Finite Group Databasebeta

← C2×C4×D105 #13132891

Subgroups — C2×C4×D105 #13132891

Order 1680.

216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×D105C211yesmaximal, characteristic
2C2×C3×C4×C5×C7C211yesmaximal, characteristic, complemented
3C2×Dic105C211yesmaximal, characteristic, complemented
4C4×D105C214yesmaximal, direct product factor
5C2×C4×D35—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic
7C2×D105C414yesdirect product factor
8C2×D105C2212yes—
9C3×C4×C5×C7C2212yescomplemented
10Dic105C2212yescomplemented
11C2×C4×D21—51nomaximal, Hall
12C22×D35—31no—
13C2×C4×C5×C7D311yescharacteristic, complemented
14C2×Dic35—31no—
15C4×D35—34no—
16C2×C4×D15—71nomaximal, Hall
17C2×C3×C5×C7C2×C412yescomplemented
18C2×C3×C5×C7C2311yescharacteristic
19D105C2×C414yesdirect product factor
20C22×D21—51no—
21C2×C3×C4×C7D511yescharacteristic, complemented
22C2×Dic21—51no—
23C4×D21—54no—
24C22×C5×C7C2×D311yescharacteristic
25C2×D35—34no—
26C2×D35—32no—
27C4×C5×C7C2×D312yescomplemented
28Dic35—32no—
29C22×D15—71no—
30C2×C3×C4×C5D711yescharacteristic, complemented
31C2×Dic15—71no—
32C4×D15—74no—
33C2×C4×D7—151noHall
34C3×C5×C7C22×C411yescharacteristic, complemented, Hall
35C22×C3×C7C2×D511yescharacteristic
36C2×D21—54no—
37C2×D21—52no—
38C3×C4×C7C2×D512yescomplemented
39Dic21—52no—
40C2×C4×D5—211noHall
41C2×C5×C7C4×D312yescomplemented
42C2×C5×C7C22×D311yescharacteristic
43D35—34no—
44C22×C3×C5C2×D711yescharacteristic
45C2×D15—74no—
46C2×D15—72no—
47C3×C4×C5C2×D712yescomplemented
48Dic15—72no—
49C22×D7—151no—
50C2×C4×C7D1511yescharacteristic, complemented
51C2×Dic7—151no—
52C4×D7—154no—
53C2×C4×D3—351noHall
54C2×C3×C7C4×D512yescomplemented
55C2×C3×C7C22×D511yescharacteristic
56D21—54no—
57C22×D5—211no—
58C2×C4×C5D2111yescharacteristic, complemented
59C2×Dic5—211no—
60C4×D5—214no—
61C5×C7C2×C4×D311yescharacteristic, complemented, Hall
62C2×C3×C5C4×D712yescomplemented
63C2×C3×C5C22×D711yescharacteristic
64D15—74no—
65C22×C7C2×D1511yescharacteristic
66C2×D7—154no—
67C2×D7—152no—
68C4×C7C2×D1512yescomplemented
69Dic7—152no—
70C22×D3—351no—
71C2×C3×C4D3511yescharacteristic, complemented
72C2×Dic3—351no—
73C4×D3—354no—
74C3×C7C2×C4×D511yescharacteristic, complemented, Hall
75C22×C5C2×D2111yescharacteristic
76C2×D5—214no—
77C2×D5—212no—
78C4×C5C2×D2112yescomplemented
79Dic5—212no—
80C22×C4—1051noSylow
81C3×C5C2×C4×D711yescharacteristic, complemented, Hall
82C2×C7C4×D1512yescomplemented
83C2×C7C22×D1511yescharacteristic
84D7—154no—
85C22×C3C2×D3511yescharacteristic
86C2×D3—354no—
87C2×D3—352no—
88C3×C4C2×D3512yescomplemented
89Dic3—352no—
90C2×C5C4×D2112yescomplemented
91C2×C5C22×D2111yescharacteristic
92D5—214no—
93C23—1051no—
94C2×C4—1051no—
95C2×C4—1054no—
96C2×C4D10511yescharacteristic, direct product factor
97C7C2×C4×D1511yescharacteristic, complemented, Sylow
98C2×C3C4×D3512yescomplemented
99C2×C3C22×D3511yescharacteristic
100D3—354no—
101C5C2×C4×D2111yescharacteristic, complemented, Sylow
102C22—1054no—
103C22—1052no—
104C22C2×D10511yescharacteristic
105C4—1052no—
106C4C2×D10512yesdirect product factor
107C3C2×C4×D3511yescharacteristic, complemented, Sylow
108C2—1054no—
109C2C4×D10512yesdirect product factor
110C2C22×D10511yescharacteristic
subgroupG/H
center, hypercenterC2×C4D105
commutator, hypocenterC3×C5×C7C22×C4
FrattiniC2C22×D105
FittingC2×C3×C4×C5×C7C2
socleC22×C3×C5×C7C22
prime radicalC22×D105C2
cosocleC2×C3×C5×C7C23
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5×C7C2semidirect
3. C2×Dic105C2semidirect
4. C4×D105C2direct (N × H)
7. C2×D105C4direct (N × H)
9. C3×C4×C5×C7C22semidirect
10. Dic105C22semidirect
13. C2×C4×C5×C7D3semidirect
17. C2×C3×C5×C7C2×C4semidirect
19. D105C2×C4direct (N × H)
21. C2×C3×C4×C7D5semidirect
27. C4×C5×C7C2×D3semidirect
30. C2×C3×C4×C5D7semidirect
34. C3×C5×C7C22×C4semidirect
38. C3×C4×C7C2×D5semidirect
41. C2×C5×C7C4×D3semidirect
47. C3×C4×C5C2×D7semidirect
50. C2×C4×C7D15semidirect
54. C2×C3×C7C4×D5semidirect
58. C2×C4×C5D21semidirect
61. C5×C7C2×C4×D3semidirect
62. C2×C3×C5C4×D7semidirect
68. C4×C7C2×D15semidirect
71. C2×C3×C4D35semidirect
74. C3×C7C2×C4×D5semidirect
78. C4×C5C2×D21semidirect
81. C3×C5C2×C4×D7semidirect
82. C2×C7C4×D15semidirect
88. C3×C4C2×D35semidirect
90. C2×C5C4×D21semidirect
96. C2×C4D105direct (N × H)
97. C7C2×C4×D15semidirect
98. C2×C3C4×D35semidirect
101. C5C2×C4×D21semidirect
106. C4C2×D105direct (N × H)
107. C3C2×C4×D35semidirect
109. C2C4×D105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D1052
C2×C3×C4×C5×C72
C2×Dic1052
C4×D1052
C2×C4×D353
C2×C4×D215
C2×C4×D157