Finite Group Databasebeta

← C32×C5×C7×D35 #36348063

Subgroups — C32×C5×C7×D35 #36348063

Order 22050.

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

normal subgroups only

This group has 384 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×C52×C72C211yesmaximal, characteristic, complemented, Hall
2C3×C5×C7×D35C314yesmaximal, direct product factor
3C32×C7×D35C511yesmaximal, characteristic, direct product factor
4C32×C5×C7×D7—51nomaximal
5C3×C52×C72C2×C314yescomplemented
6C32×C5×D35C711yesmaximal, characteristic, direct product factor
7C32×C5×C7×D5—71nomaximal
8C5×C7×D35C3211yescharacteristic, direct product factor, Hall
9C32×C5×C72—22no—
10C32×C5×C72D511yescharacteristic, complemented
11C32×C5×C72C2×C511yescharacteristic, complemented
12C32×C52×C7—23no—
13C32×C52×C7D711yescharacteristic, complemented
14C32×C52×C7C2×C711yescharacteristic, complemented
15C3×C7×D35C3×C514yesdirect product factor
16C3×C5×C7×D7—54no—
17C52×C72C2×C3211yescharacteristic, complemented, Hall
18C3×C5×D35C3×C714yesdirect product factor
19C3×C5×C7×D5—74no—
20C32×C7×D7—51noHall
21C3×C5×C72—28no—
22C3×C5×C72C3×D514yescomplemented
23C3×C5×C72C2×C3×C514yescomplemented
24C2×C32×C5×C7—351no—
25C32×D35C5×C711yescharacteristic, direct product factor
26C32×C7×D5—71no—
27C32×C5×D7—51no—
28C3×C52×C7—212no—
29C3×C52×C7C3×D714yescomplemented
30C3×C52×C7C2×C3×C714yescomplemented
31C7×D35C32×C511yescharacteristic, direct product factor
32C5×C7×D7—51no—
33C32×C5×D5—71noHall
34C32×C72C5×D511yescharacteristic, complemented, Hall
35C5×D35C32×C711yescharacteristic, direct product factor
36C5×C7×D5—71no—
37C32×C5×C7—212no—
38C32×C5×C7—23no—
39C32×C5×C7—23no—
40C32×C5×C7—22no—
41C32×C5×C7—22no—
42C32×C5×C7C7×D511yescharacteristic, complemented
43C32×C5×C7C5×D711yescharacteristic, complemented
44C32×C5×C7D3511yescharacteristic, direct product factor
45C32×C5×C7C2×C5×C711yescharacteristic, complemented
46C3×C7×D7—54no—
47C5×C72—22no—
48C5×C72C32×D511yescharacteristic, complemented
49C5×C72C2×C32×C511yescharacteristic, complemented
50C32×C52C7×D711yescharacteristic, complemented, Hall
51C2×C3×C5×C7—354no—
52C3×D35C3×C5×C714yesdirect product factor
53C3×C7×D5—74no—
54C3×C5×D7—54no—
55C52×C7—23no—
56C52×C7C32×D711yescharacteristic, complemented
57C52×C7C2×C32×C711yescharacteristic, complemented
58C3×C5×D5—74no—
59C3×C72C3×C5×D514yescomplemented
60C2×C32×C7—351no—
61C32×D7—51no—
62C3×C5×C7—248no—
63C3×C5×C7—28no—
64C3×C5×C7—28no—
65C3×C5×C7—212no—
66C3×C5×C7—212no—
67C3×C5×C7C3×C5×D714yescomplemented
68C3×C5×C7C3×C7×D514yescomplemented
69C3×C5×C7C3×D3514yesdirect product factor
70C3×C5×C7C2×C3×C5×C714yescomplemented
71C7×D7—51noHall
72C2×C32×C5—351no—
73C32×D5—71no—
74C3×C52C3×C7×D714yescomplemented
75C2×C5×C7—351no—
76D35C32×C5×C711yescharacteristic, direct product factor
77C5×D7—51no—
78C7×D5—71no—
79C32×C7—23no—
80C32×C7C5×C7×D511yescharacteristic, complemented
81C32×C7C5×D3511yescharacteristic, direct product factor
82C5×D5—71noHall
83C72C32×C5×D511yescharacteristic, complemented, Sylow
84C32×C5—22no—
85C32×C5C5×C7×D711yescharacteristic, complemented
86C32×C5C7×D3511yescharacteristic, direct product factor
87C2×C3×C7—354no—
88C3×D7—54no—
89C5×C7—212no—
90C5×C7—22no—
91C5×C7—22no—
92C5×C7—23no—
93C5×C7—23no—
94C5×C7C32×C5×D711yescharacteristic, complemented
95C5×C7C32×C7×D511yescharacteristic, complemented
96C5×C7C32×D3511yescharacteristic, direct product factor
97C5×C7C2×C32×C5×C711yescharacteristic, complemented
98C2×C3×C5—354no—
99C3×D5—74no—
100C52C32×C7×D711yescharacteristic, complemented, Sylow
101C3×C7—212no—
102C3×C7C3×C5×C7×D514yescomplemented
103C3×C7C3×C5×D3514yesdirect product factor
104C2×C32—351noHall
105C3×C5—28no—
106C3×C5C3×C5×C7×D714yescomplemented
107C3×C5C3×C7×D3514yesdirect product factor
108C2×C7—351no—
109D7—51no—
110C2×C5—351no—
111D5—71no—
112C32C5×C7×D3511yescharacteristic, direct product factor, Sylow
113C7—23no—
114C7C32×C5×C7×D511yescharacteristic, complemented
115C7C32×C5×D3511yescharacteristic, direct product factor
116C2×C3—354no—
117C5—22no—
118C5C32×C5×C7×D711yescharacteristic, complemented
119C5C32×C7×D3511yescharacteristic, direct product factor
120C3C3×C5×C7×D3514yesdirect product factor
121C2—351noSylow
subgroupG/H
center, hypercenterC32×C5×C7D35
commutator, cosocle, hypocenterC5×C7C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C5×C7
UCSC1 ◁ C32×C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
2. C3×C5×C7×D35C3direct (N × H)
3. C32×C7×D35C5direct (N × H)
5. C3×C52×C72C2×C3semidirect
6. C32×C5×D35C7direct (N × H)
8. C5×C7×D35C32direct (N × H)
10. C32×C5×C72D5semidirect
11. C32×C5×C72C2×C5semidirect
13. C32×C52×C7D7semidirect
14. C32×C52×C7C2×C7semidirect
15. C3×C7×D35C3×C5direct (N × H)
17. C52×C72C2×C32semidirect
18. C3×C5×D35C3×C7direct (N × H)
22. C3×C5×C72C3×D5semidirect
23. C3×C5×C72C2×C3×C5semidirect
25. C32×D35C5×C7direct (N × H)
29. C3×C52×C7C3×D7semidirect
30. C3×C52×C7C2×C3×C7semidirect
31. C7×D35C32×C5direct (N × H)
34. C32×C72C5×D5semidirect
35. C5×D35C32×C7direct (N × H)
42. C32×C5×C7C7×D5semidirect
43. C32×C5×C7C5×D7semidirect
44. C32×C5×C7D35direct (N × H)
45. C32×C5×C7C2×C5×C7semidirect
48. C5×C72C32×D5semidirect
49. C5×C72C2×C32×C5semidirect
50. C32×C52C7×D7semidirect
52. C3×D35C3×C5×C7direct (N × H)
56. C52×C7C32×D7semidirect
57. C52×C7C2×C32×C7semidirect
59. C3×C72C3×C5×D5semidirect
67. C3×C5×C7C3×C5×D7semidirect
68. C3×C5×C7C3×C7×D5semidirect
69. C3×C5×C7C3×D35direct (N × H)
70. C3×C5×C7C2×C3×C5×C7semidirect
74. C3×C52C3×C7×D7semidirect
76. D35C32×C5×C7direct (N × H)
80. C32×C7C5×C7×D5semidirect
81. C32×C7C5×D35direct (N × H)
83. C72C32×C5×D5semidirect
85. C32×C5C5×C7×D7semidirect
86. C32×C5C7×D35direct (N × H)
94. C5×C7C32×C5×D7semidirect
95. C5×C7C32×C7×D5semidirect
96. C5×C7C32×D35direct (N × H)
97. C5×C7C2×C32×C5×C7semidirect
100. C52C32×C7×D7semidirect
102. C3×C7C3×C5×C7×D5semidirect
103. C3×C7C3×C5×D35direct (N × H)
106. C3×C5C3×C5×C7×D7semidirect
107. C3×C5C3×C7×D35direct (N × H)
112. C32C5×C7×D35direct (N × H)
114. C7C32×C5×C7×D5semidirect
115. C7C32×C5×D35direct (N × H)
118. C5C32×C5×C7×D7semidirect
119. C5C32×C7×D35direct (N × H)
120. C3C3×C5×C7×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C722
C3×C5×C7×D353
C32×C7×D355
C32×C5×C7×D75
C32×C5×D357
C32×C5×C7×D57