Finite Group Databasebeta

← C52×D11×D21 #37528639

Subgroups — C52×D11×D21 #37528639

Order 23100.

320 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 128 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×C52×C7×D11C211yesmaximal, characteristic, complemented
2C52×C11×D21C211yesmaximal, characteristic, complemented
3C52×D231C211yesmaximal, characteristic, complemented
4C52×D7×D11—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C5×D11×D21C516yesmaximal, direct product factor
7C52×D77—31no—
8C52×C11×D7—31no—
9C52×C7×D11D311yescharacteristic, complemented
10C52×D3×D11—71nomaximal, Hall
11C5×D231C2×C516yescomplemented
12C5×C11×D21C2×C516yescomplemented
13C3×C5×C7×D11C2×C516yescomplemented
14C2×C52×D21—111nomaximal, Hall
15C52×C7×C11C2×D311yescharacteristic, complemented, Hall
16C52×D33—71no—
17C52×D3×C11—71no—
18C3×C52×D11D711yescharacteristic, complemented
19C5×D7×D11—36no—
20C3×C5×C7×C11C22×C516yescomplemented
21C2×C52×D11—211noHall
22C2×C3×C52×C7—111no—
23C52×D21—111no—
24C52×D21D1111yescharacteristic, direct product factor
25D11×D21C5211yescharacteristic, direct product factor, Hall
26C3×C52×C11C2×D711yescharacteristic, complemented, Hall
27C5×D77—36no—
28C5×C11×D7—36no—
29C5×C7×D11C5×D316yescomplemented
30C2×C52×D7—331noHall
31C5×D3×D11—76no—
32C2×C52×C11—211no—
33C52×D11—211no—
34C52×D11D2111yescharacteristic, direct product factor
35C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
36D231C2×C5211yescharacteristic, complemented
37C11×D21C2×C5211yescharacteristic, complemented
38C3×C7×D11C2×C5211yescharacteristic, complemented
39C2×C5×D21—116no—
40C5×C7×C11C2×C5×D316yescomplemented
41C2×C52×C7—111no—
42C52×D7—31no—
43C52×D7—331no—
44C5×D33—76no—
45C5×D3×C11—76no—
46C3×C5×D11C5×D716yescomplemented
47D7×D11—31noHall
48C2×C52×D3—771noHall
49C52×C11C2×D2111yescharacteristic, complemented, Hall
50C3×C7×C11C22×C5211yescharacteristic, complemented, Hall
51C2×C5×D11—216no—
52C2×C3×C5×C7—116no—
53C5×D21—116no—
54C5×D21C5×D1116yesdirect product factor
55C52×C7D3×D1111yescharacteristic, complemented, Hall
56C3×C5×C11C2×C5×D716yescomplemented
57D77—31no—
58C7×D11C52×D311yescharacteristic, complemented
59C11×D7—31no—
60C2×C3×C52—111no—
61C52×D3—71no—
62C52×D3—771no—
63C2×C5×D7—336no—
64D3×D11—71noHall
65C2×C5×C11—216no—
66C5×D11—216no—
67C5×D11C5×D2116yesdirect product factor
68C3×C5×C7C2×C5×D1116yescomplemented
69C22×C52—2311noHall
70C2×D21—111noHall
71C7×C11C2×C52×D311yescharacteristic, complemented, Hall
72C3×C52D7×D1111yescharacteristic, complemented, Hall
73C2×C5×C7—116no—
74C5×D7—36no—
75C5×D7—336no—
76D33—71no—
77C3×D11C52×D711yescharacteristic, complemented
78D3×C11—71no—
79C2×C5×D3—776no—
80C5×C11C2×C5×D2116yescomplemented
81C2×C52—111no—
82C2×C52—211no—
83C2×C52—2311no—
84C2×D11—211noHall
85C2×C3×C7—111no—
86D21—111no—
87D21C52×D1111yescharacteristic, direct product factor
88C5×C7C5×D3×D1116yescomplemented
89C3×C11C2×C52×D711yescharacteristic, complemented, Hall
90C2×C3×C5—116no—
91C5×D3—76no—
92C5×D3—776no—
93C2×D7—331noHall
94C52D11×D2111yescharacteristic, direct product factor, Sylow
95C2×C11—211no—
96D11—211no—
97D11C52×D2111yescharacteristic, direct product factor
98C3×C7C2×C52×D1111yescharacteristic, complemented, Hall
99C22×C5—2316no—
100C3×C5C5×D7×D1116yescomplemented
101C2×C7—111no—
102D7—31no—
103D7—331no—
104C2×D3—771noHall
105C11C2×C52×D2111yescharacteristic, complemented, Sylow
106C2×C5—116no—
107C2×C5—216no—
108C2×C5—2316no—
109C7C52×D3×D1111yescharacteristic, complemented, Sylow
110C2×C3—111no—
111D3—71no—
112D3—771no—
113C5C5×D11×D2116yesdirect product factor
114C22—2311noSylow
115C3C52×D7×D1111yescharacteristic, complemented, Sylow
116C2—111no—
117C2—211no—
118C2—2311no—
subgroupG/H
center, hypercenterC52D11×D21
commutator, cosocle, hypocenterC3×C7×C11C22×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×C7×D11C2semidirect
2. C52×C11×D21C2semidirect
3. C52×D231C2semidirect
5. C3×C52×C7×C11C22semidirect
6. C5×D11×D21C5direct (N × H)
9. C52×C7×D11D3semidirect
11. C5×D231C2×C5semidirect
12. C5×C11×D21C2×C5semidirect
13. C3×C5×C7×D11C2×C5semidirect
15. C52×C7×C11C2×D3semidirect
18. C3×C52×D11D7semidirect
20. C3×C5×C7×C11C22×C5semidirect
24. C52×D21D11direct (N × H)
25. D11×D21C52direct (N × H)
26. C3×C52×C11C2×D7semidirect
29. C5×C7×D11C5×D3semidirect
34. C52×D11D21direct (N × H)
35. C3×C52×C7C2×D11semidirect
36. D231C2×C52semidirect
37. C11×D21C2×C52semidirect
38. C3×C7×D11C2×C52semidirect
40. C5×C7×C11C2×C5×D3semidirect
46. C3×C5×D11C5×D7semidirect
49. C52×C11C2×D21semidirect
50. C3×C7×C11C22×C52semidirect
54. C5×D21C5×D11direct (N × H)
55. C52×C7D3×D11semidirect
56. C3×C5×C11C2×C5×D7semidirect
58. C7×D11C52×D3semidirect
67. C5×D11C5×D21direct (N × H)
68. C3×C5×C7C2×C5×D11semidirect
71. C7×C11C2×C52×D3semidirect
72. C3×C52D7×D11semidirect
77. C3×D11C52×D7semidirect
80. C5×C11C2×C5×D21semidirect
87. D21C52×D11direct (N × H)
88. C5×C7C5×D3×D11semidirect
89. C3×C11C2×C52×D7semidirect
94. C52D11×D21direct (N × H)
97. D11C52×D21direct (N × H)
98. C3×C7C2×C52×D11semidirect
100. C3×C5C5×D7×D11semidirect
105. C11C2×C52×D21semidirect
109. C7C52×D3×D11semidirect
113. C5C5×D11×D21direct (N × H)
115. C3C52×D7×D11semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C7×D112
C52×C11×D212
C52×D2312
C52×D7×D113
C5×D11×D215
C52×D3×D117
C2×C52×D2111