Finite Group Databasebeta

← C5×D4×D21 #13132874

Subgroups — C5×D4×D21 #13132874

Order 1680.

216 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 74 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×D21C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C5×#4268C212yesmaximal, complemented
4C5×D84C211yesmaximal, characteristic, complemented
5C4×C5×D21C211yesmaximal, characteristic, complemented
6C5×D4×D7—31nomaximal, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C5×D21—24no—
9C2×C5×D21C2211yescharacteristic
10C2×C5×D21C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C5×Dic21C2211yescharacteristic, complemented
13D4×D21C511yesmaximal, characteristic, direct product factor, Hall
14C22×C5×D7—32no—
15C5×C7×D4D311yescharacteristic, complemented
16C5×C22⋊D7—32no—
17C5×D28—31no—
18C4×C5×D7—31no—
19C5×D3×D4—71nomaximal, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C5×D21—22no—
23C5×D21D412yesdirect product factor
24C22×D21C2×C512yescomplemented
25C3×C7×D4C2×C511yescharacteristic, complemented
26#4268C2×C512yescomplemented
27D84C2×C511yescharacteristic, complemented
28C4×D21C2×C511yescharacteristic, complemented
29C22×C5×C7C2×D312yescomplemented
30C2×C5×D7—31no—
31C2×C5×D7—32no—
32C2×C5×D7—64no—
33C4×C5×C7C2×D311yescharacteristic, complemented
34C5×Dic7—31no—
35C22×C5×D3—72no—
36C3×C5×D4D711yescharacteristic, complemented
37C5×#67—72no—
38C5×D12—71no—
39C4×C5×D3—71no—
40D4×D7—31noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C22×C512yescomplemented
43C2×D21—24no—
44C2×D21C22×C511yescharacteristic
45C2×D21C22×C512yescomplemented
46C3×C4×C7C22×C511yescharacteristic, complemented
47Dic21C22×C511yescharacteristic, complemented
48C2×C5×D4—211noHall
49C2×C5×C7—22no—
50C2×C5×C7C22×D311yescharacteristic
51C5×D7—32no—
52C5×D7—62no—
53C22×C3×C5C2×D712yescomplemented
54C2×C5×D3—71no—
55C2×C5×D3—72no—
56C2×C5×D3—144no—
57C3×C4×C5C2×D711yescharacteristic, complemented
58C5×Dic3—71no—
59C22×D7—32no—
60C7×D4C5×D311yescharacteristic, complemented
61C22⋊D7—32no—
62D28—31no—
63C4×D7—31no—
64D3×D4—71noHall
65C2×C3×C7—22no—
66C2×C3×C7C23×C511yescharacteristic
67D21—22no—
68D21C5×D412yesdirect product factor
69C23×C5—212no—
70C5×D4—212no—
71C5×D4—211no—
72C5×D4D2111yescharacteristic, direct product factor
73C2×C4×C5—211no—
74C5×C7D3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5C22×D711yescharacteristic
77C5×D3—72no—
78C5×D3—142no—
79C22×C7C2×C5×D312yescomplemented
80C2×D7—31no—
81C2×D7—32no—
82C2×D7—64no—
83C4×C7C2×C5×D311yescharacteristic, complemented
84Dic7—31no—
85C22×D3—72no—
86C3×D4C5×D711yescharacteristic, complemented
87#67—72no—
88D12—71no—
89C4×D3—71no—
90C3×C7C2×C5×D411yescharacteristic, complemented, Hall
91C22×C5—211no—
92C22×C5—212no—
93C22×C5—424no—
94C22×C5C2×D2112yescomplemented
95C4×C5—211no—
96C4×C5C2×D2111yescharacteristic, complemented
97C2×D4—211noSylow
98C3×C5D4×D711yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7C22×C5×D311yescharacteristic
101D7—32no—
102D7—62no—
103C22×C3C2×C5×D712yescomplemented
104C2×D3—71no—
105C2×D3—72no—
106C2×D3—144no—
107C3×C4C2×C5×D711yescharacteristic, complemented
108Dic3—71no—
109C2×C5—22no—
110C2×C5—212no—
111C2×C5—422no—
112C2×C5C22×D2111yescharacteristic
113C23—212no—
114D4—212no—
115D4—211no—
116D4C5×D2111yescharacteristic, direct product factor
117C2×C4—211no—
118C7C5×D3×D411yescharacteristic, complemented, Sylow
119C2×C3—22no—
120C2×C3C22×C5×D711yescharacteristic
121D3—72no—
122D3—142no—
123C5D4×D2111yescharacteristic, direct product factor, Sylow
124C22—211no—
125C22—212no—
126C22—424no—
127C22C2×C5×D2112yescomplemented
128C4—211no—
129C4C2×C5×D2111yescharacteristic, complemented
130C3C5×D4×D711yescharacteristic, complemented, Sylow
131C2—22no—
132C2—212no—
133C2—422no—
134C2C22×C5×D2111yescharacteristic
subgroupG/H
centerC2×C5C22×D21
commutator, cosocleC2×C3×C7C23×C5
FrattiniC2C22×C5×D21
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC5×D4D21
hypocenterC3×C7C2×C5×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C5 ◁ C5×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×D21C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C5×#4268C2semidirect
4. C5×D84C2semidirect
5. C4×C5×D21C2semidirect
7. C22×C3×C5×C7C22semidirect
10. C2×C5×D21C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C5×Dic21C22semidirect
13. D4×D21C5direct (N × H)
15. C5×C7×D4D3semidirect
23. C5×D21D4direct (N × H)
24. C22×D21C2×C5semidirect
25. C3×C7×D4C2×C5semidirect
26. #4268C2×C5semidirect
27. D84C2×C5semidirect
28. C4×D21C2×C5semidirect
29. C22×C5×C7C2×D3semidirect
33. C4×C5×C7C2×D3semidirect
36. C3×C5×D4D7semidirect
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C22×C5semidirect
45. C2×D21C22×C5semidirect
46. C3×C4×C7C22×C5semidirect
47. Dic21C22×C5semidirect
53. C22×C3×C5C2×D7semidirect
57. C3×C4×C5C2×D7semidirect
60. C7×D4C5×D3semidirect
68. D21C5×D4direct (N × H)
72. C5×D4D21direct (N × H)
74. C5×C7D3×D4semidirect
79. C22×C7C2×C5×D3semidirect
83. C4×C7C2×C5×D3semidirect
86. C3×D4C5×D7semidirect
90. C3×C7C2×C5×D4semidirect
94. C22×C5C2×D21semidirect
96. C4×C5C2×D21semidirect
98. C3×C5D4×D7semidirect
103. C22×C3C2×C5×D7semidirect
107. C3×C4C2×C5×D7semidirect
116. D4C5×D21direct (N × H)
118. C7C5×D3×D4semidirect
123. C5D4×D21direct (N × H)
127. C22C2×C5×D21semidirect
129. C4C2×C5×D21semidirect
130. C3C5×D4×D7semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D212
C3×C5×C7×D42
C5×#42682
C5×D842
C4×C5×D212
C5×D4×D73
D4×D215
C5×D3×D47