Finite Group Databasebeta

← C5×C7×C3⋊D105 #36348081

Subgroups — C5×C7×C3⋊D105 #36348081

Order 22050.

384 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 100 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
2C5×C7×D105—34nomaximal
3C7×C3⋊D105C511yesmaximal, characteristic, direct product factor
4C5×C7×C3⋊D21—51nomaximal
5C3×C52×C72D314yescomplemented
6C5×C3⋊D105C711yesmaximal, characteristic, direct product factor
7C5×C7×C3⋊D15—71nomaximal
8C5×C7×D35—91noHall
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
15C7×D105—34no—
16C5×C7×D21—154no—
17C52×C72C3⋊D311yescharacteristic, complemented, Hall
18C5×D105—34no—
19C5×C7×D15—214no—
20C7×C3⋊D21—51noHall
21C3×C5×C72—28no—
22C3×C5×C72C5×D314yescomplemented
23C3×C5×C72D1514yescomplemented
24C3⋊D105C5×C711yescharacteristic, direct product factor
25C7×C3⋊D15—71no—
26C5×C3⋊D21—51no—
27C5×C7×C3⋊D3—351no—
28C3×C52×C7—212no—
29C3×C52×C7D3×C714yescomplemented
30C3×C52×C7D2114yescomplemented
31C7×D35—91no—
32C5×C7×D7—451no—
33C5×C3⋊D15—71noHall
34C32×C72C5×D511yescharacteristic, complemented, Hall
35C5×D35—91no—
36C5×C7×D5—631no—
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, complemented
45C32×C5×C7C2×C5×C711yescharacteristic, complemented
46C7×D21—154no—
47C5×C72—22no—
48C5×C72C5×C3⋊D311yescharacteristic, complemented
49C5×C72C3⋊D1511yescharacteristic, complemented
50C32×C52C7×D711yescharacteristic, complemented, Hall
51D105—34no—
52C7×D15—214no—
53C5×D21—154no—
54C5×D3×C7—1054no—
55C52×C7—23no—
56C52×C7C7×C3⋊D311yescharacteristic, complemented
57C52×C7C3⋊D2111yescharacteristic, complemented
58C5×D15—214no—
59C3×C72C5×D1514yescomplemented
60C3⋊D21—51no—
61C7×C3⋊D3—351no—
62C3×C5×C7—248no—
63C3×C5×C7—28no—
64C3×C5×C7—28no—
65C3×C5×C7—212no—
66C3×C5×C7—212no—
67C3×C5×C7C5×D3×C714yescomplemented
68C3×C5×C7C5×D2114yescomplemented
69C3×C5×C7C7×D1514yescomplemented
70C3×C5×C7D10514yescomplemented
71C7×D7—451noHall
72C3⋊D15—71no—
73C5×C3⋊D3—351no—
74C3×C52C7×D2114yescomplemented
75C2×C5×C7—3151no—
76D35—91no—
77C5×D7—451no—
78C7×D5—631no—
79C32×C7—23no—
80C32×C7C5×C7×D511yescharacteristic, complemented
81C32×C7C5×D3511yescharacteristic, complemented
82C5×D5—631noHall
83C72C5×C3⋊D1511yescharacteristic, complemented, Sylow
84C32×C5—22no—
85C32×C5C5×C7×D711yescharacteristic, complemented
86C32×C5C7×D3511yescharacteristic, complemented
87D21—154no—
88D3×C7—1054no—
89C5×C7—212no—
90C5×C7—22no—
91C5×C7—22no—
92C5×C7—23no—
93C5×C7—23no—
94C5×C7C5×C7×C3⋊D311yescharacteristic, complemented
95C5×C7C5×C3⋊D2111yescharacteristic, complemented
96C5×C7C7×C3⋊D1511yescharacteristic, complemented
97C5×C7C3⋊D10511yescharacteristic, direct product factor
98D15—214no—
99C5×D3—1054no—
100C52C7×C3⋊D2111yescharacteristic, complemented, Sylow
101C3×C7—212no—
102C3×C7C5×C7×D1514yescomplemented
103C3×C7C5×D10514yescomplemented
104C3⋊D3—351noHall
105C3×C5—28no—
106C3×C5C5×C7×D2114yescomplemented
107C3×C5C7×D10514yescomplemented
108C2×C7—3151no—
109D7—451no—
110C2×C5—3151no—
111D5—631no—
112C32C5×C7×D3511yescharacteristic, complemented, Sylow
113C7—23no—
114C7C5×C7×C3⋊D1511yescharacteristic, complemented
115C7C5×C3⋊D10511yescharacteristic, direct product factor
116D3—1054no—
117C5—22no—
118C5C5×C7×C3⋊D2111yescharacteristic, complemented
119C5C7×C3⋊D10511yescharacteristic, direct product factor
120C3C5×C7×D10514yescomplemented
121C2—3151noSylow
subgroupG/H
center, hypercenterC5×C7C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C2×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C72C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C72C2semidirect
3. C7×C3⋊D105C5direct (N × H)
5. C3×C52×C72D3semidirect
6. C5×C3⋊D105C7direct (N × H)
10. C32×C5×C72D5semidirect
11. C32×C5×C72C2×C5semidirect
13. C32×C52×C7D7semidirect
14. C32×C52×C7C2×C7semidirect
17. C52×C72C3⋊D3semidirect
22. C3×C5×C72C5×D3semidirect
23. C3×C5×C72D15semidirect
24. C3⋊D105C5×C7direct (N × H)
29. C3×C52×C7D3×C7semidirect
30. C3×C52×C7D21semidirect
34. C32×C72C5×D5semidirect
42. C32×C5×C7C7×D5semidirect
43. C32×C5×C7C5×D7semidirect
44. C32×C5×C7D35semidirect
45. C32×C5×C7C2×C5×C7semidirect
48. C5×C72C5×C3⋊D3semidirect
49. C5×C72C3⋊D15semidirect
50. C32×C52C7×D7semidirect
56. C52×C7C7×C3⋊D3semidirect
57. C52×C7C3⋊D21semidirect
59. C3×C72C5×D15semidirect
67. C3×C5×C7C5×D3×C7semidirect
68. C3×C5×C7C5×D21semidirect
69. C3×C5×C7C7×D15semidirect
70. C3×C5×C7D105semidirect
74. C3×C52C7×D21semidirect
80. C32×C7C5×C7×D5semidirect
81. C32×C7C5×D35semidirect
83. C72C5×C3⋊D15semidirect
85. C32×C5C5×C7×D7semidirect
86. C32×C5C7×D35semidirect
94. C5×C7C5×C7×C3⋊D3semidirect
95. C5×C7C5×C3⋊D21semidirect
96. C5×C7C7×C3⋊D15semidirect
97. C5×C7C3⋊D105direct (N × H)
100. C52C7×C3⋊D21semidirect
102. C3×C7C5×C7×D15semidirect
103. C3×C7C5×D105semidirect
106. C3×C5C5×C7×D21semidirect
107. C3×C5C7×D105semidirect
112. C32C5×C7×D35semidirect
114. C7C5×C7×C3⋊D15semidirect
115. C7C5×C3⋊D105direct (N × H)
118. C5C5×C7×C3⋊D21semidirect
119. C5C7×C3⋊D105direct (N × H)
120. C3C5×C7×D105semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C722
C5×C7×D1053
C7×C3⋊D1055
C5×C7×C3⋊D215
C5×C3⋊D1057
C5×C7×C3⋊D157