Finite Group Databasebeta

← C2×C5×C3⋊D105 #20263158

Subgroups — C2×C5×C3⋊D105 #20263158

Order 6300.

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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
1C5×C3⋊D105C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C5×D105—34nomaximal
4C32×C52×C7C2211yescharacteristic, complemented, Hall
5C2×C3⋊D105C511yesmaximal, characteristic, direct product factor
6C2×C5×C3⋊D21—51nomaximal
7C2×C3×C52×C7D314yescomplemented
8C5×D105—38no—
9C2×C5×C3⋊D15—71nomaximal, Hall
10C2×C5×D35—91noHall
11C2×C32×C5×C7—22no—
12C2×C32×C5×C7D511yescharacteristic, complemented
13C2×C32×C5×C7C2×C511yescharacteristic, complemented
14C3⋊D105C2×C512yesdirect product factor
15C5×C3⋊D21—52no—
16C3×C52×C7C2×D314yescomplemented
17C2×C32×C52D711yescharacteristic, complemented
18C5×C3⋊D15—72no—
19C2×D105—34no—
20C2×C5×D21—154no—
21C2×C52×C7C3⋊D311yescharacteristic, complemented
22C5×D35—92no—
23C32×C5×C7—22no—
24C32×C5×C7C2×D511yescharacteristic, complemented
25C32×C5×C7C22×C511yescharacteristic, complemented
26C2×C5×D15—214no—
27C2×C3⋊D21—51noHall
28C32×C52C2×D711yescharacteristic, complemented, Hall
29C2×C3×C5×C7—28no—
30C2×C3×C5×C7C5×D314yescomplemented
31C2×C3×C5×C7D1514yescomplemented
32D105—38no—
33C5×D21—158no—
34C2×C3⋊D15—71no—
35C2×C5×C3⋊D3—351no—
36C52×C7C2×C3⋊D311yescharacteristic, complemented, Hall
37C2×C3×C52D2114yescomplemented
38C5×D15—218no—
39C2×D35—91no—
40C2×C5×D7—451no—
41C2×C32×C7C5×D511yescharacteristic, complemented
42C3⋊D21—52no—
43C3×C5×C7—28no—
44C3×C5×C7C2×C5×D314yescomplemented
45C3×C5×C7C2×D1514yescomplemented
46C2×C5×D5—631noHall
47C2×C32×C5—22no—
48C2×C32×C5C5×D711yescharacteristic, complemented
49C2×C32×C5D3511yescharacteristic, complemented
50C3⋊D15—72no—
51C5×C3⋊D3—352no—
52C2×D21—154no—
53C3×C52C2×D2114yescomplemented
54C2×C5×C7—22no—
55C2×C5×C7C5×C3⋊D311yescharacteristic, complemented
56C2×C5×C7C3⋊D1511yescharacteristic, complemented
57D35—92no—
58C5×D7—452no—
59C32×C7C2×C5×D511yescharacteristic, complemented, Hall
60C2×D15—214no—
61C2×C5×D3—1054no—
62C2×C52C3⋊D2111yescharacteristic, complemented
63C5×D5—632no—
64C32×C5—22no—
65C32×C5C2×C5×D711yescharacteristic, complemented
66C32×C5C2×D3511yescharacteristic, complemented
67C2×C3×C7C5×D1514yescomplemented
68D21—158no—
69C2×C3⋊D3—351noHall
70C5×C7—22no—
71C5×C7C2×C5×C3⋊D311yescharacteristic, complemented
72C5×C7C2×C3⋊D1511yescharacteristic, complemented
73C2×C3×C5—28no—
74C2×C3×C5C5×D2114yescomplemented
75C2×C3×C5D10514yescomplemented
76D15—218no—
77C5×D3—1058no—
78C2×D7—451noHall
79C52C2×C3⋊D2111yescharacteristic, complemented, Sylow
80C3×C7C2×C5×D1514yescomplemented
81C22×C5—3151no—
82C2×D5—631no—
83C2×C32C5×D3511yescharacteristic, complemented
84C3⋊D3—352no—
85C3×C5—28no—
86C3×C5C2×C5×D2114yescomplemented
87C3×C5C2×D10514yescomplemented
88C2×C7C5×C3⋊D1511yescharacteristic, complemented
89D7—452no—
90C2×D3—1054no—
91C2×C5—22no—
92C2×C5—3152no—
93C2×C5C5×C3⋊D2111yescharacteristic, complemented
94C2×C5C3⋊D10511yescharacteristic, direct product factor
95D5—632no—
96C32C2×C5×D3511yescharacteristic, complemented, Sylow
97C7C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
98C2×C3C5×D10514yescomplemented
99D3—1058no—
100C5—22no—
101C5C2×C5×C3⋊D2111yescharacteristic, complemented
102C5C2×C3⋊D10511yescharacteristic, direct product factor
103C22—3151noSylow
104C3C2×C5×D10514yescomplemented
105C2—3152no—
106C2C5×C3⋊D10511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊D105
commutator, hypocenterC32×C5×C7C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D105C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
4. C32×C52×C7C22semidirect
5. C2×C3⋊D105C5direct (N × H)
7. C2×C3×C52×C7D3semidirect
12. C2×C32×C5×C7D5semidirect
13. C2×C32×C5×C7C2×C5semidirect
14. C3⋊D105C2×C5direct (N × H)
16. C3×C52×C7C2×D3semidirect
17. C2×C32×C52D7semidirect
21. C2×C52×C7C3⋊D3semidirect
24. C32×C5×C7C2×D5semidirect
25. C32×C5×C7C22×C5semidirect
28. C32×C52C2×D7semidirect
30. C2×C3×C5×C7C5×D3semidirect
31. C2×C3×C5×C7D15semidirect
36. C52×C7C2×C3⋊D3semidirect
37. C2×C3×C52D21semidirect
41. C2×C32×C7C5×D5semidirect
44. C3×C5×C7C2×C5×D3semidirect
45. C3×C5×C7C2×D15semidirect
48. C2×C32×C5C5×D7semidirect
49. C2×C32×C5D35semidirect
53. C3×C52C2×D21semidirect
55. C2×C5×C7C5×C3⋊D3semidirect
56. C2×C5×C7C3⋊D15semidirect
59. C32×C7C2×C5×D5semidirect
62. C2×C52C3⋊D21semidirect
65. C32×C5C2×C5×D7semidirect
66. C32×C5C2×D35semidirect
67. C2×C3×C7C5×D15semidirect
71. C5×C7C2×C5×C3⋊D3semidirect
72. C5×C7C2×C3⋊D15semidirect
74. C2×C3×C5C5×D21semidirect
75. C2×C3×C5D105semidirect
79. C52C2×C3⋊D21semidirect
80. C3×C7C2×C5×D15semidirect
83. C2×C32C5×D35semidirect
86. C3×C5C2×C5×D21semidirect
87. C3×C5C2×D105semidirect
88. C2×C7C5×C3⋊D15semidirect
93. C2×C5C5×C3⋊D21semidirect
94. C2×C5C3⋊D105direct (N × H)
96. C32C2×C5×D35semidirect
97. C7C2×C5×C3⋊D15semidirect
98. C2×C3C5×D105semidirect
101. C5C2×C5×C3⋊D21semidirect
102. C5C2×C3⋊D105direct (N × H)
104. C3C2×C5×D105semidirect
106. C2C5×C3⋊D105direct (N × H)