Finite Group Databasebeta

← C2×C3×C22⋊D35 #13132859

Subgroups — C2×C3×C22⋊D35 #13132859

Order 1680.

216 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C23×C3×C5×C7C211yesmaximal, characteristic, complemented
2C22×C3×D35C211yesmaximal, characteristic, complemented
3C3×C22⋊D35C214yesmaximal, direct product factor
4C2×C3×Dic35C211yesmaximal, characteristic, complemented
5C2×C22⋊D35C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×C7—22no—
7C22×C3×C5×C7C2211yescharacteristic
8C22×C3×C5×C7C2212yescomplemented
9C2×C3×D35—22no—
10C2×C3×D35C2212yescomplemented
11C3×Dic35C2212yescomplemented
12C2×C3×C22⋊D7—51nomaximal, Hall
13C23×C5×C7C2×C311yescharacteristic, complemented
14C22×D35C2×C311yescharacteristic, complemented
15C22⋊D35C2×C314yesdirect product factor
16C2×Dic35C2×C311yescharacteristic, complemented
17C2×C3×C22⋊D5—71nomaximal, Hall
18C2×C3×C5×C7—22no—
19C2×C3×C5×C7D412yescomplemented
20C2×C3×C5×C7C2311yescharacteristic
21C3×D35—22no—
22C23×C3×C7D511yescharacteristic, complemented
23C22×C3×D7—51no—
24C3×C22⋊D7—54no—
25C2×C3×Dic7—51no—
26C22×C5×C7—22no—
27C22×C5×C7C22×C311yescharacteristic
28C22×C5×C7C22×C312yescomplemented
29C2×D35—22no—
30C2×D35C22×C312yescomplemented
31Dic35C22×C312yescomplemented
32C23×C3×C5D711yescharacteristic, complemented
33C22×C3×D5—71no—
34C3×C22⋊D5—74no—
35C2×C3×Dic5—71no—
36C2×C22⋊D7—51noHall
37C3×C5×C7C2×D411yescharacteristic, complemented, Hall
38C22×C3×C7—22no—
39C22×C3×C7C2×D511yescharacteristic
40C22×C3×C7C2×D512yescomplemented
41C2×C3×D7—52no—
42C2×C3×D7—102no—
43C3×Dic7—52no—
44C2×C22⋊D5—71noHall
45C2×C5×C7—22no—
46C2×C5×C7C3×D412yescomplemented
47C2×C5×C7C23×C311yescharacteristic
48D35—22no—
49C22×C3×C5—22no—
50C22×C3×C5C2×D711yescharacteristic
51C22×C3×C5C2×D712yescomplemented
52C2×C3×D5—72no—
53C2×C3×D5—142no—
54C3×Dic5—72no—
55C23×C7C3×D511yescharacteristic, complemented
56C22×D7—51no—
57C22⋊D7—54no—
58C2×Dic7—51no—
59C2×C3×D4—351noHall
60C2×C3×C7—22no—
61C2×C3×C7C22⋊D512yescomplemented
62C2×C3×C7C22×D511yescharacteristic
63C3×D7—102no—
64C23×C5C3×D711yescharacteristic, complemented
65C22×D5—71no—
66C22⋊D5—74no—
67C2×Dic5—71no—
68C5×C7C2×C3×D411yescharacteristic, complemented, Hall
69C2×C3×C5—22no—
70C2×C3×C5C22⋊D712yescomplemented
71C2×C3×C5C22×D711yescharacteristic
72C3×D5—142no—
73C22×C7—22no—
74C22×C7C2×C3×D511yescharacteristic
75C22×C7C2×C3×D512yescomplemented
76C2×D7—52no—
77C2×D7—102no—
78Dic7—52no—
79C23×C3—351no—
80C23×C3D3511yescharacteristic, complemented
81C3×D4—354no—
82C2×C3×C4—351no—
83C3×C7C2×C22⋊D511yescharacteristic, complemented, Hall
84C22×C5—22no—
85C22×C5C2×C3×D711yescharacteristic
86C22×C5C2×C3×D712yescomplemented
87C2×D5—72no—
88C2×D5—142no—
89Dic5—72no—
90C2×D4—351noSylow
91C3×C5C2×C22⋊D711yescharacteristic, complemented, Hall
92C2×C7—22no—
93C2×C7C3×C22⋊D512yescomplemented
94C2×C7C22×C3×D511yescharacteristic
95D7—102no—
96C22×C3—22no—
97C22×C3—352no—
98C22×C3—702no—
99C22×C3C2×D3511yescharacteristic
100C22×C3C2×D3512yescomplemented
101C3×C4—352no—
102C2×C5—22no—
103C2×C5C3×C22⋊D712yescomplemented
104C2×C5C22×C3×D711yescharacteristic
105D5—142no—
106C23—351no—
107C23C3×D3511yescharacteristic, complemented
108D4—354no—
109C2×C4—351no—
110C7C2×C3×C22⋊D511yescharacteristic, complemented, Sylow
111C2×C3—22no—
112C2×C3—702no—
113C2×C3C22⋊D3512yesdirect product factor
114C2×C3C22×D3511yescharacteristic
115C5C2×C3×C22⋊D711yescharacteristic, complemented, Sylow
116C22—22no—
117C22—352no—
118C22—702no—
119C22C2×C3×D3511yescharacteristic
120C22C2×C3×D3512yescomplemented
121C4—352no—
122C3C2×C22⋊D3511yescharacteristic, direct product factor, Sylow
123C2—22no—
124C2—702no—
125C2C3×C22⋊D3512yesdirect product factor
126C2C22×C3×D3511yescharacteristic
subgroupG/H
centerC22×C3C2×D35
commutator, cosocleC2×C5×C7C23×C3
FrattiniC2C22×C3×D35
FittingC23×C3×C5×C7C2
socleC22×C3×C5×C7C22
hypercenterC23×C3D35
hypocenterC5×C7C2×C3×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C3×D35C2semidirect
3. C3×C22⋊D35C2direct (N × H)
4. C2×C3×Dic35C2semidirect
5. C2×C22⋊D35C3direct (N × H)
8. C22×C3×C5×C7C22semidirect
10. C2×C3×D35C22semidirect
11. C3×Dic35C22semidirect
13. C23×C5×C7C2×C3semidirect
14. C22×D35C2×C3semidirect
15. C22⋊D35C2×C3direct (N × H)
16. C2×Dic35C2×C3semidirect
19. C2×C3×C5×C7D4semidirect
22. C23×C3×C7D5semidirect
28. C22×C5×C7C22×C3semidirect
30. C2×D35C22×C3semidirect
31. Dic35C22×C3semidirect
32. C23×C3×C5D7semidirect
37. C3×C5×C7C2×D4semidirect
40. C22×C3×C7C2×D5semidirect
46. C2×C5×C7C3×D4semidirect
51. C22×C3×C5C2×D7semidirect
55. C23×C7C3×D5semidirect
61. C2×C3×C7C22⋊D5semidirect
64. C23×C5C3×D7semidirect
68. C5×C7C2×C3×D4semidirect
70. C2×C3×C5C22⋊D7semidirect
75. C22×C7C2×C3×D5semidirect
80. C23×C3D35semidirect
83. C3×C7C2×C22⋊D5semidirect
86. C22×C5C2×C3×D7semidirect
91. C3×C5C2×C22⋊D7semidirect
93. C2×C7C3×C22⋊D5semidirect
100. C22×C3C2×D35semidirect
103. C2×C5C3×C22⋊D7semidirect
107. C23C3×D35semidirect
110. C7C2×C3×C22⋊D5semidirect
113. C2×C3C22⋊D35direct (N × H)
115. C5C2×C3×C22⋊D7semidirect
120. C22C2×C3×D35semidirect
122. C3C2×C22⋊D35direct (N × H)
125. C2C3×C22⋊D35direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×C72
C22×C3×D352
C3×C22⋊D352
C2×C3×Dic352
C2×C22⋊D353
C2×C3×C22⋊D75
C2×C3×C22⋊D57