Finite Group Databasebeta

← C22×C3×C31×C52⋊C3 #42124977

Subgroups — C22×C3×C31×C52⋊C3 #42124977

Order 27900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C31×C52⋊C3C213yesmaximal, direct product factor
2C22×C31×C52⋊C3C313yesmaximal, direct product factor
3C22×C3×C52×C31C311yesmaximal, characteristic, complemented
4C3×C31×C52⋊C3C2211yescharacteristic, direct product factor, Hall
5C2×C31×C52⋊C3C2×C319yesdirect product factor
6C2×C3×C52×C31C2×C313yescomplemented
7C22×C52×C31C3211yescharacteristic, complemented, Hall
8C31×C52⋊C3C22×C313yesdirect product factor
9C3×C52×C31C22×C311yescharacteristic, complemented
10C22×C3×C5×C31—32no—
11C2×C52×C31C2×C3213yescomplemented
12C22×C32×C31—251nomaximal, Hall
13C2×C3×C5×C31—36no—
14C22×C3×C52⋊C3C3111yesmaximal, characteristic, direct product factor, Hall
15C52×C31C22×C3211yescharacteristic, complemented, Hall
16C22×C5×C31—32no—
17C2×C32×C31—253no—
18C3×C5×C31—32no—
19C2×C3×C52⋊C3C2×C3113yesdirect product factor
20C22×C3×C31—253no—
21C22×C3×C31C52⋊C311yescharacteristic, direct product factor
22C2×C5×C31—36no—
23C22×C3×C52C3×C3111yescharacteristic, complemented
24C22×C52⋊C3C3×C3113yesdirect product factor
25C32×C31—251noHall
26C3×C52⋊C3C22×C3111yescharacteristic, direct product factor, Hall
27C2×C3×C31—259no—
28C2×C3×C31C2×C52⋊C313yesdirect product factor
29C5×C31—32no—
30C2×C3×C52C2×C3×C3113yescomplemented
31C2×C52⋊C3C2×C3×C3119yesdirect product factor
32C22×C31C3×C52⋊C311yescharacteristic, direct product factor, Hall
33C22×C52C32×C3111yescharacteristic, complemented, Hall
34C3×C31—253no—
35C3×C31C22×C52⋊C311yescharacteristic, direct product factor
36C3×C52C22×C3×C3111yescharacteristic, complemented
37C52⋊C3C22×C3×C3113yesdirect product factor
38C2×C31C2×C3×C52⋊C313yesdirect product factor
39C22×C3×C5—32no—
40C2×C52C2×C32×C3113yescomplemented
41C22×C32—251noHall
42C31C22×C3×C52⋊C311yescharacteristic, direct product factor, Sylow
43C2×C3×C5—36no—
44C52C22×C32×C3111yescharacteristic, complemented, Sylow
45C22×C5—32no—
46C2×C32—253no—
47C3×C5—32no—
48C22×C3—253no—
49C22×C3C31×C52⋊C311yescharacteristic, direct product factor
50C2×C5—36no—
51C32—251noSylow
52C2×C3—259no—
53C2×C3C2×C31×C52⋊C313yesdirect product factor
54C5—32no—
55C22C3×C31×C52⋊C311yescharacteristic, direct product factor, Sylow
56C3—253no—
57C3C22×C31×C52⋊C311yescharacteristic, direct product factor
58C2C2×C3×C31×C52⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C31C52⋊C3
commutator, cosocle, hypocenterC52C22×C32×C31
FrattiniC1G
Fitting, socleC22×C3×C52×C31C3
LCSG ▷ C52
UCSC1 ◁ C22×C3×C31

Complements

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

NH ≅ G/Ntype
1. C2×C3×C31×C52⋊C3C2direct (N × H)
2. C22×C31×C52⋊C3C3direct (N × H)
3. C22×C3×C52×C31C3semidirect
4. C3×C31×C52⋊C3C22direct (N × H)
5. C2×C31×C52⋊C3C2×C3direct (N × H)
6. C2×C3×C52×C31C2×C3semidirect
7. C22×C52×C31C32semidirect
8. C31×C52⋊C3C22×C3direct (N × H)
9. C3×C52×C31C22×C3semidirect
11. C2×C52×C31C2×C32semidirect
14. C22×C3×C52⋊C3C31direct (N × H)
15. C52×C31C22×C32semidirect
19. C2×C3×C52⋊C3C2×C31direct (N × H)
21. C22×C3×C31C52⋊C3direct (N × H)
23. C22×C3×C52C3×C31semidirect
24. C22×C52⋊C3C3×C31direct (N × H)
26. C3×C52⋊C3C22×C31direct (N × H)
28. C2×C3×C31C2×C52⋊C3direct (N × H)
30. C2×C3×C52C2×C3×C31semidirect
31. C2×C52⋊C3C2×C3×C31direct (N × H)
32. C22×C31C3×C52⋊C3direct (N × H)
33. C22×C52C32×C31semidirect
35. C3×C31C22×C52⋊C3direct (N × H)
36. C3×C52C22×C3×C31semidirect
37. C52⋊C3C22×C3×C31direct (N × H)
38. C2×C31C2×C3×C52⋊C3direct (N × H)
40. C2×C52C2×C32×C31semidirect
42. C31C22×C3×C52⋊C3direct (N × H)
44. C52C22×C32×C31semidirect
49. C22×C3C31×C52⋊C3direct (N × H)
53. C2×C3C2×C31×C52⋊C3direct (N × H)
55. C22C3×C31×C52⋊C3direct (N × H)
57. C3C22×C31×C52⋊C3direct (N × H)
58. C2C2×C3×C31×C52⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C31×C52⋊C32
C22×C31×C52⋊C33
C22×C3×C52×C313
C22×C32×C3125
C22×C3×C52⋊C331