Finite Group Databasebeta

← C3×C5×#1159 #13132835

Subgroups — C3×C5×#1159 #13132835

Order 1680.

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

normal subgroups only

This group has 160 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
1C3×C5×C7×D4C211yesmaximal, characteristic, complemented
2C3×C5×C22⋊D7C212yesmaximal, complemented
3C2×C3×C5×Dic7C212yesmaximal, complemented
4C3×C4×C5×D7C211yesmaximal, characteristic, complemented
5C3×C5×Dic14C211yesmaximal, characteristic, complemented
6C5×#1159C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C7C2212yes—
8C2×C3×C5×D7C2211yescharacteristic
9C3×C4×C5×C7C2211yescharacteristic
10C3×C5×Dic7C2212yes—
11C3×C5×Dic7C2211yescharacteristic
12C3×#1159C511yesmaximal, characteristic, direct product factor, Hall
13C5×C7×D4C2×C311yescharacteristic, complemented
14C5×C22⋊D7C2×C312yescomplemented
15C2×C5×Dic7C2×C312yescomplemented
16C4×C5×D7C2×C311yescharacteristic, complemented
17C5×Dic14C2×C311yescharacteristic, complemented
18C3×C5×#41—71nomaximal, Hall
19C2×C3×C5×C7—22no—
20C2×C3×C5×C7C2311yescharacteristic
21C3×C5×D7—21no—
22C3×C7×D4C2×C511yescharacteristic, complemented
23C3×C22⋊D7C2×C512yescomplemented
24C2×C3×Dic7C2×C512yescomplemented
25C3×C4×D7C2×C511yescharacteristic, complemented
26C3×Dic14C2×C511yescharacteristic, complemented
27C22×C5×C7C22×C312yes—
28C2×C5×D7C22×C311yescharacteristic
29C4×C5×C7C22×C311yescharacteristic
30C5×Dic7C22×C312yes—
31C5×Dic7C22×C311yescharacteristic
32C3×C5×Q8—71no—
33C3×C5×D4—72no—
34C3×C5×D4D711yescharacteristic, complemented
35C2×C3×C4×C5—72no—
36C2×C3×C4×C5—71no—
37#1159C3×C511yescharacteristic, direct product factor, Hall
38C3×C5×C7#4111yescharacteristic, complemented, Hall
39C22×C3×C7C22×C512yes—
40C2×C3×D7C22×C511yescharacteristic
41C3×C4×C7C22×C511yescharacteristic
42C3×Dic7C22×C512yes—
43C3×Dic7C22×C511yescharacteristic
44C5×#41—71noHall
45C2×C5×C7—22no—
46C2×C5×C7C23×C311yescharacteristic
47C5×D7—21no—
48C22×C3×C5—71no—
49C22×C3×C5C2×D712yes—
50C3×C4×C5—71no—
51C3×C4×C5—72no—
52C3×C4×C5C2×D711yescharacteristic
53C7×D4C2×C3×C511yescharacteristic, complemented
54C22⋊D7C2×C3×C512yescomplemented
55C2×Dic7C2×C3×C512yescomplemented
56C4×D7C2×C3×C511yescharacteristic, complemented
57Dic14C2×C3×C511yescharacteristic, complemented
58C3×#41—71noHall
59C2×C3×C7—22no—
60C2×C3×C7C23×C511yescharacteristic
61C3×D7—21no—
62C5×Q8—71no—
63C5×D4—72no—
64C5×D4C3×D711yescharacteristic, complemented
65C2×C4×C5—72no—
66C2×C4×C5—71no—
67C5×C7C3×#4111yescharacteristic, complemented, Hall
68C2×C3×C5—22no—
69C2×C3×C5—141no—
70C2×C3×C5C22×D711yescharacteristic
71C22×C7C22×C3×C512yes—
72C2×D7C22×C3×C511yescharacteristic
73C4×C7C22×C3×C511yescharacteristic
74Dic7C22×C3×C512yes—
75Dic7C22×C3×C511yescharacteristic
76C3×Q8—71no—
77C3×D4—72no—
78C3×D4C5×D711yescharacteristic, complemented
79C2×C3×C4—72no—
80C2×C3×C4—71no—
81C3×C7C5×#4111yescharacteristic, complemented, Hall
82C22×C5—71no—
83C22×C5C2×C3×D712yes—
84C4×C5—71no—
85C4×C5—72no—
86C4×C5C2×C3×D711yescharacteristic
87#41—71noSylow
88C3×C5#115911yescharacteristic, direct product factor, Hall
89C2×C7—22no—
90C2×C7C23×C3×C511yescharacteristic
91D7—21no—
92C22×C3—71no—
93C22×C3C2×C5×D712yes—
94C3×C4—71no—
95C3×C4—72no—
96C3×C4C2×C5×D711yescharacteristic
97C2×C5—22no—
98C2×C5—141no—
99C2×C5C22×C3×D711yescharacteristic
100Q8—71no—
101D4—72no—
102D4C3×C5×D711yescharacteristic, complemented
103C2×C4—72no—
104C2×C4—71no—
105C7C3×C5×#4111yescharacteristic, complemented, Sylow
106C2×C3—22no—
107C2×C3—141no—
108C2×C3C22×C5×D711yescharacteristic
109C5C3×#115911yescharacteristic, direct product factor, Sylow
110C22—71no—
111C22C2×C3×C5×D712yes—
112C4—71no—
113C4—72no—
114C4C2×C3×C5×D711yescharacteristic
115C3C5×#115911yescharacteristic, direct product factor, Sylow
116C2—22no—
117C2—141no—
118C2C22×C3×C5×D711yescharacteristic
subgroupG/H
centerC2×C3×C5C22×D7
commutator, cosocleC2×C7C23×C3×C5
FrattiniC2C22×C3×C5×D7
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC3×C5×D4D7
hypocenterC7C3×C5×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C5 ◁ C3×C5×D4

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D4C2semidirect
2. C3×C5×C22⋊D7C2semidirect
3. C2×C3×C5×Dic7C2semidirect
4. C3×C4×C5×D7C2semidirect
5. C3×C5×Dic14C2semidirect
6. C5×#1159C3direct (N × H)
12. C3×#1159C5direct (N × H)
13. C5×C7×D4C2×C3semidirect
14. C5×C22⋊D7C2×C3semidirect
15. C2×C5×Dic7C2×C3semidirect
16. C4×C5×D7C2×C3semidirect
17. C5×Dic14C2×C3semidirect
22. C3×C7×D4C2×C5semidirect
23. C3×C22⋊D7C2×C5semidirect
24. C2×C3×Dic7C2×C5semidirect
25. C3×C4×D7C2×C5semidirect
26. C3×Dic14C2×C5semidirect
34. C3×C5×D4D7semidirect
37. #1159C3×C5direct (N × H)
38. C3×C5×C7#41semidirect
53. C7×D4C2×C3×C5semidirect
54. C22⋊D7C2×C3×C5semidirect
55. C2×Dic7C2×C3×C5semidirect
56. C4×D7C2×C3×C5semidirect
57. Dic14C2×C3×C5semidirect
64. C5×D4C3×D7semidirect
67. C5×C7C3×#41semidirect
78. C3×D4C5×D7semidirect
81. C3×C7C5×#41semidirect
88. C3×C5#1159direct (N × H)
102. D4C3×C5×D7semidirect
105. C7C3×C5×#41semidirect
109. C5C3×#1159direct (N × H)
115. C3C5×#1159direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D42
C3×C5×C22⋊D72
C2×C3×C5×Dic72
C3×C4×C5×D72
C3×C5×Dic142
C5×#11593
C3×#11595
C3×C5×#417