Finite Group Databasebeta

← C2×C5×D21⋊C4 #13132677

Subgroups — C2×C5×D21⋊C4 #13132677

Order 1680.

216 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 96 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
2C2×C5×C7×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×C5×Dic7C211yesmaximal, characteristic, complemented
4C5×D21⋊C4C214yesmaximal, direct product factor
5C2×C4×C5×D7—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic
7C2×C5×D21C414yescomplemented
8C2×C5×D21C2212yes—
9C5×C7×Dic3C2212yescomplemented
10C3×C5×Dic7C2212yescomplemented
11C2×D21⋊C4C511yesmaximal, characteristic, direct product factor, Hall
12C22×C5×D7—31no—
13C2×C4×C5×C7—31no—
14C2×C5×Dic7D311yescharacteristic, complemented
15C4×C5×D7—34no—
16C2×C4×C5×D3—71nomaximal, Hall
17C2×C3×C5×C7C2×C412yescomplemented
18C2×C3×C5×C7C2311yescharacteristic
19C5×D21C2×C414yescomplemented
20C22×D21C2×C511yescharacteristic
21C2×C7×Dic3C2×C511yescharacteristic, complemented
22C2×C3×Dic7C2×C511yescharacteristic, complemented
23D21⋊C4C2×C514yesdirect product factor
24C22×C5×C7C2×D311yescharacteristic
25C2×C5×D7—34no—
26C2×C5×D7—32no—
27C4×C5×C7—32no—
28C5×Dic7C2×D312yescomplemented
29C22×C5×D3—71no—
30C2×C3×C4×C5—71no—
31C2×C5×Dic3D711yescharacteristic, complemented
32C4×C5×D3—74no—
33C2×C4×D7—31noHall
34C3×C5×C7C22×C411yescharacteristic, complemented, Hall
35C22×C3×C7C22×C511yescharacteristic
36C2×D21C4×C514yescomplemented
37C2×D21C22×C512yes—
38C3×Dic7C22×C512yescomplemented
39C7×Dic3C22×C512yescomplemented
40C22×C4×C5—211noHall
41C2×C5×C7C4×D312yescomplemented
42C2×C5×C7C22×D311yescharacteristic
43C5×D7—34no—
44C22×C3×C5C2×D711yescharacteristic
45C2×C5×D3—74no—
46C2×C5×D3—72no—
47C3×C4×C5—72no—
48C5×Dic3C2×D712yescomplemented
49C22×D7—31no—
50C2×C4×C7—31no—
51C2×Dic7C5×D311yescharacteristic, complemented
52C4×D7—34no—
53C2×C4×D3—71noHall
54C2×C3×C7C2×C4×C512yescomplemented
55C2×C3×C7C23×C511yescharacteristic
56D21C2×C4×C514yescomplemented
57C23×C5—211no—
58C2×C4×C5—31no—
59C2×C4×C5—71no—
60C2×C4×C5—214no—
61C5×C7C2×C4×D311yescharacteristic, complemented, Hall
62C2×C3×C5C4×D712yescomplemented
63C2×C3×C5C22×D711yescharacteristic
64C5×D3—74no—
65C22×C7C2×C5×D311yescharacteristic
66C2×D7—34no—
67C2×D7—32no—
68C4×C7—32no—
69Dic7C2×C5×D312yescomplemented
70C22×D3—71no—
71C2×C3×C4—71no—
72C2×Dic3C5×D711yescharacteristic, complemented
73C4×D3—74no—
74C3×C7C22×C4×C511yescharacteristic, complemented, Hall
75C22×C5—214no—
76C22×C5—212no—
77C22×C5D3×D711yescharacteristic
78C4×C5—32no—
79C4×C5—72no—
80C22×C4—211noSylow
81C3×C5C2×C4×D711yescharacteristic, complemented, Hall
82C2×C7C4×C5×D312yescomplemented
83C2×C7C22×C5×D311yescharacteristic
84D7—34no—
85C22×C3C2×C5×D711yescharacteristic
86C2×D3—74no—
87C2×D3—72no—
88C3×C4—72no—
89Dic3C2×C5×D712yescomplemented
90C2×C5—214no—
91C2×C5D21⋊C412yesdirect product factor
92C2×C5C2×D3×D711yescharacteristic
93C23—211no—
94C2×C4—31no—
95C2×C4—71no—
96C2×C4—214no—
97C7C2×C4×C5×D311yescharacteristic, complemented, Sylow
98C2×C3C4×C5×D712yescomplemented
99C2×C3C22×C5×D711yescharacteristic
100D3—74no—
101C5C2×D21⋊C411yescharacteristic, direct product factor, Sylow
102C22—214no—
103C22—212no—
104C22C5×D3×D711yescharacteristic
105C4—32no—
106C4—72no—
107C3C2×C4×C5×D711yescharacteristic, complemented, Sylow
108C2—214no—
109C2C5×D21⋊C412yesdirect product factor
110C2C2×C5×D3×D711yescharacteristic
subgroupG/H
center, hypercenterC22×C5D3×D7
commutator, hypocenterC3×C7C22×C4×C5
FrattiniC2C2×C5×D3×D7
Fitting, socleC22×C3×C5×C7C22
prime radicalC22×C5×D21C2
cosocleC2×C3×C7C23×C5
LCSG ▷ C3×C7
UCSC1 ◁ C22×C5

Complements

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

NH ≅ G/Ntype
2. C2×C5×C7×Dic3C2semidirect
3. C2×C3×C5×Dic7C2semidirect
4. C5×D21⋊C4C2direct (N × H)
7. C2×C5×D21C4semidirect
9. C5×C7×Dic3C22semidirect
10. C3×C5×Dic7C22semidirect
11. C2×D21⋊C4C5direct (N × H)
14. C2×C5×Dic7D3semidirect
17. C2×C3×C5×C7C2×C4semidirect
19. C5×D21C2×C4semidirect
21. C2×C7×Dic3C2×C5semidirect
22. C2×C3×Dic7C2×C5semidirect
23. D21⋊C4C2×C5direct (N × H)
28. C5×Dic7C2×D3semidirect
31. C2×C5×Dic3D7semidirect
34. C3×C5×C7C22×C4semidirect
36. C2×D21C4×C5semidirect
38. C3×Dic7C22×C5semidirect
39. C7×Dic3C22×C5semidirect
41. C2×C5×C7C4×D3semidirect
48. C5×Dic3C2×D7semidirect
51. C2×Dic7C5×D3semidirect
54. C2×C3×C7C2×C4×C5semidirect
56. D21C2×C4×C5semidirect
61. C5×C7C2×C4×D3semidirect
62. C2×C3×C5C4×D7semidirect
69. Dic7C2×C5×D3semidirect
72. C2×Dic3C5×D7semidirect
74. C3×C7C22×C4×C5semidirect
81. C3×C5C2×C4×D7semidirect
82. C2×C7C4×C5×D3semidirect
89. Dic3C2×C5×D7semidirect
91. C2×C5D21⋊C4direct (N × H)
97. C7C2×C4×C5×D3semidirect
98. C2×C3C4×C5×D7semidirect
101. C5C2×D21⋊C4direct (N × H)
107. C3C2×C4×C5×D7semidirect
109. C2C5×D21⋊C4direct (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
C2×C5×C7×Dic32
C2×C3×C5×Dic72
C5×D21⋊C42
C2×C4×C5×D73
C2×D21⋊C45
C2×C4×C5×D37