Finite Group Databasebeta

← C5×D3×C72×D11 #44568839

Subgroups — C5×D3×C72×D11 #44568839

Order 32340.

400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C3×C5×C72×D11C211yesmaximal, characteristic, complemented
2C5×D3×C72×C11C211yesmaximal, characteristic, complemented
3C5×C72×D33C211yesmaximal, characteristic, complemented
4C2×C5×C72×D11—31nomaximal, Hall
5C3×C5×C72×C11C2211yescharacteristic, complemented, Hall
6D3×C72×D11C511yesmaximal, characteristic, direct product factor, Hall
7C5×C72×D11—31no—
8C5×C72×D11D311yescharacteristic, direct product factor
9C2×C5×C72×C11—31no—
10C5×D3×C7×D11C718yesmaximal, direct product factor
11C72×D33C2×C511yescharacteristic, complemented
12D3×C72×C11C2×C511yescharacteristic, complemented
13C3×C72×D11C2×C511yescharacteristic, complemented
14C2×C5×D3×C72—111nomaximal, Hall
15C5×C72×C11C2×D311yescharacteristic, complemented, Hall
16C5×C7×D33C2×C718yescomplemented
17C5×D3×C7×C11C2×C718yescomplemented
18C3×C5×C7×D11C2×C718yescomplemented
19C2×C72×D11—31noHall
20C3×C72×C11C22×C511yescharacteristic, complemented, Hall
21C2×C5×C7×D11—38no—
22C2×C3×C5×C72—111no—
23C5×D3×C72—111no—
24C5×D3×C72D1111yescharacteristic, direct product factor
25C3×C5×C7×C11C22×C718yescomplemented
26C2×C72×C11—31no—
27C72×D11—31no—
28C72×D11C5×D311yescharacteristic, direct product factor
29C22×C5×C72—331noHall
30D3×C7×D11C5×C718yesdirect product factor
31C2×C5×C7×C11—38no—
32C5×C7×D11—38no—
33C5×C7×D11D3×C718yesdirect product factor
34C3×C5×C72C2×D1111yescharacteristic, complemented, Hall
35C5×D3×D11C7211yescharacteristic, direct product factor, Hall
36C2×D3×C72—111noHall
37C72×C11C2×C5×D311yescharacteristic, complemented, Hall
38C2×C5×C72—31no—
39C2×C5×C72—111no—
40C2×C5×C72—331no—
41C7×D33C2×C5×C718yescomplemented
42D3×C7×C11C2×C5×C718yescomplemented
43C3×C7×D11C2×C5×C718yescomplemented
44C2×C5×D3×C7—118no—
45C5×C7×C11C2×D3×C718yescomplemented
46C5×D33C2×C7211yescharacteristic, complemented
47C5×D3×C11C2×C7211yescharacteristic, complemented
48C3×C5×D11C2×C7211yescharacteristic, complemented
49C2×C7×D11—38no—
50C2×C3×C72—111no—
51D3×C72—111no—
52D3×C72C5×D1111yescharacteristic, direct product factor
53C5×C72D3×D1111yescharacteristic, direct product factor, Hall
54C3×C7×C11C22×C5×C718yescomplemented
55C2×C5×D11—31noHall
56C2×C3×C5×C7—118no—
57C5×D3×C7—118no—
58C5×D3×C7C7×D1118yesdirect product factor
59C22×C72—331noHall
60C3×C5×C11C22×C7211yescharacteristic, complemented, Hall
61C2×C7×C11—38no—
62C7×D11—38no—
63C7×D11C5×D3×C718yesdirect product factor
64C3×C72C2×C5×D1111yescharacteristic, complemented, Hall
65C22×C5×C7—338no—
66D3×D11C5×C7211yescharacteristic, direct product factor, Hall
67C2×C5×C11—31no—
68C5×D11—31no—
69C5×D11D3×C7211yescharacteristic, direct product factor
70C3×C5×C7C2×C7×D1118yescomplemented
71C2×C72—31no—
72C2×C72—111no—
73C2×C72—331no—
74C2×D3×C7—118no—
75C7×C11C2×C5×D3×C718yescomplemented
76C2×C5×C7—38no—
77C2×C5×C7—118no—
78C2×C5×C7—338no—
79D33C2×C5×C7211yescharacteristic, complemented
80C3×D11C2×C5×C7211yescharacteristic, complemented
81D3×C11C2×C5×C7211yescharacteristic, complemented
82C2×C5×D3—111noHall
83C5×C11C2×D3×C7211yescharacteristic, complemented, Hall
84C72C5×D3×D1111yescharacteristic, direct product factor, Sylow
85C2×D11—31noHall
86C2×C3×C7—118no—
87D3×C7—118no—
88D3×C7C5×C7×D1118yesdirect product factor
89C5×C7D3×C7×D1118yesdirect product factor
90C3×C11C22×C5×C7211yescharacteristic, complemented, Hall
91C2×C3×C5—111no—
92C5×D3—111no—
93C5×D3C72×D1111yescharacteristic, direct product factor
94C22×C7—338no—
95C2×C11—31no—
96D11—31no—
97D11C5×D3×C7211yescharacteristic, direct product factor
98C3×C7C2×C5×C7×D1118yescomplemented
99C22×C5—331noHall
100C3×C5C2×C72×D1111yescharacteristic, complemented, Hall
101C2×C7—38no—
102C2×C7—118no—
103C2×C7—338no—
104C2×D3—111noHall
105C11C2×C5×D3×C7211yescharacteristic, complemented, Sylow
106C2×C5—31no—
107C2×C5—111no—
108C2×C5—331no—
109C7C5×D3×C7×D1118yesdirect product factor
110C2×C3—111no—
111D3—111no—
112D3C5×C72×D1111yescharacteristic, direct product factor
113C5D3×C72×D1111yescharacteristic, direct product factor, Sylow
114C22—331noSylow
115C3C2×C5×C72×D1111yescharacteristic, complemented, Sylow
116C2—31no—
117C2—111no—
118C2—331no—
subgroupG/H
center, hypercenterC5×C72D3×D11
commutator, cosocle, hypocenterC3×C11C22×C5×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C11
UCSC1 ◁ C5×C72

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D11C2semidirect
2. C5×D3×C72×C11C2semidirect
3. C5×C72×D33C2semidirect
5. C3×C5×C72×C11C22semidirect
6. D3×C72×D11C5direct (N × H)
8. C5×C72×D11D3direct (N × H)
10. C5×D3×C7×D11C7direct (N × H)
11. C72×D33C2×C5semidirect
12. D3×C72×C11C2×C5semidirect
13. C3×C72×D11C2×C5semidirect
15. C5×C72×C11C2×D3semidirect
16. C5×C7×D33C2×C7semidirect
17. C5×D3×C7×C11C2×C7semidirect
18. C3×C5×C7×D11C2×C7semidirect
20. C3×C72×C11C22×C5semidirect
24. C5×D3×C72D11direct (N × H)
25. C3×C5×C7×C11C22×C7semidirect
28. C72×D11C5×D3direct (N × H)
30. D3×C7×D11C5×C7direct (N × H)
33. C5×C7×D11D3×C7direct (N × H)
34. C3×C5×C72C2×D11semidirect
35. C5×D3×D11C72direct (N × H)
37. C72×C11C2×C5×D3semidirect
41. C7×D33C2×C5×C7semidirect
42. D3×C7×C11C2×C5×C7semidirect
43. C3×C7×D11C2×C5×C7semidirect
45. C5×C7×C11C2×D3×C7semidirect
46. C5×D33C2×C72semidirect
47. C5×D3×C11C2×C72semidirect
48. C3×C5×D11C2×C72semidirect
52. D3×C72C5×D11direct (N × H)
53. C5×C72D3×D11direct (N × H)
54. C3×C7×C11C22×C5×C7semidirect
58. C5×D3×C7C7×D11direct (N × H)
60. C3×C5×C11C22×C72semidirect
63. C7×D11C5×D3×C7direct (N × H)
64. C3×C72C2×C5×D11semidirect
66. D3×D11C5×C72direct (N × H)
69. C5×D11D3×C72direct (N × H)
70. C3×C5×C7C2×C7×D11semidirect
75. C7×C11C2×C5×D3×C7semidirect
79. D33C2×C5×C72semidirect
80. C3×D11C2×C5×C72semidirect
81. D3×C11C2×C5×C72semidirect
83. C5×C11C2×D3×C72semidirect
84. C72C5×D3×D11direct (N × H)
88. D3×C7C5×C7×D11direct (N × H)
89. C5×C7D3×C7×D11direct (N × H)
90. C3×C11C22×C5×C72semidirect
93. C5×D3C72×D11direct (N × H)
97. D11C5×D3×C72direct (N × H)
98. C3×C7C2×C5×C7×D11semidirect
100. C3×C5C2×C72×D11semidirect
105. C11C2×C5×D3×C72semidirect
109. C7C5×D3×C7×D11direct (N × H)
112. D3C5×C72×D11direct (N × H)
113. C5D3×C72×D11direct (N × H)
115. C3C2×C5×C72×D11semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C72×D112
C5×D3×C72×C112
C5×C72×D332
C2×C5×C72×D113
D3×C72×D115
C5×D3×C7×D117
C2×C5×D3×C7211