Finite Group Databasebeta

← C32×C5×C7×D55 #46831655

Subgroups — C32×C5×C7×D55 #46831655

Order 34650.

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C5×C7×D55C314yesmaximal, direct product factor
3C32×C7×D55C511yesmaximal, characteristic, direct product factor
4C32×C5×C7×D11—51nomaximal
5C3×C52×C7×C11C2×C314yescomplemented
6C32×C5×D55C711yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D55C3211yescharacteristic, direct product factor, Hall
8C32×C5×C7×C11—22no—
9C32×C5×C7×C11D511yescharacteristic, complemented
10C32×C5×C7×C11C2×C511yescharacteristic, complemented
11C32×C5×C7×D5—111nomaximal, Hall
12C32×C52×C11C2×C711yescharacteristic, complemented, Hall
13C3×C7×D55C3×C514yesdirect product factor
14C3×C5×C7×D11—54no—
15C52×C7×C11C2×C3211yescharacteristic, complemented, Hall
16C3×C5×D55C3×C714yesdirect product factor
17C32×C52×C7D1111yescharacteristic, complemented, Hall
18C32×C7×D11—51noHall
19C3×C5×C7×C11—28no—
20C3×C5×C7×C11C3×D514yescomplemented
21C3×C5×C7×C11C2×C3×C514yescomplemented
22C3×C5×C7×D5—114no—
23C32×D55C5×C711yescharacteristic, direct product factor
24C32×C5×D11—51no—
25C3×C52×C11C2×C3×C714yescomplemented
26C7×D55C32×C511yescharacteristic, direct product factor
27C5×C7×D11—51no—
28C32×C7×C11C5×D511yescharacteristic, complemented, Hall
29C2×C32×C5×C7—551no—
30C32×C7×D5—111no—
31C5×D55C32×C711yescharacteristic, direct product factor, Hall
32C3×C52×C7C3×D1114yescomplemented
33C32×C5×C11—22no—
34C32×C5×C11C7×D511yescharacteristic, complemented
35C32×C5×C11C2×C5×C711yescharacteristic, complemented
36C3×C7×D11—54no—
37C32×C5×D5—111noHall
38C5×C7×C11—22no—
39C5×C7×C11C32×D511yescharacteristic, complemented
40C5×C7×C11C2×C32×C511yescharacteristic, complemented
41C5×C7×D5—111noHall
42C3×D55C3×C5×C714yesdirect product factor
43C3×C5×D11—54no—
44C32×C5×C7—22no—
45C32×C5×C7C5×D1111yescharacteristic, complemented
46C32×C5×C7D5511yescharacteristic, direct product factor
47C52×C11C2×C32×C711yescharacteristic, complemented, Hall
48C3×C7×C11C3×C5×D514yescomplemented
49C32×C52C7×D1111yescharacteristic, complemented, Hall
50C2×C3×C5×C7—554no—
51C3×C7×D5—114no—
52C32×D11—51noHall
53C52×C7C32×D1111yescharacteristic, complemented, Hall
54C3×C5×C11—28no—
55C3×C5×C11C3×C7×D514yescomplemented
56C3×C5×C11C2×C3×C5×C714yescomplemented
57C7×D11—51noHall
58C3×C5×D5—114no—
59C2×C32×C7—551noHall
60D55C32×C5×C711yescharacteristic, direct product factor
61C5×D11—51no—
62C3×C5×C7—28no—
63C3×C5×C7C3×C5×D1114yescomplemented
64C3×C5×C7C3×D5514yesdirect product factor
65C32×C11C5×C7×D511yescharacteristic, complemented, Hall
66C2×C32×C5—551no—
67C32×D5—111no—
68C7×C11C32×C5×D511yescharacteristic, complemented, Hall
69C3×C52C3×C7×D1114yescomplemented
70C2×C5×C7—551no—
71C7×D5—111no—
72C3×D11—54no—
73C32×C7C5×D5511yescharacteristic, direct product factor, Hall
74C5×C11—22no—
75C5×C11C32×C7×D511yescharacteristic, complemented
76C5×C11C2×C32×C5×C711yescharacteristic, complemented
77C5×D5—111noHall
78C32×C5—22no—
79C32×C5C5×C7×D1111yescharacteristic, complemented
80C32×C5C7×D5511yescharacteristic, direct product factor
81C2×C3×C7—554no—
82C5×C7—22no—
83C5×C7C32×C5×D1111yescharacteristic, complemented
84C5×C7C32×D5511yescharacteristic, direct product factor
85C3×C11C3×C5×C7×D514yescomplemented
86C2×C3×C5—554no—
87C3×D5—114no—
88C52C32×C7×D1111yescharacteristic, complemented, Sylow
89D11—51noHall
90C3×C7C3×C5×D5514yesdirect product factor
91C2×C32—551noHall
92C3×C5—28no—
93C3×C5C3×C5×C7×D1114yescomplemented
94C3×C5C3×C7×D5514yesdirect product factor
95C2×C7—551noHall
96C11C32×C5×C7×D511yescharacteristic, complemented, Sylow
97C2×C5—551no—
98D5—111no—
99C32C5×C7×D5511yescharacteristic, direct product factor, Sylow
100C7C32×C5×D5511yescharacteristic, direct product factor, Sylow
101C2×C3—554no—
102C5—22no—
103C5C32×C5×C7×D1111yescharacteristic, complemented
104C5C32×C7×D5511yescharacteristic, direct product factor
105C3C3×C5×C7×D5514yesdirect product factor
106C2—551noSylow
subgroupG/H
center, hypercenterC32×C5×C7D55
commutator, cosocle, hypocenterC5×C11C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C5×C11
UCSC1 ◁ C32×C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
2. C3×C5×C7×D55C3direct (N × H)
3. C32×C7×D55C5direct (N × H)
5. C3×C52×C7×C11C2×C3semidirect
6. C32×C5×D55C7direct (N × H)
7. C5×C7×D55C32direct (N × H)
9. C32×C5×C7×C11D5semidirect
10. C32×C5×C7×C11C2×C5semidirect
12. C32×C52×C11C2×C7semidirect
13. C3×C7×D55C3×C5direct (N × H)
15. C52×C7×C11C2×C32semidirect
16. C3×C5×D55C3×C7direct (N × H)
17. C32×C52×C7D11semidirect
20. C3×C5×C7×C11C3×D5semidirect
21. C3×C5×C7×C11C2×C3×C5semidirect
23. C32×D55C5×C7direct (N × H)
25. C3×C52×C11C2×C3×C7semidirect
26. C7×D55C32×C5direct (N × H)
28. C32×C7×C11C5×D5semidirect
31. C5×D55C32×C7direct (N × H)
32. C3×C52×C7C3×D11semidirect
34. C32×C5×C11C7×D5semidirect
35. C32×C5×C11C2×C5×C7semidirect
39. C5×C7×C11C32×D5semidirect
40. C5×C7×C11C2×C32×C5semidirect
42. C3×D55C3×C5×C7direct (N × H)
45. C32×C5×C7C5×D11semidirect
46. C32×C5×C7D55direct (N × H)
47. C52×C11C2×C32×C7semidirect
48. C3×C7×C11C3×C5×D5semidirect
49. C32×C52C7×D11semidirect
53. C52×C7C32×D11semidirect
55. C3×C5×C11C3×C7×D5semidirect
56. C3×C5×C11C2×C3×C5×C7semidirect
60. D55C32×C5×C7direct (N × H)
63. C3×C5×C7C3×C5×D11semidirect
64. C3×C5×C7C3×D55direct (N × H)
65. C32×C11C5×C7×D5semidirect
68. C7×C11C32×C5×D5semidirect
69. C3×C52C3×C7×D11semidirect
73. C32×C7C5×D55direct (N × H)
75. C5×C11C32×C7×D5semidirect
76. C5×C11C2×C32×C5×C7semidirect
79. C32×C5C5×C7×D11semidirect
80. C32×C5C7×D55direct (N × H)
83. C5×C7C32×C5×D11semidirect
84. C5×C7C32×D55direct (N × H)
85. C3×C11C3×C5×C7×D5semidirect
88. C52C32×C7×D11semidirect
90. C3×C7C3×C5×D55direct (N × H)
93. C3×C5C3×C5×C7×D11semidirect
94. C3×C5C3×C7×D55direct (N × H)
96. C11C32×C5×C7×D5semidirect
99. C32C5×C7×D55direct (N × H)
100. C7C32×C5×D55direct (N × H)
103. C5C32×C5×C7×D11semidirect
104. C5C32×C7×D55direct (N × H)
105. C3C3×C5×C7×D55direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C5×C7×D553
C32×C7×D555
C32×C5×C7×D115
C32×C5×D557
C32×C5×C7×D511