Finite Group Databasebeta

← C52×D17×D21 #49087924

Subgroups — C52×D17×D21 #49087924

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×C7×D17C211yesmaximal, characteristic, complemented
2C52×C17×D21C211yesmaximal, characteristic, complemented
3C52×D357C211yesmaximal, characteristic, complemented
4C52×D7×D17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C5×D17×D21C516yesmaximal, direct product factor
7C52×D119—31no—
8C52×D7×C17—31no—
9C52×C7×D17D311yescharacteristic, complemented
10C52×D3×D17—71nomaximal, Hall
11C5×D357C2×C516yescomplemented
12C5×C17×D21C2×C516yescomplemented
13C3×C5×C7×D17C2×C516yescomplemented
14C52×C7×C17C2×D311yescharacteristic, complemented, Hall
15C52×D51—71no—
16C52×D3×C17—71no—
17C3×C52×D17D711yescharacteristic, complemented
18C5×D7×D17—36no—
19C2×C52×D21—171nomaximal, Hall
20C3×C5×C7×C17C22×C516yescomplemented
21C2×C52×D17—211noHall
22D17×D21C5211yescharacteristic, direct product factor, Hall
23C3×C52×C17C2×D711yescharacteristic, complemented, Hall
24C5×D119—36no—
25C5×D7×C17—36no—
26C5×C7×D17C5×D316yescomplemented
27C2×C3×C52×C7—171no—
28C52×D21—171no—
29C52×D21D1711yescharacteristic, direct product factor
30C5×D3×D17—76no—
31C2×C52×C17—211no—
32C52×D17—211no—
33C52×D17D2111yescharacteristic, direct product factor
34D357C2×C5211yescharacteristic, complemented
35C17×D21C2×C5211yescharacteristic, complemented
36C3×C7×D17C2×C5211yescharacteristic, complemented
37C2×C52×D7—511noHall
38C5×C7×C17C2×C5×D316yescomplemented
39C3×C52×C7C2×D1711yescharacteristic, complemented, Hall
40C5×D51—76no—
41C5×D3×C17—76no—
42C3×C5×D17C5×D716yescomplemented
43D7×D17—31noHall
44C52×C17C2×D2111yescharacteristic, complemented, Hall
45C2×C5×D21—176no—
46C3×C7×C17C22×C5211yescharacteristic, complemented, Hall
47C2×C52×C7—171no—
48C52×D7—31no—
49C52×D7—511no—
50C2×C5×D17—216no—
51C2×C52×D3—1191noHall
52C3×C5×C17C2×C5×D716yescomplemented
53D119—31no—
54C7×D17C52×D311yescharacteristic, complemented
55D7×C17—31no—
56C2×C3×C5×C7—176no—
57C5×D21—176no—
58C5×D21C5×D1716yesdirect product factor
59D3×D17—71noHall
60C52×C7D3×D1711yescharacteristic, complemented, Hall
61C2×C5×C17—216no—
62C5×D17—216no—
63C5×D17C5×D2116yesdirect product factor
64C2×C3×C52—171no—
65C52×D3—71no—
66C52×D3—1191no—
67C2×C5×D7—516no—
68C7×C17C2×C52×D311yescharacteristic, complemented, Hall
69C3×C5×C7C2×C5×D1716yescomplemented
70D51—71no—
71C3×D17C52×D711yescharacteristic, complemented
72D3×C17—71no—
73C22×C52—3571noHall
74C5×C17C2×C5×D2116yescomplemented
75C2×D21—171noHall
76C3×C52D7×D1711yescharacteristic, complemented, Hall
77C2×C5×C7—176no—
78C5×D7—36no—
79C5×D7—516no—
80C2×D17—211noHall
81C2×C5×D3—1196no—
82C3×C17C2×C52×D711yescharacteristic, complemented, Hall
83C2×C52—171no—
84C2×C52—211no—
85C2×C52—3571no—
86C2×C3×C7—171no—
87D21—171no—
88D21C52×D1711yescharacteristic, direct product factor
89C5×C7C5×D3×D1716yescomplemented
90C2×C17—211no—
91D17—211no—
92D17C52×D2111yescharacteristic, direct product factor
93C2×C3×C5—176no—
94C5×D3—76no—
95C5×D3—1196no—
96C2×D7—511noHall
97C52D17×D2111yescharacteristic, direct product factor, Sylow
98C3×C7C2×C52×D1711yescharacteristic, complemented, Hall
99C22×C5—3576no—
100C17C2×C52×D2111yescharacteristic, complemented, Sylow
101C3×C5C5×D7×D1716yescomplemented
102C2×C7—171no—
103D7—31no—
104D7—511no—
105C2×D3—1191noHall
106C2×C5—176no—
107C2×C5—216no—
108C2×C5—3576no—
109C7C52×D3×D1711yescharacteristic, complemented, Sylow
110C2×C3—171no—
111D3—71no—
112D3—1191no—
113C5C5×D17×D2116yesdirect product factor
114C22—3571noSylow
115C3C52×D7×D1711yescharacteristic, complemented, Sylow
116C2—171no—
117C2—211no—
118C2—3571no—
subgroupG/H
center, hypercenterC52D17×D21
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×C7×D17C2semidirect
2. C52×C17×D21C2semidirect
3. C52×D357C2semidirect
5. C3×C52×C7×C17C22semidirect
6. C5×D17×D21C5direct (N × H)
9. C52×C7×D17D3semidirect
11. C5×D357C2×C5semidirect
12. C5×C17×D21C2×C5semidirect
13. C3×C5×C7×D17C2×C5semidirect
14. C52×C7×C17C2×D3semidirect
17. C3×C52×D17D7semidirect
20. C3×C5×C7×C17C22×C5semidirect
22. D17×D21C52direct (N × H)
23. C3×C52×C17C2×D7semidirect
26. C5×C7×D17C5×D3semidirect
29. C52×D21D17direct (N × H)
33. C52×D17D21direct (N × H)
34. D357C2×C52semidirect
35. C17×D21C2×C52semidirect
36. C3×C7×D17C2×C52semidirect
38. C5×C7×C17C2×C5×D3semidirect
39. C3×C52×C7C2×D17semidirect
42. C3×C5×D17C5×D7semidirect
44. C52×C17C2×D21semidirect
46. C3×C7×C17C22×C52semidirect
52. C3×C5×C17C2×C5×D7semidirect
54. C7×D17C52×D3semidirect
58. C5×D21C5×D17direct (N × H)
60. C52×C7D3×D17semidirect
63. C5×D17C5×D21direct (N × H)
68. C7×C17C2×C52×D3semidirect
69. C3×C5×C7C2×C5×D17semidirect
71. C3×D17C52×D7semidirect
74. C5×C17C2×C5×D21semidirect
76. C3×C52D7×D17semidirect
82. C3×C17C2×C52×D7semidirect
88. D21C52×D17direct (N × H)
89. C5×C7C5×D3×D17semidirect
92. D17C52×D21direct (N × H)
97. C52D17×D21direct (N × H)
98. C3×C7C2×C52×D17semidirect
100. C17C2×C52×D21semidirect
101. C3×C5C5×D7×D17semidirect
109. C7C52×D3×D17semidirect
113. C5C5×D17×D21direct (N × H)
115. C3C52×D7×D17semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C7×D172
C52×C17×D212
C52×D3572
C52×D7×D173
C5×D17×D215
C52×D3×D177
C2×C52×D2117