Finite Group Databasebeta

← C4×C5×D3×D7 #13132668

Subgroups — C4×C5×D3×D7 #13132668

Order 1680.

216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×C5×D3×D7C211yesmaximal, characteristic
2C4×C5×D21C211yesmaximal, characteristic, complemented
3C4×C5×D3×C7C211yesmaximal, characteristic, complemented
4C3×C4×C5×D7C211yesmaximal, characteristic, complemented
5C5×D21⋊C4C211yesmaximal, characteristic, complemented
6C5×D3×Dic7C211yesmaximal, characteristic, complemented
7C5×Dic3×D7C211yesmaximal, characteristic, complemented
8C2×C4×C5×D7—31nomaximal, Hall
9C2×C5×D21C2211yescharacteristic
10C2×C5×D3×C7C2211yescharacteristic
11C2×C3×C5×D7C2211yescharacteristic
12C5×D3×D7C414yesdirect product factor
13C3×C4×C5×C7C2211yescharacteristic, complemented
14C5×Dic21C2211yescharacteristic, complemented
15C5×C7×Dic3C2211yescharacteristic, complemented
16C3×C5×Dic7C2211yescharacteristic, complemented
17C4×D3×D7C511yesmaximal, characteristic, direct product factor, Hall
18C22×C5×D7—31no—
19C2×C4×C5×C7—31no—
20C2×C5×Dic7—31no—
21C4×C5×D7—31no—
22C4×C5×D7—31no—
23C4×C5×D7—31no—
24C4×C5×D7D311yescharacteristic, direct product factor
25C2×C4×C5×D3—71nomaximal, Hall
26C2×C3×C5×C7C2311yescharacteristic
27C5×D21C2×C412yescomplemented
28C5×D3×C7C2×C412yescomplemented
29C3×C5×D7C2×C412yescomplemented
30C2×D3×D7C2×C511yescharacteristic
31C4×D21C2×C511yescharacteristic, complemented
32C4×D3×C7C2×C511yescharacteristic, complemented
33C3×C4×D7C2×C511yescharacteristic, complemented
34D21⋊C4C2×C511yescharacteristic, complemented
35D3×Dic7C2×C511yescharacteristic, complemented
36Dic3×D7C2×C511yescharacteristic, complemented
37C22×C5×C7—31no—
38C2×C5×D7—31no—
39C2×C5×D7—34no—
40C2×C5×D7C2×D311yescharacteristic
41C4×C5×C7—31no—
42C4×C5×C7C2×D311yescharacteristic, complemented
43C5×Dic7—31no—
44C5×Dic7C2×D311yescharacteristic, complemented
45C22×C5×D3—71no—
46C2×C3×C4×C5—71no—
47C2×C5×Dic3—71no—
48C4×C5×D3—71no—
49C4×C5×D3—71no—
50C4×C5×D3—71no—
51C4×C5×D3D711yescharacteristic, direct product factor
52C2×C4×D7—31noHall
53C3×C5×C7C22×C411yescharacteristic, complemented, Hall
54C2×D21C22×C511yescharacteristic
55C2×D3×C7C22×C511yescharacteristic
56C2×C3×D7C22×C511yescharacteristic
57D3×D7C4×C514yesdirect product factor
58C3×C4×C7C22×C511yescharacteristic, complemented
59Dic21C22×C511yescharacteristic, complemented
60C3×Dic7C22×C511yescharacteristic, complemented
61C7×Dic3C22×C511yescharacteristic, complemented
62C22×C4×C5—211noHall
63C2×C5×C7—32no—
64C2×C5×C7C22×D311yescharacteristic
65C5×D7—32no—
66C5×D7C4×D312yesdirect product factor
67C22×C3×C5—71no—
68C2×C5×D3—71no—
69C2×C5×D3—74no—
70C2×C5×D3C2×D711yescharacteristic
71C3×C4×C5—71no—
72C3×C4×C5C2×D711yescharacteristic, complemented
73C5×Dic3—71no—
74C5×Dic3C2×D711yescharacteristic, complemented
75C22×D7—31no—
76C2×C4×C7—31no—
77C2×Dic7—31no—
78C4×D7—31no—
79C4×D7—31no—
80C4×D7—31no—
81C4×D7C5×D311yescharacteristic, direct product factor
82C2×C4×D3—71noHall
83C2×C3×C7C23×C511yescharacteristic
84D21C2×C4×C512yescomplemented
85C3×D7C2×C4×C512yescomplemented
86D3×C7C2×C4×C512yescomplemented
87C23×C5—211no—
88C2×C4×C5—31no—
89C2×C4×C5—71no—
90C2×C4×C5—211no—
91C2×C4×C5—211no—
92C2×C4×C5—211no—
93C2×C4×C5—211no—
94C5×C7C2×C4×D311yescharacteristic, complemented, Hall
95C2×C3×C5—72no—
96C2×C3×C5C22×D711yescharacteristic
97C5×D3—72no—
98C5×D3C4×D712yesdirect product factor
99C22×C7—31no—
100C2×D7—31no—
101C2×D7—34no—
102C2×D7C2×C5×D311yescharacteristic
103C4×C7—31no—
104C4×C7C2×C5×D311yescharacteristic, complemented
105Dic7—31no—
106Dic7C2×C5×D311yescharacteristic, complemented
107C22×D3—71no—
108C2×C3×C4—71no—
109C2×Dic3—71no—
110C4×D3—71no—
111C4×D3—71no—
112C4×D3—71no—
113C4×D3C5×D711yescharacteristic, direct product factor
114C3×C7C22×C4×C511yescharacteristic, complemented, Hall
115C22×C5—31no—
116C22×C5—71no—
117C22×C5—214no—
118C22×C5—211no—
119C4×C5—31no—
120C4×C5—71no—
121C4×C5—211no—
122C4×C5D3×D711yescharacteristic, direct product factor
123C22×C4—211noSylow
124C3×C5C2×C4×D711yescharacteristic, complemented, Hall
125C2×C7—32no—
126C2×C7C22×C5×D311yescharacteristic
127D7—32no—
128D7C4×C5×D312yesdirect product factor
129C22×C3—71no—
130C2×D3—71no—
131C2×D3—74no—
132C2×D3C2×C5×D711yescharacteristic
133C3×C4—71no—
134C3×C4C2×C5×D711yescharacteristic, complemented
135Dic3—71no—
136Dic3C2×C5×D711yescharacteristic, complemented
137C2×C5—32no—
138C2×C5—72no—
139C2×C5—212no—
140C2×C5C2×D3×D711yescharacteristic
141C23—211no—
142C2×C4—31no—
143C2×C4—71no—
144C2×C4—211no—
145C2×C4—211no—
146C2×C4—211no—
147C2×C4—211no—
148C7C2×C4×C5×D311yescharacteristic, complemented, Sylow
149C2×C3—72no—
150C2×C3C22×C5×D711yescharacteristic
151D3—72no—
152D3C4×C5×D712yesdirect product factor
153C5C4×D3×D711yescharacteristic, direct product factor, Sylow
154C22—31no—
155C22—71no—
156C22—214no—
157C22—211no—
158C4—31no—
159C4—71no—
160C4—211no—
161C4C5×D3×D711yescharacteristic, direct product factor
162C3C2×C4×C5×D711yescharacteristic, complemented, Sylow
163C2—32no—
164C2—72no—
165C2—212no—
166C2C2×C5×D3×D711yescharacteristic
subgroupG/H
center, hypercenterC4×C5D3×D7
commutator, hypocenterC3×C7C22×C4×C5
FrattiniC2C2×C5×D3×D7
FittingC3×C4×C5×C7C22
socleC2×C3×C5×C7C23
prime radicalC2×C5×D3×D7C2
cosocleC2×C3×C7C23×C5
LCSG ▷ C3×C7
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
2. C4×C5×D21C2semidirect
3. C4×C5×D3×C7C2semidirect
4. C3×C4×C5×D7C2semidirect
5. C5×D21⋊C4C2semidirect
6. C5×D3×Dic7C2semidirect
7. C5×Dic3×D7C2semidirect
12. C5×D3×D7C4direct (N × H)
13. C3×C4×C5×C7C22semidirect
14. C5×Dic21C22semidirect
15. C5×C7×Dic3C22semidirect
16. C3×C5×Dic7C22semidirect
17. C4×D3×D7C5direct (N × H)
24. C4×C5×D7D3direct (N × H)
27. C5×D21C2×C4semidirect
28. C5×D3×C7C2×C4semidirect
29. C3×C5×D7C2×C4semidirect
31. C4×D21C2×C5semidirect
32. C4×D3×C7C2×C5semidirect
33. C3×C4×D7C2×C5semidirect
34. D21⋊C4C2×C5semidirect
35. D3×Dic7C2×C5semidirect
36. Dic3×D7C2×C5semidirect
42. C4×C5×C7C2×D3semidirect
44. C5×Dic7C2×D3semidirect
51. C4×C5×D3D7direct (N × H)
53. C3×C5×C7C22×C4semidirect
57. D3×D7C4×C5direct (N × H)
58. C3×C4×C7C22×C5semidirect
59. Dic21C22×C5semidirect
60. C3×Dic7C22×C5semidirect
61. C7×Dic3C22×C5semidirect
66. C5×D7C4×D3direct (N × H)
72. C3×C4×C5C2×D7semidirect
74. C5×Dic3C2×D7semidirect
81. C4×D7C5×D3direct (N × H)
84. D21C2×C4×C5semidirect
85. C3×D7C2×C4×C5semidirect
86. D3×C7C2×C4×C5semidirect
94. C5×C7C2×C4×D3semidirect
98. C5×D3C4×D7direct (N × H)
104. C4×C7C2×C5×D3semidirect
106. Dic7C2×C5×D3semidirect
113. C4×D3C5×D7direct (N × H)
114. C3×C7C22×C4×C5semidirect
122. C4×C5D3×D7direct (N × H)
124. C3×C5C2×C4×D7semidirect
128. D7C4×C5×D3direct (N × H)
134. C3×C4C2×C5×D7semidirect
136. Dic3C2×C5×D7semidirect
148. C7C2×C4×C5×D3semidirect
152. D3C4×C5×D7direct (N × H)
153. C5C4×D3×D7direct (N × H)
161. C4C5×D3×D7direct (N × H)
162. C3C2×C4×C5×D7semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×D72
C4×C5×D212
C4×C5×D3×C72
C3×C4×C5×D72
C5×D21⋊C42
C5×D3×Dic72
C5×Dic3×D72
C2×C4×C5×D73
C4×D3×D75
C2×C4×C5×D37