Finite Group Databasebeta

← C2×C5×#4246 #13132679

Subgroups — C2×C5×#4246 #13132679

Order 1680.

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

normal subgroups only

This group has 216 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
1C22×C5×D21C211yesmaximal, characteristic, complemented
2C22×C3×C5×D7C211yesmaximal, characteristic, complemented
3C2×C5×C7×Dic3C211yesmaximal, characteristic, complemented
4C5×#4246C214yesmaximal, direct product factor
5C2×C5×D28—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic
7C2×C5×D21—22no—
8C2×C5×D21C2212yescomplemented
9C2×C3×C5×D7—22no—
10C2×C3×C5×D7C2212yescomplemented
11C5×C7×Dic3C2212yescomplemented
12C2×#4246C511yesmaximal, characteristic, direct product factor, Hall
13C22×C5×D7—31no—
14C22×C5×D7D311yescharacteristic, complemented
15C2×C4×C5×C7—31no—
16C5×D28—34no—
17C2×C5×#67—71nomaximal, Hall
18C2×C3×C5×C7D412yescomplemented
19C2×C3×C5×C7C2311yescharacteristic
20C5×D21—22no—
21C3×C5×D7—22no—
22C22×D21C2×C511yescharacteristic, complemented
23C22×C3×D7C2×C511yescharacteristic, complemented
24C2×C7×Dic3C2×C511yescharacteristic, complemented
25#4246C2×C514yesdirect product factor
26C22×C5×C7C2×D311yescharacteristic
27C2×C5×D7—22no—
28C2×C5×D7—32no—
29C2×C5×D7—62no—
30C2×C5×D7C2×D312yescomplemented
31C4×C5×C7—32no—
32C23×C3×C5—71no—
33C22×C5×D3—71no—
34C5×#67—74no—
35C2×C5×Dic3D711yescharacteristic, complemented
36C2×D28—31noHall
37C3×C5×C7C2×D411yescharacteristic, complemented, Hall
38C22×C3×C7C22×C511yescharacteristic
39C2×D21—22no—
40C2×D21C22×C512yescomplemented
41C2×C3×D7—22no—
42C2×C3×D7C22×C512yescomplemented
43C7×Dic3C22×C512yescomplemented
44C2×C5×D4—211noHall
45C2×C5×C7#6712yescomplemented
46C2×C5×C7C22×D311yescharacteristic
47C5×D7—22no—
48C5×D7—62no—
49C22×C3×C5—72no—
50C22×C3×C5—142no—
51C22×C3×C5C2×D711yescharacteristic
52C2×C5×D3—72no—
53C2×C5×D3—142no—
54C5×Dic3C2×D712yescomplemented
55C22×D7—31no—
56C22×D7C5×D311yescharacteristic, complemented
57C2×C4×C7—31no—
58D28—34no—
59C2×#67—71noHall
60C2×C3×C7C5×D412yescomplemented
61C2×C3×C7C23×C511yescharacteristic
62D21—22no—
63C3×D7—22no—
64C23×C5—71no—
65C23×C5—211no—
66C5×D4—214no—
67C2×C4×C5—31no—
68C5×C7C2×#6711yescharacteristic, complemented, Hall
69C2×C3×C5—142no—
70C2×C3×C5D2812yescomplemented
71C2×C3×C5C22×D711yescharacteristic
72C5×D3—142no—
73C22×C7C2×C5×D311yescharacteristic
74C2×D7—22no—
75C2×D7—32no—
76C2×D7—62no—
77C2×D7C2×C5×D312yescomplemented
78C4×C7—32no—
79C23×C3—71no—
80C22×D3—71no—
81#67—74no—
82C2×Dic3C5×D711yescharacteristic, complemented
83C3×C7C2×C5×D411yescharacteristic, complemented, Hall
84C22×C5—72no—
85C22×C5—142no—
86C22×C5—212no—
87C22×C5—422no—
88C22×C5D3×D711yescharacteristic
89C4×C5—32no—
90C2×D4—211noSylow
91C3×C5C2×D2811yescharacteristic, complemented, Hall
92C2×C7C5×#6712yescomplemented
93C2×C7C22×C5×D311yescharacteristic
94D7—22no—
95D7—62no—
96C22×C3—72no—
97C22×C3—142no—
98C22×C3C2×C5×D711yescharacteristic
99C2×D3—72no—
100C2×D3—142no—
101Dic3C2×C5×D712yescomplemented
102C2×C5—142no—
103C2×C5—422no—
104C2×C5#424612yesdirect product factor
105C2×C5C2×D3×D711yescharacteristic
106C23—71no—
107C23—211no—
108D4—214no—
109C2×C4—31no—
110C7C2×C5×#6711yescharacteristic, complemented, Sylow
111C2×C3—142no—
112C2×C3C5×D2812yescomplemented
113C2×C3C22×C5×D711yescharacteristic
114D3—142no—
115C5C2×#424611yescharacteristic, direct product factor, Sylow
116C22—72no—
117C22—142no—
118C22—212no—
119C22—422no—
120C22C5×D3×D711yescharacteristic
121C4—32no—
122C3C2×C5×D2811yescharacteristic, complemented, Sylow
123C2—142no—
124C2—422no—
125C2C5×#424612yesdirect product factor
126C2C2×C5×D3×D711yescharacteristic
subgroupG/H
center, hypercenterC22×C5D3×D7
commutator, cosocleC2×C3×C7C23×C5
FrattiniC2C2×C5×D3×D7
Fitting, socleC22×C3×C5×C7C22
hypocenterC3×C7C2×C5×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
1. C22×C5×D21C2semidirect
2. C22×C3×C5×D7C2semidirect
3. C2×C5×C7×Dic3C2semidirect
4. C5×#4246C2direct (N × H)
8. C2×C5×D21C22semidirect
10. C2×C3×C5×D7C22semidirect
11. C5×C7×Dic3C22semidirect
12. C2×#4246C5direct (N × H)
14. C22×C5×D7D3semidirect
18. C2×C3×C5×C7D4semidirect
22. C22×D21C2×C5semidirect
23. C22×C3×D7C2×C5semidirect
24. C2×C7×Dic3C2×C5semidirect
25. #4246C2×C5direct (N × H)
30. C2×C5×D7C2×D3semidirect
35. C2×C5×Dic3D7semidirect
37. C3×C5×C7C2×D4semidirect
40. C2×D21C22×C5semidirect
42. C2×C3×D7C22×C5semidirect
43. C7×Dic3C22×C5semidirect
45. C2×C5×C7#67semidirect
54. C5×Dic3C2×D7semidirect
56. C22×D7C5×D3semidirect
60. C2×C3×C7C5×D4semidirect
68. C5×C7C2×#67semidirect
70. C2×C3×C5D28semidirect
77. C2×D7C2×C5×D3semidirect
82. C2×Dic3C5×D7semidirect
83. C3×C7C2×C5×D4semidirect
91. C3×C5C2×D28semidirect
92. C2×C7C5×#67semidirect
101. Dic3C2×C5×D7semidirect
104. C2×C5#4246direct (N × H)
110. C7C2×C5×#67semidirect
112. C2×C3C5×D28semidirect
115. C5C2×#4246direct (N × H)
122. C3C2×C5×D28semidirect
125. C2C5×#4246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D212
C22×C3×C5×D72
C2×C5×C7×Dic32
C5×#42462
C2×C5×D283
C2×#42465
C2×C5×#677