Finite Group Databasebeta

← C32×D5×D133 #37561518

Subgroups — C32×D5×D133 #37561518

Order 23940.

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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×C5×D133C211yesmaximal, characteristic, complemented
2C32×C7×D5×C19C211yesmaximal, characteristic, complemented
3C32×D665C211yesmaximal, characteristic, complemented
4C3×D5×D133C314yesmaximal, direct product factor
5C32×C5×C7×C19C2211yescharacteristic, complemented, Hall
6C2×C32×D133—51nomaximal, Hall
7C3×D665C2×C314yescomplemented
8C3×C7×D5×C19C2×C314yescomplemented
9C3×C5×D133C2×C314yescomplemented
10C32×D5×D19—71nomaximal, Hall
11D5×D133C3211yescharacteristic, direct product factor, Hall
12C32×D133—51no—
13C32×D133D511yescharacteristic, direct product factor
14C2×C32×C7×C19—51no—
15C3×C5×C7×C19C22×C314yescomplemented
16C32×D95—71no—
17C32×D5×C19D711yescharacteristic, complemented
18C32×C5×D19—71no—
19C2×C3×D133—54no—
20D665C2×C3211yescharacteristic, complemented
21C7×D5×C19C2×C3211yescharacteristic, complemented
22C5×D133C2×C3211yescharacteristic, complemented
23C32×D5×D7—191nomaximal, Hall
24C32×C7×C19C2×D511yescharacteristic, complemented, Hall
25C3×D5×D19—74no—
26C32×C5×C19C2×D711yescharacteristic, complemented, Hall
27C2×C3×C7×C19—54no—
28C3×D133—54no—
29C3×D133C3×D514yesdirect product factor
30C2×C32×D19—351noHall
31C5×C7×C19C22×C3211yescharacteristic, complemented, Hall
32C32×D35—191no—
33C32×C7×D5D1911yescharacteristic, complemented
34C32×C5×D7—191no—
35C3×D95—74no—
36C3×D5×C19C3×D714yescomplemented
37C3×C5×D19—74no—
38C2×D133—51noHall
39C3×D5×D7—194no—
40C3×C7×C19C2×C3×D514yescomplemented
41D5×D19—71noHall
42C2×C32×C19—51no—
43C32×D19—71no—
44C32×D19—351no—
45C32×C5×C7C2×D1911yescharacteristic, complemented, Hall
46C3×C5×C19C2×C3×D714yescomplemented
47C2×C7×C19—51no—
48D133—51no—
49D133C32×D511yescharacteristic, direct product factor
50C2×C32×D7—951noHall
51C2×C3×D19—354no—
52C3×D35—194no—
53C3×C7×D5C3×D1914yescomplemented
54C3×C5×D7—194no—
55D95—71no—
56C5×D19—71no—
57D5×C19C32×D711yescharacteristic, complemented
58C2×C32×D5—1331noHall
59C32×C19D5×D711yescharacteristic, complemented, Hall
60D5×D7—191noHall
61C7×C19C2×C32×D511yescharacteristic, complemented, Hall
62C2×C32×C7—51no—
63C32×D7—191no—
64C32×D7—951no—
65C2×C3×C19—54no—
66C3×D19—74no—
67C3×D19—354no—
68C3×C5×C7C2×C3×D1914yescomplemented
69C5×C19C2×C32×D711yescharacteristic, complemented, Hall
70C2×C32×C5—1331no—
71C32×D5—1331no—
72C32×D5D13311yescharacteristic, direct product factor
73C2×C3×D7—954no—
74C2×D19—351noHall
75D35—191no—
76C5×D7—191no—
77C7×D5C32×D1911yescharacteristic, complemented
78C32×C7D5×D1911yescharacteristic, complemented, Hall
79C2×C3×D5—1334no—
80C3×C19C3×D5×D714yescomplemented
81C32×C5C2×D13311yescharacteristic, complemented, Hall
82C2×C3×C7—54no—
83C3×D7—194no—
84C3×D7—954no—
85C2×C19—51no—
86D19—71no—
87D19—351no—
88C22×C32—6651noHall
89C5×C7C2×C32×D1911yescharacteristic, complemented, Hall
90C2×C3×C5—1334no—
91C3×D5—1334no—
92C3×D5C3×D13314yesdirect product factor
93C2×D7—951noHall
94C3×C7C3×D5×D1914yescomplemented
95C2×D5—1331noHall
96C19C32×D5×D711yescharacteristic, complemented, Sylow
97C2×C32—51no—
98C2×C32—1331no—
99C2×C32—6651no—
100C3×C5C2×C3×D13314yescomplemented
101C2×C7—51no—
102D7—191no—
103D7—951no—
104C22×C3—6654no—
105C2×C5—1331no—
106D5—1331no—
107D5C32×D13311yescharacteristic, direct product factor
108C32D5×D13311yescharacteristic, direct product factor, Sylow
109C7C32×D5×D1911yescharacteristic, complemented, Sylow
110C2×C3—54no—
111C2×C3—1334no—
112C2×C3—6654no—
113C5C2×C32×D13311yescharacteristic, complemented, Sylow
114C22—6651noSylow
115C3C3×D5×D13314yesdirect product factor
116C2—51no—
117C2—1331no—
118C2—6651no—
subgroupG/H
center, hypercenterC32D5×D133
commutator, cosocle, hypocenterC5×C7×C19C22×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C19C22
LCSG ▷ C5×C7×C19
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5×D133C2semidirect
2. C32×C7×D5×C19C2semidirect
3. C32×D665C2semidirect
4. C3×D5×D133C3direct (N × H)
5. C32×C5×C7×C19C22semidirect
7. C3×D665C2×C3semidirect
8. C3×C7×D5×C19C2×C3semidirect
9. C3×C5×D133C2×C3semidirect
11. D5×D133C32direct (N × H)
13. C32×D133D5direct (N × H)
15. C3×C5×C7×C19C22×C3semidirect
17. C32×D5×C19D7semidirect
20. D665C2×C32semidirect
21. C7×D5×C19C2×C32semidirect
22. C5×D133C2×C32semidirect
24. C32×C7×C19C2×D5semidirect
26. C32×C5×C19C2×D7semidirect
29. C3×D133C3×D5direct (N × H)
31. C5×C7×C19C22×C32semidirect
33. C32×C7×D5D19semidirect
36. C3×D5×C19C3×D7semidirect
40. C3×C7×C19C2×C3×D5semidirect
45. C32×C5×C7C2×D19semidirect
46. C3×C5×C19C2×C3×D7semidirect
49. D133C32×D5direct (N × H)
53. C3×C7×D5C3×D19semidirect
57. D5×C19C32×D7semidirect
59. C32×C19D5×D7semidirect
61. C7×C19C2×C32×D5semidirect
68. C3×C5×C7C2×C3×D19semidirect
69. C5×C19C2×C32×D7semidirect
72. C32×D5D133direct (N × H)
77. C7×D5C32×D19semidirect
78. C32×C7D5×D19semidirect
80. C3×C19C3×D5×D7semidirect
81. C32×C5C2×D133semidirect
89. C5×C7C2×C32×D19semidirect
92. C3×D5C3×D133direct (N × H)
94. C3×C7C3×D5×D19semidirect
96. C19C32×D5×D7semidirect
100. C3×C5C2×C3×D133semidirect
107. D5C32×D133direct (N × H)
108. C32D5×D133direct (N × H)
109. C7C32×D5×D19semidirect
113. C5C2×C32×D133semidirect
115. C3C3×D5×D133direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1332
C32×C7×D5×C192
C32×D6652
C3×D5×D1333
C2×C32×D1335
C32×D5×D197
C32×D5×D719