Finite Group Databasebeta

← C3×C4×C5×C7×C11⋊C5 #37528381

Subgroups — C3×C4×C5×C7×C11⋊C5 #37528381

Order 23100.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C7×C11⋊C5C211yesmaximal, characteristic
2C4×C5×C7×C11⋊C5C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C7×C11⋊C5C411yescharacteristic, direct product factor, Hall
4C3×C4×C7×C11⋊C5C515yesmaximal, direct product factor
5C3×C4×C5×C7×C11C511yesmaximal, characteristic, complemented
6C2×C5×C7×C11⋊C5C2×C311yescharacteristic
7C3×C4×C5×C11⋊C5C711yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C7×C11⋊C5C2×C515yes—
9C2×C3×C5×C7×C11C2×C511yescharacteristic
10C3×C4×C52×C7—111nomaximal, Hall
11C5×C7×C11⋊C5C3×C411yescharacteristic, direct product factor, Hall
12C2×C3×C5×C11⋊C5C2×C711yescharacteristic
13C4×C5×C7×C11C3×C511yescharacteristic, complemented
14C4×C7×C11⋊C5C3×C515yesdirect product factor
15C3×C5×C7×C11C4×C511yescharacteristic, complemented
16C3×C7×C11⋊C5C4×C515yesdirect product factor
17C4×C5×C11⋊C5C3×C711yescharacteristic, direct product factor, Hall
18C2×C3×C52×C7—111no—
19C3×C4×C7×C11C5211yescharacteristic, complemented, Hall
20C3×C5×C11⋊C5C4×C711yescharacteristic, direct product factor, Hall
21C2×C5×C7×C11C2×C3×C511yescharacteristic
22C2×C7×C11⋊C5C2×C3×C515yes—
23C4×C52×C7—111noHall
24C3×C4×C5×C11C5×C711yescharacteristic, complemented
25C3×C4×C11⋊C5C5×C715yesdirect product factor
26C2×C5×C11⋊C5C2×C3×C711yescharacteristic
27C3×C52×C7—111noHall
28C2×C3×C7×C11C2×C5211yescharacteristic
29C3×C4×C5×C7—115no—
30C3×C4×C5×C7C11⋊C511yescharacteristic, direct product factor
31C5×C7×C11C3×C4×C511yescharacteristic, complemented
32C7×C11⋊C5C3×C4×C515yesdirect product factor
33C2×C52×C7—111no—
34C2×C3×C5×C11C2×C5×C711yescharacteristic
35C2×C3×C11⋊C5C2×C5×C715yes—
36C4×C7×C11C3×C5211yescharacteristic, complemented, Hall
37C3×C4×C52—111noHall
38C5×C11⋊C5C3×C4×C711yescharacteristic, direct product factor, Hall
39C3×C7×C11C4×C5211yescharacteristic, complemented, Hall
40C4×C5×C11C3×C5×C711yescharacteristic, complemented
41C4×C11⋊C5C3×C5×C715yesdirect product factor
42C2×C3×C5×C7—115no—
43C2×C3×C5×C7C2×C11⋊C511yescharacteristic
44C52×C7—111noHall
45C3×C5×C11C4×C5×C711yescharacteristic, complemented
46C3×C11⋊C5C4×C5×C715yesdirect product factor
47C2×C7×C11C2×C3×C5211yescharacteristic
48C2×C3×C52—111no—
49C4×C5×C7—115no—
50C4×C5×C7C3×C11⋊C511yescharacteristic, direct product factor
51C3×C4×C11C52×C711yescharacteristic, complemented, Hall
52C2×C5×C11C2×C3×C5×C711yescharacteristic
53C2×C11⋊C5C2×C3×C5×C715yes—
54C3×C5×C7—115no—
55C3×C5×C7C4×C11⋊C511yescharacteristic, direct product factor
56C4×C52—111noHall
57C3×C4×C7C5×C11⋊C511yescharacteristic, direct product factor, Hall
58C7×C11C3×C4×C5211yescharacteristic, complemented, Hall
59C3×C52—111noHall
60C2×C5×C7—115no—
61C2×C5×C7C2×C3×C11⋊C511yescharacteristic
62C2×C3×C11C2×C52×C711yescharacteristic
63C3×C4×C5—115no—
64C3×C4×C5C7×C11⋊C511yescharacteristic, direct product factor
65C5×C11C3×C4×C5×C711yescharacteristic, complemented
66C11⋊C5C3×C4×C5×C715yesdirect product factor
67C2×C52—111no—
68C4×C11C3×C52×C711yescharacteristic, complemented, Hall
69C2×C3×C7C2×C5×C11⋊C511yescharacteristic
70C5×C7—115no—
71C5×C7C3×C4×C11⋊C511yescharacteristic, direct product factor
72C3×C11C4×C52×C711yescharacteristic, complemented, Hall
73C2×C3×C5—115no—
74C2×C3×C5C2×C7×C11⋊C511yescharacteristic
75C4×C7C3×C5×C11⋊C511yescharacteristic, direct product factor, Hall
76C52—111noSylow
77C2×C11C2×C3×C52×C711yescharacteristic
78C3×C7C4×C5×C11⋊C511yescharacteristic, direct product factor, Hall
79C4×C5—115no—
80C4×C5C3×C7×C11⋊C511yescharacteristic, direct product factor
81C3×C5—115no—
82C3×C5C4×C7×C11⋊C511yescharacteristic, direct product factor
83C2×C7C2×C3×C5×C11⋊C511yescharacteristic
84C3×C4C5×C7×C11⋊C511yescharacteristic, direct product factor, Hall
85C11C3×C4×C52×C711yescharacteristic, complemented, Sylow
86C2×C5—115no—
87C2×C5C2×C3×C7×C11⋊C511yescharacteristic
88C7C3×C4×C5×C11⋊C511yescharacteristic, direct product factor, Sylow
89C2×C3C2×C5×C7×C11⋊C511yescharacteristic
90C5—115no—
91C5C3×C4×C7×C11⋊C511yescharacteristic, direct product factor
92C4C3×C5×C7×C11⋊C511yescharacteristic, direct product factor, Sylow
93C3C4×C5×C7×C11⋊C511yescharacteristic, direct product factor, Sylow
94C2C2×C3×C5×C7×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC3×C4×C5×C7C11⋊C5
commutator, hypocenterC11C3×C4×C52×C7
FrattiniC2C2×C3×C5×C7×C11⋊C5
FittingC3×C4×C5×C7×C11C5
socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C11C2×C3×C52×C7
LCSG ▷ C11
UCSC1 ◁ C3×C4×C5×C7

Complements

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

NH ≅ G/Ntype
2. C4×C5×C7×C11⋊C5C3direct (N × H)
3. C3×C5×C7×C11⋊C5C4direct (N × H)
4. C3×C4×C7×C11⋊C5C5direct (N × H)
5. C3×C4×C5×C7×C11C5semidirect
7. C3×C4×C5×C11⋊C5C7direct (N × H)
11. C5×C7×C11⋊C5C3×C4direct (N × H)
13. C4×C5×C7×C11C3×C5semidirect
14. C4×C7×C11⋊C5C3×C5direct (N × H)
15. C3×C5×C7×C11C4×C5semidirect
16. C3×C7×C11⋊C5C4×C5direct (N × H)
17. C4×C5×C11⋊C5C3×C7direct (N × H)
19. C3×C4×C7×C11C52semidirect
20. C3×C5×C11⋊C5C4×C7direct (N × H)
24. C3×C4×C5×C11C5×C7semidirect
25. C3×C4×C11⋊C5C5×C7direct (N × H)
30. C3×C4×C5×C7C11⋊C5direct (N × H)
31. C5×C7×C11C3×C4×C5semidirect
32. C7×C11⋊C5C3×C4×C5direct (N × H)
36. C4×C7×C11C3×C52semidirect
38. C5×C11⋊C5C3×C4×C7direct (N × H)
39. C3×C7×C11C4×C52semidirect
40. C4×C5×C11C3×C5×C7semidirect
41. C4×C11⋊C5C3×C5×C7direct (N × H)
45. C3×C5×C11C4×C5×C7semidirect
46. C3×C11⋊C5C4×C5×C7direct (N × H)
50. C4×C5×C7C3×C11⋊C5direct (N × H)
51. C3×C4×C11C52×C7semidirect
55. C3×C5×C7C4×C11⋊C5direct (N × H)
57. C3×C4×C7C5×C11⋊C5direct (N × H)
58. C7×C11C3×C4×C52semidirect
64. C3×C4×C5C7×C11⋊C5direct (N × H)
65. C5×C11C3×C4×C5×C7semidirect
66. C11⋊C5C3×C4×C5×C7direct (N × H)
68. C4×C11C3×C52×C7semidirect
71. C5×C7C3×C4×C11⋊C5direct (N × H)
72. C3×C11C4×C52×C7semidirect
75. C4×C7C3×C5×C11⋊C5direct (N × H)
78. C3×C7C4×C5×C11⋊C5direct (N × H)
80. C4×C5C3×C7×C11⋊C5direct (N × H)
82. C3×C5C4×C7×C11⋊C5direct (N × H)
84. C3×C4C5×C7×C11⋊C5direct (N × H)
85. C11C3×C4×C52×C7semidirect
88. C7C3×C4×C5×C11⋊C5direct (N × H)
91. C5C3×C4×C7×C11⋊C5direct (N × H)
92. C4C3×C5×C7×C11⋊C5direct (N × H)
93. C3C4×C5×C7×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C7×C11⋊C52
C4×C5×C7×C11⋊C53
C3×C4×C7×C11⋊C55
C3×C4×C5×C7×C115
C3×C4×C5×C11⋊C57
C3×C4×C52×C711