⋊C3) #42124978

Subgroups — C22×C3×C52⋊(C31⋊C3) #42124978

Order 27900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C52⋊(C31⋊C3)C213yesmaximal, direct product factor
2C22×C52⋊(C31⋊C3)C313yesmaximal, direct product factor
3C22×C3×C52×C31C311yesmaximal, characteristic, complemented
4C3×C52⋊(C31⋊C3)C2211yescharacteristic, direct product factor, Hall
5C2×C52⋊(C31⋊C3)C2×C319yesdirect product factor
6C2×C3×C52×C31C2×C313yescomplemented
7C22×C52×C31C3211yescharacteristic, complemented, Hall
8C52⋊(C31⋊C3)C22×C313yesdirect product factor
9C3×C52×C31C22×C311yescharacteristic, complemented
10C22×C3×C5×C31—32no—
11C2×C52×C31C2×C3213yescomplemented
12C22×C3×C31⋊C3—251nomaximal, Hall
13C2×C3×C5×C31—36no—
14C22×C3×C52⋊C3—311nomaximal, Hall
15C52×C31C22×C3211yescharacteristic, complemented, Hall
16C22×C5×C31—32no—
17C2×C3×C31⋊C3—253no—
18C3×C5×C31—32no—
19C2×C3×C52⋊C3—313no—
20C22×C3×C31C52⋊C311yescharacteristic, complemented
21C22×C31⋊C3—253no—
22C2×C5×C31—36no—
23C22×C3×C52C31⋊C311yescharacteristic, complemented
24C22×C52⋊C3—313no—
25C3×C31⋊C3—251noHall
26C3×C52⋊C3—311noHall
27C2×C3×C31C2×C52⋊C313yescomplemented
28C2×C31⋊C3—259no—
29C5×C31—32no—
30C2×C3×C52C2×C31⋊C313yescomplemented
31C2×C52⋊C3—319no—
32C22×C31C3×C52⋊C311yescharacteristic, complemented, Hall
33C22×C52C3×C31⋊C311yescharacteristic, complemented, Hall
34C3×C31C22×C52⋊C311yescharacteristic, complemented
35C31⋊C3—253no—
36C3×C52C22×C31⋊C311yescharacteristic, complemented
37C52⋊C3—313no—
38C2×C31C2×C3×C52⋊C313yescomplemented
39C22×C3×C5—32no—
40C2×C52C2×C3×C31⋊C313yescomplemented
41C22×C32—7751noHall
42C31C22×C3×C52⋊C311yescharacteristic, complemented, Sylow
43C2×C3×C5—36no—
44C52C22×C3×C31⋊C311yescharacteristic, complemented, Sylow
45C22×C5—32no—
46C2×C32—7753no—
47C3×C5—32no—
48C22×C3—7753no—
49C22×C3C52⋊(C31⋊C3)11yescharacteristic, direct product factor
50C2×C5—36no—
51C32—7751noSylow
52C2×C3—7759no—
53C2×C3C2×C52⋊(C31⋊C3)13yesdirect product factor
54C5—32no—
55C22C3×C52⋊(C31⋊C3)11yescharacteristic, direct product factor, Sylow
56C3—7753no—
57C3C22×C52⋊(C31⋊C3)11yescharacteristic, direct product factor
58C2C2×C3×C52⋊(C31⋊C3)13yesdirect product factor
subgroupG/H
center, hypercenterC22×C3C52⋊(C31⋊C3)
commutator, cosocle, hypocenterC52×C31C22×C32
FrattiniC1G
Fitting, socleC22×C3×C52×C31C3
LCSG ▷ C52×C31
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C52⋊(C31⋊C3)C2direct (N × H)
2. C22×C52⋊(C31⋊C3)C3direct (N × H)
3. C22×C3×C52×C31C3semidirect
4. C3×C52⋊(C31⋊C3)C22direct (N × H)
5. C2×C52⋊(C31⋊C3)C2×C3direct (N × H)
6. C2×C3×C52×C31C2×C3semidirect
7. C22×C52×C31C32semidirect
8. C52⋊(C31⋊C3)C22×C3direct (N × H)
9. C3×C52×C31C22×C3semidirect
11. C2×C52×C31C2×C32semidirect
15. C52×C31C22×C32semidirect
20. C22×C3×C31C52⋊C3semidirect
23. C22×C3×C52C31⋊C3semidirect
27. C2×C3×C31C2×C52⋊C3semidirect
30. C2×C3×C52C2×C31⋊C3semidirect
32. C22×C31C3×C52⋊C3semidirect
33. C22×C52C3×C31⋊C3semidirect
34. C3×C31C22×C52⋊C3semidirect
36. C3×C52C22×C31⋊C3semidirect
38. C2×C31C2×C3×C52⋊C3semidirect
40. C2×C52C2×C3×C31⋊C3semidirect
42. C31C22×C3×C52⋊C3semidirect
44. C52C22×C3×C31⋊C3semidirect
49. C22×C3C52⋊(C31⋊C3)direct (N × H)
53. C2×C3C2×C52⋊(C31⋊C3)direct (N × H)
55. C22C3×C52⋊(C31⋊C3)direct (N × H)
57. C3C22×C52⋊(C31⋊C3)direct (N × H)
58. C2C2×C3×C52⋊(C31⋊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×C52⋊(C31⋊C3)2
C22×C52⋊(C31⋊C3)3
C22×C3×C52×C313
C22×C3×C31⋊C325
C22×C3×C52⋊C331