Finite Group Databasebeta

← C22×C3×(C31⋊C3)⋊C25 #42124392

Subgroups — C22×C3×(C31⋊C3)⋊C25 #42124392

Order 27900.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C31⋊C3)⋊C25C213yesmaximal, direct product factor
2C22×C3×C31⋊C25C311yesmaximal, characteristic, complemented
3C22×(C31⋊C3)⋊C25C313yesmaximal, direct product factor
4C3×(C31⋊C3)⋊C25C2211yescharacteristic, direct product factor, Hall
5C22×C3×C5×C31⋊C3C511yesmaximal, characteristic
6C2×C3×C31⋊C25C2×C313yescomplemented
7C2×(C31⋊C3)⋊C25C2×C319yesdirect product factor
8C22×C31⋊C25C3211yescharacteristic, complemented, Hall
9C2×C3×C5×C31⋊C3C2×C513yes—
10C3×C31⋊C25C22×C311yescharacteristic, complemented
11(C31⋊C3)⋊C25C22×C313yesdirect product factor
12C22×C3×C5×C31C3×C511yescharacteristic
13C22×C5×C31⋊C3C3×C513yes—
14C2×C31⋊C25C2×C3213yescomplemented
15C3×C5×C31⋊C3C22×C511yescharacteristic
16C22×C3×C31⋊C3C2511yescharacteristic, complemented, Hall
17C2×C3×C5×C31C2×C3×C513yes—
18C2×C5×C31⋊C3C2×C3×C519yes—
19C22×C32×C25—311nomaximal, Hall
20C31⋊C25C22×C3211yescharacteristic, complemented, Hall
21C22×C5×C31C32×C511yescharacteristic
22C2×C3×C31⋊C3C2×C2513yescomplemented
23C3×C5×C31C22×C3×C511yescharacteristic
24C5×C31⋊C3C22×C3×C513yes—
25C2×C32×C25—313no—
26C22×C3×C31C3×C2511yescharacteristic, complemented
27C22×C31⋊C3C3×C2513yescomplemented
28C2×C5×C31C2×C32×C513yes—
29C22×C3×C25—313no—
30C22×C3×C25—311no—
31C3×C31⋊C3C22×C2511yescharacteristic, complemented, Hall
32C32×C25—311noHall
33C2×C3×C31C2×C3×C2513yescomplemented
34C2×C31⋊C3C2×C3×C2519yescomplemented
35C22×C32×C5—311no—
36C5×C31C22×C32×C511yescharacteristic
37C2×C3×C25—319no—
38C2×C3×C25—313no—
39C22×C31C32×C2511yescharacteristic, complemented, Hall
40C22×C25—311noHall
41C3×C31C22×C3×C2511yescharacteristic, complemented
42C31⋊C3C22×C3×C2513yescomplemented
43C2×C32×C5—313no—
44C3×C25—313no—
45C3×C25—311no—
46C2×C31C2×C32×C2513yescomplemented
47C22×C3×C5—313no—
48C22×C3×C5(C31⋊C3)⋊C511yescharacteristic
49C2×C25—313no—
50C32×C5—311no—
51C22×C32—311noHall
52C31C22×C32×C2511yescharacteristic, complemented, Sylow
53C2×C3×C5—319no—
54C2×C3×C5C2×(C31⋊C3)⋊C513yes—
55C25—311noSylow
56C22×C5C3×(C31⋊C3)⋊C511yescharacteristic
57C2×C32—313no—
58C3×C5—313no—
59C3×C5C22×(C31⋊C3)⋊C511yescharacteristic
60C22×C3—313no—
61C22×C3(C31⋊C3)⋊C2511yescharacteristic, direct product factor
62C2×C5C2×C3×(C31⋊C3)⋊C513yes—
63C32—311noSylow
64C2×C3—319no—
65C2×C3C2×(C31⋊C3)⋊C2513yesdirect product factor
66C5C22×C3×(C31⋊C3)⋊C511yescharacteristic
67C22C3×(C31⋊C3)⋊C2511yescharacteristic, direct product factor, Sylow
68C3—313no—
69C3C22×(C31⋊C3)⋊C2511yescharacteristic, direct product factor
70C2C2×C3×(C31⋊C3)⋊C2513yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C22×C32×C25
FrattiniC5C22×C3×(C31⋊C3)⋊C5
Fitting, socleC22×C3×C5×C31C3×C5
prime radicalC22×C3×C5×C31⋊C3C5
cosocleC5×C31C22×C32×C5
LCSG ▷ C31
UCSC1 ◁ C22×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×(C31⋊C3)⋊C25C2direct (N × H)
2. C22×C3×C31⋊C25C3semidirect
3. C22×(C31⋊C3)⋊C25C3direct (N × H)
4. C3×(C31⋊C3)⋊C25C22direct (N × H)
6. C2×C3×C31⋊C25C2×C3semidirect
7. C2×(C31⋊C3)⋊C25C2×C3direct (N × H)
8. C22×C31⋊C25C32semidirect
10. C3×C31⋊C25C22×C3semidirect
11. (C31⋊C3)⋊C25C22×C3direct (N × H)
14. C2×C31⋊C25C2×C32semidirect
16. C22×C3×C31⋊C3C25semidirect
20. C31⋊C25C22×C32semidirect
22. C2×C3×C31⋊C3C2×C25semidirect
26. C22×C3×C31C3×C25semidirect
27. C22×C31⋊C3C3×C25semidirect
31. C3×C31⋊C3C22×C25semidirect
33. C2×C3×C31C2×C3×C25semidirect
34. C2×C31⋊C3C2×C3×C25semidirect
39. C22×C31C32×C25semidirect
41. C3×C31C22×C3×C25semidirect
42. C31⋊C3C22×C3×C25semidirect
46. C2×C31C2×C32×C25semidirect
52. C31C22×C32×C25semidirect
61. C22×C3(C31⋊C3)⋊C25direct (N × H)
65. C2×C3C2×(C31⋊C3)⋊C25direct (N × H)
67. C22C3×(C31⋊C3)⋊C25direct (N × H)
69. C3C22×(C31⋊C3)⋊C25direct (N × H)
70. C2C2×C3×(C31⋊C3)⋊C25direct (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⋊C3)⋊C252
C22×C3×C31⋊C253
C22×(C31⋊C3)⋊C253
C22×C3×C5×C31⋊C35
C22×C32×C2531