Finite Group Databasebeta

← D7×C29×C3⋊D15 #49141650

Subgroups — D7×C29×C3⋊D15 #49141650

Order 36540.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×D7×C29C211yesmaximal, characteristic, complemented
2C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
3C29×C3⋊D105C211yesmaximal, characteristic, complemented
4D7×C29×D15—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6D7×C3⋊D3×C29—51nomaximal, Hall
7C29×D105—34no—
8C7×C29×D15—34no—
9C3×C5×D7×C29D314yescomplemented
10C2×C29×C3⋊D15—71nomaximal, Hall
11D5×D7×C29—91noHall
12C29×C3⋊D21—51no—
13C7×C3⋊D3×C29—51no—
14C32×D7×C29D511yescharacteristic, complemented
15C3×C5×C7×C29C2×D314yescomplemented
16C29×C3⋊D15—71no—
17C29×C3⋊D15D711yescharacteristic, direct product factor
18C2×C32×C5×C29—71no—
19D3×D7×C29—154no—
20C29×D35—91no—
21C7×D5×C29—91no—
22C5×D7×C29C3⋊D311yescharacteristic, complemented
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24C2×C29×D15—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26D7×C3⋊D15C2911yesmaximal, characteristic, direct product factor, Hall
27C29×D21—154no—
28D3×C7×C29—154no—
29C3×D7×C29D1514yescomplemented
30C2×C3⋊D3×C29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C2×C3×C5×C29—74no—
33C29×D15—34no—
34C29×D15—214no—
35C2×D7×C29—451noHall
36C3⋊D105C2×C2911yescharacteristic, complemented
37C7×C3⋊D15C2×C2911yescharacteristic, complemented
38C32×C5×D7C2×C2911yescharacteristic, complemented
39C3×C7×C29C2×D1514yescomplemented
40C2×D5×C29—631noHall
41C2×C32×C29—71no—
42C3⋊D3×C29—51no—
43C3⋊D3×C29—351no—
44C3×C5×C29D3×D714yescomplemented
45D7×D15—34no—
46C2×C7×C29—451no—
47D7×C29—451no—
48D7×C29C3⋊D1511yescharacteristic, direct product factor
49C2×D3×C29—1054no—
50C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
51C2×C5×C29—71no—
52D5×C29—91no—
53D5×C29—631no—
54C32×C29D5×D711yescharacteristic, complemented, Hall
55D7×C3⋊D3—51noHall
56D105—34no—
57C7×D15—34no—
58C3×C5×D7D3×C2914yescomplemented
59C7×C29C2×C3⋊D1511yescharacteristic, complemented, Hall
60C2×C3⋊D15—71noHall
61C2×C3×C29—74no—
62D3×C29—154no—
63D3×C29—1054no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65D5×D7—91noHall
66C3⋊D21—51no—
67C7×C3⋊D3—51no—
68C32×D7D5×C2911yescharacteristic, complemented
69C22×C29—3151noHall
70C3×C5×C7C2×D3×C2914yescomplemented
71C2×C32×C5—71no—
72C3⋊D15—71no—
73C3⋊D15D7×C2911yescharacteristic, direct product factor
74C3×C29D7×D1514yescomplemented
75D3×D7—154no—
76D35—91no—
77C5×D7C3⋊D3×C2911yescharacteristic, complemented
78C7×D5—91no—
79C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
80C2×D15—214no—
81C2×C29—71no—
82C2×C29—451no—
83C2×C29—3151no—
84C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
85D21—154no—
86C3×D7C29×D1514yescomplemented
87D3×C7—154no—
88C2×C3⋊D3—351noHall
89C5×C7C2×C3⋊D3×C2911yescharacteristic, complemented, Hall
90C2×C3×C5—74no—
91D15—34no—
92D15—214no—
93C29D7×C3⋊D1511yescharacteristic, direct product factor, Sylow
94C2×D7—451noHall
95C3×C7C2×C29×D1514yescomplemented
96C2×D5—631noHall
97C2×C32—71no—
98C3⋊D3—51no—
99C3⋊D3—351no—
100C3×C5D3×D7×C2914yescomplemented
101C2×C7—451no—
102D7—451no—
103D7C29×C3⋊D1511yescharacteristic, direct product factor
104C2×D3—1054no—
105C2×C5—71no—
106D5—91no—
107D5—631no—
108C32D5×D7×C2911yescharacteristic, complemented, Sylow
109C7C2×C29×C3⋊D1511yescharacteristic, complemented, Sylow
110C2×C3—74no—
111D3—154no—
112D3—1054no—
113C5D7×C3⋊D3×C2911yescharacteristic, complemented, Sylow
114C22—3151noSylow
115C3D7×C29×D1514yescomplemented
116C2—71no—
117C2—451no—
118C2—3151no—
subgroupG/H
center, hypercenterC29D7×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C7C22×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C32×C5×D7×C29C2semidirect
2. C7×C29×C3⋊D15C2semidirect
3. C29×C3⋊D105C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C5×D7×C29D3semidirect
14. C32×D7×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
17. C29×C3⋊D15D7direct (N × H)
22. C5×D7×C29C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
26. D7×C3⋊D15C29direct (N × H)
29. C3×D7×C29D15semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
36. C3⋊D105C2×C29semidirect
37. C7×C3⋊D15C2×C29semidirect
38. C32×C5×D7C2×C29semidirect
39. C3×C7×C29C2×D15semidirect
44. C3×C5×C29D3×D7semidirect
48. D7×C29C3⋊D15direct (N × H)
50. C32×C5×C7C22×C29semidirect
54. C32×C29D5×D7semidirect
58. C3×C5×D7D3×C29semidirect
59. C7×C29C2×C3⋊D15semidirect
64. C5×C29D7×C3⋊D3semidirect
68. C32×D7D5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
73. C3⋊D15D7×C29direct (N × H)
74. C3×C29D7×D15semidirect
77. C5×D7C3⋊D3×C29semidirect
79. C32×C7C2×D5×C29semidirect
84. C32×C5C2×D7×C29semidirect
86. C3×D7C29×D15semidirect
89. C5×C7C2×C3⋊D3×C29semidirect
93. C29D7×C3⋊D15direct (N × H)
95. C3×C7C2×C29×D15semidirect
100. C3×C5D3×D7×C29semidirect
103. D7C29×C3⋊D15direct (N × H)
108. C32D5×D7×C29semidirect
109. C7C2×C29×C3⋊D15semidirect
113. C5D7×C3⋊D3×C29semidirect
115. C3D7×C29×D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D7×C292
C7×C29×C3⋊D152
C29×C3⋊D1052
D7×C29×D153
D7×C3⋊D3×C295
C2×C29×C3⋊D157
D7×C3⋊D1529