Finite Group Databasebeta

← C3×C7×D525 #36347776

Subgroups — C3×C7×D525 #36347776

Order 22050.

162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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×C72×C25C211yesmaximal, characteristic, complemented, Hall
2C7×D525C311yesmaximal, characteristic, direct product factor
3C3×C7×D175—31nomaximal
4C3×C7×D105—51nomaximal
5C3×C72×C25—21no—
6C3×C72×C25D311yescharacteristic, complemented
7C3×C72×C25C2×C311yescharacteristic, complemented
8C3×D525C711yesmaximal, characteristic, direct product factor
9C3×C7×D75—71nomaximal
10C7×D175—31noHall
11C32×C5×C72D511yescharacteristic
12C32×C7×C25—23no—
13C32×C7×C25D711yescharacteristic, complemented
14C32×C7×C25C2×C711yescharacteristic, complemented
15C7×D105—51no—
16C3×C7×D35—151no—
17C72×C25C3×D311yescharacteristic, complemented, Hall
18D525C3×C711yescharacteristic, direct product factor
19C7×D75—71no—
20C3×D175—31no—
21C3×C7×D25—211no—
22C3×C7×D21—251noHall
23C3×C5×C72—21no—
24C3×C5×C72C3×D511yescharacteristic
25C3×C5×C72D1511yescharacteristic
26C3×D105—51no—
27C3×C7×D15—351no—
28C3×C7×C25—26no—
29C3×C7×C25—21no—
30C3×C7×C25—21no—
31C3×C7×C25—23no—
32C3×C7×C25—23no—
33C3×C7×C25D3×C711yescharacteristic, complemented
34C3×C7×C25C3×D711yescharacteristic, complemented
35C3×C7×C25D2111yescharacteristic, complemented
36C3×C7×C25C2×C3×C711yescharacteristic, complemented
37C7×D35—151no—
38C3×D75—71noHall
39C32×C72D2511yescharacteristic, complemented, Hall
40D175—31no—
41C7×D25—211no—
42C32×C5×C7—23no—
43C32×C5×C7C7×D511yescharacteristic
44C32×C5×C7D3511yescharacteristic
45C7×D21—251no—
46C3×C7×D7—751no—
47C5×C72C3×D1511yescharacteristic
48C32×C25C7×D711yescharacteristic, complemented, Hall
49D105—51no—
50C7×D15—351no—
51C3×D35—151no—
52C3×C7×D5—1051no—
53C7×C25—23no—
54C7×C25C3×D3×C711yescharacteristic, complemented
55C7×C25C3×D2111yescharacteristic, complemented
56D75—71no—
57C3×D25—211no—
58C3×C72—21no—
59C3×C72C3×D2511yescharacteristic, complemented
60C3×C72D7511yescharacteristic, complemented
61C3×D21—251no—
62C3×D3×C7—1751no—
63C3×C5×C7—26no—
64C3×C5×C7—21no—
65C3×C5×C7—21no—
66C3×C5×C7—23no—
67C3×C5×C7—23no—
68C3×C5×C7C3×C7×D511yescharacteristic
69C3×C5×C7C3×D3511yescharacteristic
70C3×C5×C7C7×D1511yescharacteristic
71C3×C5×C7D10511yescharacteristic
72C7×D7—751noHall
73C3×D15—351no—
74C3×C25—21no—
75C3×C25C3×C7×D711yescharacteristic, complemented
76C3×C25C7×D2111yescharacteristic, complemented
77D35—151no—
78C7×D5—1051no—
79C32×C7—23no—
80C32×C7C7×D2511yescharacteristic, complemented
81C32×C7D17511yescharacteristic, complemented
82D25—211noHall
83C72C3×D7511yescharacteristic, complemented, Sylow
84C32×C5C7×D3511yescharacteristic
85C2×C3×C7—5251no—
86D21—251no—
87C3×D7—751no—
88D3×C7—1751no—
89C5×C7—23no—
90C5×C7C3×C7×D1511yescharacteristic
91C5×C7C3×D10511yescharacteristic
92D15—351no—
93C3×D5—1051no—
94C25C3×C7×D2111yescharacteristic, complemented, Sylow
95C3×C7—26no—
96C3×C7—21no—
97C3×C7—21no—
98C3×C7—23no—
99C3×C7—23no—
100C3×C7C3×C7×D2511yescharacteristic, complemented
101C3×C7C3×D17511yescharacteristic, complemented
102C3×C7C7×D7511yescharacteristic, complemented
103C3×C7D52511yescharacteristic, direct product factor
104C3×D3—1751noHall
105C3×C5—21no—
106C3×C5C3×C7×D3511yescharacteristic
107C3×C5C7×D10511yescharacteristic
108C2×C7—5251no—
109D7—751no—
110D5—1051no—
111C32C7×D17511yescharacteristic, complemented, Sylow
112C7—23no—
113C7C3×C7×D7511yescharacteristic, complemented
114C7C3×D52511yescharacteristic, direct product factor
115C2×C3—5251no—
116D3—1751no—
117C5C3×C7×D10511yescharacteristic
118C3—21no—
119C3C3×C7×D17511yescharacteristic, complemented
120C3C7×D52511yescharacteristic, direct product factor
121C2—5251noSylow
subgroupG/H
center, hypercenterC3×C7D525
commutator, cosocle, hypocenterC3×C7×C25C2×C3×C7
FrattiniC5C3×C7×D105
FittingC32×C72×C25C2
socleC32×C5×C72D5
LCSG ▷ C3×C7×C25
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C32×C72×C25C2semidirect
2. C7×D525C3direct (N × H)
6. C3×C72×C25D3semidirect
7. C3×C72×C25C2×C3semidirect
8. C3×D525C7direct (N × H)
13. C32×C7×C25D7semidirect
14. C32×C7×C25C2×C7semidirect
17. C72×C25C3×D3semidirect
18. D525C3×C7direct (N × H)
33. C3×C7×C25D3×C7semidirect
34. C3×C7×C25C3×D7semidirect
35. C3×C7×C25D21semidirect
36. C3×C7×C25C2×C3×C7semidirect
39. C32×C72D25semidirect
48. C32×C25C7×D7semidirect
54. C7×C25C3×D3×C7semidirect
55. C7×C25C3×D21semidirect
59. C3×C72C3×D25semidirect
60. C3×C72D75semidirect
75. C3×C25C3×C7×D7semidirect
76. C3×C25C7×D21semidirect
80. C32×C7C7×D25semidirect
81. C32×C7D175semidirect
83. C72C3×D75semidirect
94. C25C3×C7×D21semidirect
100. C3×C7C3×C7×D25semidirect
101. C3×C7C3×D175semidirect
102. C3×C7C7×D75semidirect
103. C3×C7D525direct (N × H)
111. C32C7×D175semidirect
113. C7C3×C7×D75semidirect
114. C7C3×D525direct (N × H)
119. C3C3×C7×D175semidirect
120. C3C7×D525direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C72×C252
C7×D5253
C3×C7×D1753
C3×C7×D1055
C3×D5257
C3×C7×D757