Finite Group Databasebeta

← C32×C7×D5×D29 #49141547

Subgroups — C32×C7×D5×D29 #49141547

Order 36540.

240 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 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×C7×D29C211yesmaximal, characteristic, complemented
2C32×C7×D5×C29C211yesmaximal, characteristic, complemented
3C32×C7×D145C211yesmaximal, characteristic, complemented
4C3×C7×D5×D29C314yesmaximal, direct product factor
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C2×C32×C7×D29—51nomaximal, Hall
7C3×C7×D145C2×C314yescomplemented
8C3×C7×D5×C29C2×C314yescomplemented
9C3×C5×C7×D29C2×C314yescomplemented
10C32×D5×D29C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D29C3211yescharacteristic, direct product factor, Hall
12C32×C7×D29—51no—
13C32×C7×D29D511yescharacteristic, direct product factor
14C2×C32×C7×C29—51no—
15C3×C5×C7×C29C22×C314yescomplemented
16C32×D145C2×C711yescharacteristic, complemented
17C32×D5×C29C2×C711yescharacteristic, complemented
18C32×C5×D29C2×C711yescharacteristic, complemented
19C2×C3×C7×D29—54no—
20C7×D145C2×C3211yescharacteristic, complemented
21C7×D5×C29C2×C3211yescharacteristic, complemented
22C5×C7×D29C2×C3211yescharacteristic, complemented
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24C3×D5×D29C3×C714yesdirect product factor
25C32×C5×C29C22×C711yescharacteristic, complemented, Hall
26C2×C32×C7×D5—291nomaximal, Hall
27C2×C3×C7×C29—54no—
28C3×C7×D29—54no—
29C3×C7×D29C3×D514yesdirect product factor
30C2×C32×D29—51noHall
31C5×C7×C29C22×C3211yescharacteristic, complemented, Hall
32C3×D145C2×C3×C714yescomplemented
33C3×D5×C29C2×C3×C714yescomplemented
34C3×C5×D29C2×C3×C714yescomplemented
35C2×C7×D29—51noHall
36C2×C32×C5×C7—291no—
37C32×C7×D5—291no—
38C32×C7×D5D2911yescharacteristic, direct product factor
39C3×C7×C29C2×C3×D514yescomplemented
40D5×D29C32×C711yescharacteristic, direct product factor, Hall
41C2×C32×C29—51no—
42C32×D29—51no—
43C32×D29C7×D511yescharacteristic, direct product factor
44C3×C5×C29C22×C3×C714yescomplemented
45C2×C3×C7×D5—294no—
46C2×C7×C29—51no—
47C7×D29—51no—
48C7×D29C32×D511yescharacteristic, direct product factor
49C2×C3×D29—54no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51D145C2×C32×C711yescharacteristic, complemented
52C5×D29C2×C32×C711yescharacteristic, complemented
53D5×C29C2×C32×C711yescharacteristic, complemented
54C32×C29C2×C7×D511yescharacteristic, complemented, Hall
55C22×C32×C7—1451noHall
56C2×C3×C5×C7—294no—
57C3×C7×D5—294no—
58C3×C7×D5C3×D2914yesdirect product factor
59C7×C29C2×C32×D511yescharacteristic, complemented, Hall
60C2×C32×D5—291noHall
61C2×C3×C29—54no—
62C3×D29—54no—
63C3×D29C3×C7×D514yesdirect product factor
64C5×C29C22×C32×C711yescharacteristic, complemented, Hall
65C2×C7×D5—291noHall
66C2×C32×C7—51no—
67C2×C32×C7—291no—
68C2×C32×C7—1451no—
69C2×D29—51noHall
70C3×C5×C7C2×C3×D2914yescomplemented
71C2×C32×C5—291no—
72C32×D5—291no—
73C32×D5C7×D2911yescharacteristic, direct product factor
74C3×C29C2×C3×C7×D514yescomplemented
75C22×C3×C7—1454no—
76C2×C5×C7—291no—
77C7×D5—291no—
78C7×D5C32×D2911yescharacteristic, direct product factor
79C32×C7D5×D2911yescharacteristic, direct product factor, Hall
80C2×C3×D5—294no—
81C2×C29—51no—
82D29—51no—
83D29C32×C7×D511yescharacteristic, direct product factor
84C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86C2×C3×C7—294no—
87C2×C3×C7—1454no—
88C22×C32—1451noHall
89C5×C7C2×C32×D2911yescharacteristic, complemented, Hall
90C2×C3×C5—294no—
91C3×D5—294no—
92C3×D5C3×C7×D2914yesdirect product factor
93C29C2×C32×C7×D511yescharacteristic, complemented, Sylow
94C22×C7—1451noHall
95C3×C7C3×D5×D2914yesdirect product factor
96C2×D5—291noHall
97C2×C32—51no—
98C2×C32—291no—
99C2×C32—1451no—
100C3×C5C2×C3×C7×D2914yescomplemented
101C2×C7—51no—
102C2×C7—291no—
103C2×C7—1451no—
104C22×C3—1454no—
105C2×C5—291no—
106D5—291no—
107D5C32×C7×D2911yescharacteristic, direct product factor
108C32C7×D5×D2911yescharacteristic, direct product factor, Sylow
109C7C32×D5×D2911yescharacteristic, direct product factor, Sylow
110C2×C3—54no—
111C2×C3—294no—
112C2×C3—1454no—
113C5C2×C32×C7×D2911yescharacteristic, complemented, Sylow
114C22—1451noSylow
115C3C3×C7×D5×D2914yesdirect product factor
116C2—51no—
117C2—291no—
118C2—1451no—
subgroupG/H
center, hypercenterC32×C7D5×D29
commutator, cosocle, hypocenterC5×C29C22×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C5×C29
UCSC1 ◁ C32×C7

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×D29C2semidirect
2. C32×C7×D5×C29C2semidirect
3. C32×C7×D145C2semidirect
4. C3×C7×D5×D29C3direct (N × H)
5. C32×C5×C7×C29C22semidirect
7. C3×C7×D145C2×C3semidirect
8. C3×C7×D5×C29C2×C3semidirect
9. C3×C5×C7×D29C2×C3semidirect
10. C32×D5×D29C7direct (N × H)
11. C7×D5×D29C32direct (N × H)
13. C32×C7×D29D5direct (N × H)
15. C3×C5×C7×C29C22×C3semidirect
16. C32×D145C2×C7semidirect
17. C32×D5×C29C2×C7semidirect
18. C32×C5×D29C2×C7semidirect
20. C7×D145C2×C32semidirect
21. C7×D5×C29C2×C32semidirect
22. C5×C7×D29C2×C32semidirect
23. C32×C7×C29C2×D5semidirect
24. C3×D5×D29C3×C7direct (N × H)
25. C32×C5×C29C22×C7semidirect
29. C3×C7×D29C3×D5direct (N × H)
31. C5×C7×C29C22×C32semidirect
32. C3×D145C2×C3×C7semidirect
33. C3×D5×C29C2×C3×C7semidirect
34. C3×C5×D29C2×C3×C7semidirect
38. C32×C7×D5D29direct (N × H)
39. C3×C7×C29C2×C3×D5semidirect
40. D5×D29C32×C7direct (N × H)
43. C32×D29C7×D5direct (N × H)
44. C3×C5×C29C22×C3×C7semidirect
48. C7×D29C32×D5direct (N × H)
50. C32×C5×C7C2×D29semidirect
51. D145C2×C32×C7semidirect
52. C5×D29C2×C32×C7semidirect
53. D5×C29C2×C32×C7semidirect
54. C32×C29C2×C7×D5semidirect
58. C3×C7×D5C3×D29direct (N × H)
59. C7×C29C2×C32×D5semidirect
63. C3×D29C3×C7×D5direct (N × H)
64. C5×C29C22×C32×C7semidirect
70. C3×C5×C7C2×C3×D29semidirect
73. C32×D5C7×D29direct (N × H)
74. C3×C29C2×C3×C7×D5semidirect
78. C7×D5C32×D29direct (N × H)
79. C32×C7D5×D29direct (N × H)
83. D29C32×C7×D5direct (N × H)
84. C32×C5C2×C7×D29semidirect
89. C5×C7C2×C32×D29semidirect
92. C3×D5C3×C7×D29direct (N × H)
93. C29C2×C32×C7×D5semidirect
95. C3×C7C3×D5×D29direct (N × H)
100. C3×C5C2×C3×C7×D29semidirect
107. D5C32×C7×D29direct (N × H)
108. C32C7×D5×D29direct (N × H)
109. C7C32×D5×D29direct (N × H)
113. C5C2×C32×C7×D29semidirect
115. C3C3×C7×D5×D29direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C32×C7×D5×C292
C32×C7×D1452
C3×C7×D5×D293
C2×C32×C7×D295
C32×D5×D297
C2×C32×C7×D529