Finite Group Databasebeta

← C52×D3×D119 #49087927

Subgroups — C52×D3×D119 #49087927

Order 35700.

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×D119C211yesmaximal, characteristic, complemented
2C52×D3×C7×C17C211yesmaximal, characteristic, complemented
3C52×D357C211yesmaximal, characteristic, complemented
4C2×C52×D119—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C5×D3×D119C516yesmaximal, direct product factor
7C52×D119—31no—
8C52×D119D311yescharacteristic, direct product factor
9C2×C52×C7×C17—31no—
10C52×D3×D17—71nomaximal, Hall
11C5×D357C2×C516yescomplemented
12C5×D3×C7×C17C2×C516yescomplemented
13C3×C5×D119C2×C516yescomplemented
14C52×C7×C17C2×D311yescharacteristic, complemented, Hall
15C52×D51—71no—
16C52×D3×C17D711yescharacteristic, complemented
17C3×C52×D17—71no—
18C2×C5×D119—36no—
19C52×D3×D7—171nomaximal, Hall
20C3×C5×C7×C17C22×C516yescomplemented
21C2×C52×D17—211noHall
22D3×D119C5211yescharacteristic, direct product factor, Hall
23C3×C52×C17C2×D711yescharacteristic, complemented, Hall
24C2×C5×C7×C17—36no—
25C5×D119—36no—
26C5×D119C5×D316yesdirect product factor
27C52×D21—171no—
28C52×D3×C7D1711yescharacteristic, complemented
29C3×C52×D7—171no—
30C5×D3×D17—76no—
31C2×C52×C17—31no—
32C52×D17—71no—
33C52×D17—211no—
34D357C2×C5211yescharacteristic, complemented
35D3×C7×C17C2×C5211yescharacteristic, complemented
36C3×D119C2×C5211yescharacteristic, complemented
37C2×C52×D7—511noHall
38C5×C7×C17C2×C5×D316yescomplemented
39C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
40C5×D51—76no—
41C5×D3×C17C5×D716yescomplemented
42C3×C5×D17—76no—
43C2×D119—31noHall
44C52×C17D3×D711yescharacteristic, complemented, Hall
45C5×D3×D7—176no—
46C3×C7×C17C22×C5211yescharacteristic, complemented, Hall
47C2×C52×C7—31no—
48C52×D7—171no—
49C52×D7—511no—
50C2×C5×D17—216no—
51C2×C52×D3—1191noHall
52C3×C5×C17C2×C5×D716yescomplemented
53C2×C7×C17—31no—
54D119—31no—
55D119C52×D311yescharacteristic, direct product factor
56C5×D21—176no—
57C5×D3×C7C5×D1716yescomplemented
58C3×C5×D7—176no—
59D3×D17—71noHall
60C52×C7D3×D1711yescharacteristic, complemented, Hall
61C2×C5×C17—36no—
62C5×D17—76no—
63C5×D17—216no—
64C2×C3×C52—1191no—
65C52×D3—1191no—
66C52×D3D11911yescharacteristic, direct product factor
67C2×C5×D7—516no—
68C7×C17C2×C52×D311yescharacteristic, complemented, Hall
69C3×C5×C7C2×C5×D1716yescomplemented
70D51—71no—
71C3×D17—71no—
72D3×C17C52×D711yescharacteristic, complemented
73C22×C52—3571noHall
74C5×C17C5×D3×D716yescomplemented
75D3×D7—171noHall
76C3×C52C2×D11911yescharacteristic, complemented, Hall
77C2×C5×C7—36no—
78C5×D7—176no—
79C5×D7—516no—
80C2×D17—211noHall
81C2×C5×D3—1196no—
82C3×C17C2×C52×D711yescharacteristic, complemented, Hall
83C2×C52—31no—
84C2×C52—3571no—
85C2×C52—1191no—
86D21—171no—
87C3×D7—171no—
88D3×C7C52×D1711yescharacteristic, complemented
89C5×C7C5×D3×D1716yescomplemented
90C2×C17—31no—
91D17—71no—
92D17—211no—
93C2×C3×C5—1196no—
94C5×D3—1196no—
95C5×D3C5×D11916yesdirect product factor
96C2×D7—511noHall
97C52D3×D11911yescharacteristic, direct product factor, Sylow
98C3×C7C2×C52×D1711yescharacteristic, complemented, Hall
99C22×C5—3576no—
100C17C52×D3×D711yescharacteristic, complemented, Sylow
101C3×C5C2×C5×D11916yescomplemented
102C2×C7—31no—
103D7—171no—
104D7—511no—
105C2×D3—1191noHall
106C2×C5—36no—
107C2×C5—3576no—
108C2×C5—1196no—
109C7C52×D3×D1711yescharacteristic, complemented, Sylow
110C2×C3—1191no—
111D3—1191no—
112D3C52×D11911yescharacteristic, direct product factor
113C5C5×D3×D11916yesdirect product factor
114C22—3571noSylow
115C3C2×C52×D11911yescharacteristic, complemented, Sylow
116C2—31no—
117C2—3571no—
118C2—1191no—
subgroupG/H
center, hypercenterC52D3×D119
commutator, cosocle, hypocenterC3×C7×C17C22×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C7×C17
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×D119C2semidirect
2. C52×D3×C7×C17C2semidirect
3. C52×D357C2semidirect
5. C3×C52×C7×C17C22semidirect
6. C5×D3×D119C5direct (N × H)
8. C52×D119D3direct (N × H)
11. C5×D357C2×C5semidirect
12. C5×D3×C7×C17C2×C5semidirect
13. C3×C5×D119C2×C5semidirect
14. C52×C7×C17C2×D3semidirect
16. C52×D3×C17D7semidirect
20. C3×C5×C7×C17C22×C5semidirect
22. D3×D119C52direct (N × H)
23. C3×C52×C17C2×D7semidirect
26. C5×D119C5×D3direct (N × H)
28. C52×D3×C7D17semidirect
34. D357C2×C52semidirect
35. D3×C7×C17C2×C52semidirect
36. C3×D119C2×C52semidirect
38. C5×C7×C17C2×C5×D3semidirect
39. C3×C52×C7C2×D17semidirect
41. C5×D3×C17C5×D7semidirect
44. C52×C17D3×D7semidirect
46. C3×C7×C17C22×C52semidirect
52. C3×C5×C17C2×C5×D7semidirect
55. D119C52×D3direct (N × H)
57. C5×D3×C7C5×D17semidirect
60. C52×C7D3×D17semidirect
66. C52×D3D119direct (N × H)
68. C7×C17C2×C52×D3semidirect
69. C3×C5×C7C2×C5×D17semidirect
72. D3×C17C52×D7semidirect
74. C5×C17C5×D3×D7semidirect
76. C3×C52C2×D119semidirect
82. C3×C17C2×C52×D7semidirect
88. D3×C7C52×D17semidirect
89. C5×C7C5×D3×D17semidirect
95. C5×D3C5×D119direct (N × H)
97. C52D3×D119direct (N × H)
98. C3×C7C2×C52×D17semidirect
100. C17C52×D3×D7semidirect
101. C3×C5C2×C5×D119semidirect
109. C7C52×D3×D17semidirect
112. D3C52×D119direct (N × H)
113. C5C5×D3×D119direct (N × H)
115. C3C2×C52×D119semidirect

Maximal subgroups

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

subgroupindex
C3×C52×D1192
C52×D3×C7×C172
C52×D3572
C2×C52×D1193
C5×D3×D1195
C52×D3×D177
C52×D3×D717