Finite Group Databasebeta

← C2×C5×#4268 #13132879

Subgroups — C2×C5×#4268 #13132879

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×C5×D21C211yesmaximal, characteristic, complemented
3C5×#4268C214yesmaximal, direct product factor
4C2×C5×Dic21C211yesmaximal, characteristic, complemented
5C2×C5×C22⋊D7—31nomaximal, Hall
6C22×C3×C5×C7—22no—
7C22×C3×C5×C7C2211yescharacteristic
8C22×C3×C5×C7C2212yescomplemented
9C2×C5×D21—22no—
10C2×C5×D21C2212yescomplemented
11C5×Dic21C2212yescomplemented
12C2×#4268C511yesmaximal, characteristic, direct product factor, Hall
13C23×C5×C7D311yescharacteristic, complemented
14C22×C5×D7—31no—
15C5×C22⋊D7—34no—
16C2×C5×Dic7—31no—
17C2×C5×#67—71nomaximal, Hall
18C2×C3×C5×C7—22no—
19C2×C3×C5×C7D412yescomplemented
20C2×C3×C5×C7C2311yescharacteristic
21C5×D21—22no—
22C23×C3×C7C2×C511yescharacteristic, complemented
23C22×D21C2×C511yescharacteristic, complemented
24#4268C2×C514yesdirect product factor
25C2×Dic21C2×C511yescharacteristic, complemented
26C22×C5×C7—22no—
27C22×C5×C7C2×D311yescharacteristic
28C22×C5×C7C2×D312yescomplemented
29C2×C5×D7—32no—
30C2×C5×D7—62no—
31C5×Dic7—32no—
32C23×C3×C5D711yescharacteristic, complemented
33C22×C5×D3—71no—
34C5×#67—74no—
35C2×C5×Dic3—71no—
36C2×C22⋊D7—31noHall
37C3×C5×C7C2×D411yescharacteristic, complemented, Hall
38C22×C3×C7—22no—
39C22×C3×C7C22×C511yescharacteristic
40C22×C3×C7C22×C512yescomplemented
41C2×D21—22no—
42C2×D21C22×C512yescomplemented
43Dic21C22×C512yescomplemented
44C2×C5×D4—211noHall
45C2×C5×C7—22no—
46C2×C5×C7#6712yescomplemented
47C2×C5×C7C22×D311yescharacteristic
48C5×D7—62no—
49C22×C3×C5—22no—
50C22×C3×C5C2×D711yescharacteristic
51C22×C3×C5C2×D712yescomplemented
52C2×C5×D3—72no—
53C2×C5×D3—142no—
54C5×Dic3—72no—
55C23×C7C5×D311yescharacteristic, complemented
56C22×D7—31no—
57C22⋊D7—34no—
58C2×Dic7—31no—
59C2×#67—71noHall
60C2×C3×C7—22no—
61C2×C3×C7C5×D412yescomplemented
62C2×C3×C7C23×C511yescharacteristic
63D21—22no—
64C23×C5—211no—
65C23×C5D2111yescharacteristic, complemented
66C5×D4—214no—
67C2×C4×C5—211no—
68C5×C7C2×#6711yescharacteristic, complemented, Hall
69C2×C3×C5—22no—
70C2×C3×C5C22⋊D712yescomplemented
71C2×C3×C5C22×D711yescharacteristic
72C5×D3—142no—
73C22×C7—22no—
74C22×C7C2×C5×D311yescharacteristic
75C22×C7C2×C5×D312yescomplemented
76C2×D7—32no—
77C2×D7—62no—
78Dic7—32no—
79C23×C3C5×D711yescharacteristic, complemented
80C22×D3—71no—
81#67—74no—
82C2×Dic3—71no—
83C3×C7C2×C5×D411yescharacteristic, complemented, Hall
84C22×C5—22no—
85C22×C5—212no—
86C22×C5—422no—
87C22×C5C2×D2111yescharacteristic
88C22×C5C2×D2112yescomplemented
89C4×C5—212no—
90C2×D4—211noSylow
91C3×C5C2×C22⋊D711yescharacteristic, complemented, Hall
92C2×C7—22no—
93C2×C7C5×#6712yescomplemented
94C2×C7C22×C5×D311yescharacteristic
95D7—62no—
96C22×C3—22no—
97C22×C3C2×C5×D711yescharacteristic
98C22×C3C2×C5×D712yescomplemented
99C2×D3—72no—
100C2×D3—142no—
101Dic3—72no—
102C2×C5—22no—
103C2×C5—422no—
104C2×C5#426812yesdirect product factor
105C2×C5C22×D2111yescharacteristic
106C23—211no—
107C23C5×D2111yescharacteristic, complemented
108D4—214no—
109C2×C4—211no—
110C7C2×C5×#6711yescharacteristic, complemented, Sylow
111C2×C3—22no—
112C2×C3C5×C22⋊D712yescomplemented
113C2×C3C22×C5×D711yescharacteristic
114D3—142no—
115C5C2×#426811yescharacteristic, direct product factor, Sylow
116C22—22no—
117C22—212no—
118C22—422no—
119C22C2×C5×D2111yescharacteristic
120C22C2×C5×D2112yescomplemented
121C4—212no—
122C3C2×C5×C22⋊D711yescharacteristic, complemented, Sylow
123C2—22no—
124C2—422no—
125C2C5×#426812yesdirect product factor
126C2C22×C5×D2111yescharacteristic
subgroupG/H
centerC22×C5C2×D21
commutator, cosocleC2×C3×C7C23×C5
FrattiniC2C22×C5×D21
FittingC23×C3×C5×C7C2
socleC22×C3×C5×C7C22
hypercenterC23×C5D21
hypocenterC3×C7C2×C5×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22×C5 ◁ C23×C5

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C5×D21C2semidirect
3. C5×#4268C2direct (N × H)
4. C2×C5×Dic21C2semidirect
8. C22×C3×C5×C7C22semidirect
10. C2×C5×D21C22semidirect
11. C5×Dic21C22semidirect
12. C2×#4268C5direct (N × H)
13. C23×C5×C7D3semidirect
19. C2×C3×C5×C7D4semidirect
22. C23×C3×C7C2×C5semidirect
23. C22×D21C2×C5semidirect
24. #4268C2×C5direct (N × H)
25. C2×Dic21C2×C5semidirect
28. C22×C5×C7C2×D3semidirect
32. C23×C3×C5D7semidirect
37. C3×C5×C7C2×D4semidirect
40. C22×C3×C7C22×C5semidirect
42. C2×D21C22×C5semidirect
43. Dic21C22×C5semidirect
46. C2×C5×C7#67semidirect
51. C22×C3×C5C2×D7semidirect
55. C23×C7C5×D3semidirect
61. C2×C3×C7C5×D4semidirect
65. C23×C5D21semidirect
68. C5×C7C2×#67semidirect
70. C2×C3×C5C22⋊D7semidirect
75. C22×C7C2×C5×D3semidirect
79. C23×C3C5×D7semidirect
83. C3×C7C2×C5×D4semidirect
88. C22×C5C2×D21semidirect
91. C3×C5C2×C22⋊D7semidirect
93. C2×C7C5×#67semidirect
98. C22×C3C2×C5×D7semidirect
104. C2×C5#4268direct (N × H)
107. C23C5×D21semidirect
110. C7C2×C5×#67semidirect
112. C2×C3C5×C22⋊D7semidirect
115. C5C2×#4268direct (N × H)
120. C22C2×C5×D21semidirect
122. C3C2×C5×C22⋊D7semidirect
125. C2C5×#4268direct (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×C5×D212
C5×#42682
C2×C5×Dic212
C2×C5×C22⋊D73
C2×#42685
C2×C5×#677