Finite Group Databasebeta

← C2×Dic7×D15 #13132702

Subgroups — C2×Dic7×D15 #13132702

Order 1680.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×C7×D15C211yesmaximal, characteristic
2C2×Dic105C211yesmaximal, characteristic, complemented
3C2×C3×C5×Dic7C211yesmaximal, characteristic, complemented
4Dic7×D15C214yesmaximal, direct product factor
5C2×D5×Dic7—31nomaximal, Hall
6C22×C3×C5×C7C2211yescharacteristic
7C2×C7×D15C414yescomplemented
8C2×C7×D15C2212yes—
9Dic105C2212yescomplemented
10C3×C5×Dic7C2212yescomplemented
11C2×D3×Dic7—51nomaximal, Hall
12C22×C7×D5—31no—
13C2×Dic35—31no—
14C2×C5×Dic7D311yescharacteristic, complemented
15D5×Dic7—34no—
16C2×C4×D15—71nomaximal, Hall
17C2×C3×C5×C7C2×C412yescomplemented
18C2×C3×C5×C7C2311yescharacteristic
19C7×D15C2×C414yescomplemented
20C22×D3×C7—51no—
21C2×Dic21—51no—
22C2×C3×Dic7D511yescharacteristic, complemented
23D3×Dic7—54no—
24C22×C5×C7C2×D311yescharacteristic
25C2×C7×D5—34no—
26C2×C7×D5—32no—
27Dic35—32no—
28C5×Dic7C2×D312yescomplemented
29C22×D15D711yescharacteristic
30C2×C3×C4×C5—71no—
31C2×Dic15—71no—
32C4×D15—74no—
33C22×Dic7—151noHall
34C3×C5×C7C22×C411yescharacteristic, complemented, Hall
35C22×C3×C7C2×D511yescharacteristic
36C2×D3×C7—54no—
37C2×D3×C7—52no—
38Dic21—52no—
39C3×Dic7C2×D512yescomplemented
40C2×C4×D5—211noHall
41C2×C5×C7C4×D312yescomplemented
42C2×C5×C7C22×D311yescharacteristic
43C7×D5—34no—
44C22×C3×C5C2×D711yescharacteristic
45C2×D15Dic714yesdirect product factor
46C2×D15C2×D712yes—
47C3×C4×C5—72no—
48Dic15—72no—
49C23×C7—151no—
50C2×Dic7—151no—
51C2×Dic7—154no—
52C2×Dic7D1511yescharacteristic, direct product factor
53C2×C4×D3—351noHall
54C2×C3×C7C4×D512yescomplemented
55C2×C3×C7C22×D511yescharacteristic
56D3×C7—54no—
57C22×D5—31no—
58C2×C4×C5—71no—
59C2×Dic5—211no—
60C4×D5—214no—
61C5×C7C2×C4×D311yescharacteristic, complemented, Hall
62C2×C3×C5C2×Dic712yescomplemented
63C2×C3×C5C22×D711yescharacteristic
64D15C2×Dic714yesdirect product factor
65C22×C7—154no—
66C22×C7—152no—
67C22×C7C2×D1511yescharacteristic
68Dic7—152no—
69Dic7C2×D1512yesdirect product factor
70C22×D3—51no—
71C2×C3×C4—71no—
72C2×Dic3—351no—
73C4×D3—354no—
74C3×C7C2×C4×D511yescharacteristic, complemented, Hall
75C22×C5D3×D711yescharacteristic
76C2×D5—34no—
77C2×D5—32no—
78C4×C5—72no—
79Dic5—212no—
80C22×C4—1051noSylow
81C3×C5C22×Dic711yescharacteristic, complemented, Hall
82C2×C7—154no—
83C2×C7C4×D1512yescomplemented
84C2×C7C22×D1511yescharacteristic
85C22×C3D5×D711yescharacteristic
86C2×D3—54no—
87C2×D3—52no—
88C3×C4—72no—
89Dic3—352no—
90C2×C5D3×Dic712yescomplemented
91C2×C5C2×D3×D711yescharacteristic
92D5—34no—
93C23—151no—
94C2×C4—71no—
95C2×C4—1054no—
96C2×C4—1051no—
97C7C2×C4×D1511yescharacteristic, complemented, Sylow
98C2×C3D5×Dic712yescomplemented
99C2×C3C2×D5×D711yescharacteristic
100D3—54no—
101C5C2×D3×Dic711yescharacteristic, complemented, Sylow
102C22—154no—
103C22—152no—
104C22D7×D1511yescharacteristic
105C4—72no—
106C4—1052no—
107C3C2×D5×Dic711yescharacteristic, complemented, Sylow
108C2—154no—
109C2Dic7×D1512yesdirect product factor
110C2C2×D7×D1511yescharacteristic
subgroupG/H
center, hypercenterC22D7×D15
commutator, hypocenterC3×C5×C7C22×C4
FrattiniC2C2×D7×D15
Fitting, socleC22×C3×C5×C7C22
prime radicalC22×C7×D15C2
cosocleC2×C3×C5×C7C23
LCSG ▷ C3×C5×C7
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×Dic105C2semidirect
3. C2×C3×C5×Dic7C2semidirect
4. Dic7×D15C2direct (N × H)
7. C2×C7×D15C4semidirect
9. Dic105C22semidirect
10. C3×C5×Dic7C22semidirect
14. C2×C5×Dic7D3semidirect
17. C2×C3×C5×C7C2×C4semidirect
19. C7×D15C2×C4semidirect
22. C2×C3×Dic7D5semidirect
28. C5×Dic7C2×D3semidirect
34. C3×C5×C7C22×C4semidirect
39. C3×Dic7C2×D5semidirect
41. C2×C5×C7C4×D3semidirect
45. C2×D15Dic7direct (N × H)
52. C2×Dic7D15direct (N × H)
54. C2×C3×C7C4×D5semidirect
61. C5×C7C2×C4×D3semidirect
62. C2×C3×C5C2×Dic7semidirect
64. D15C2×Dic7direct (N × H)
69. Dic7C2×D15direct (N × H)
74. C3×C7C2×C4×D5semidirect
81. C3×C5C22×Dic7semidirect
83. C2×C7C4×D15semidirect
90. C2×C5D3×Dic7semidirect
97. C7C2×C4×D15semidirect
98. C2×C3D5×Dic7semidirect
101. C5C2×D3×Dic7semidirect
107. C3C2×D5×Dic7semidirect
109. C2Dic7×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×D152
C2×Dic1052
C2×C3×C5×Dic72
Dic7×D152
C2×D5×Dic73
C2×D3×Dic75
C2×C4×D157