Finite Group Databasebeta

← C3×C5×#1157 #13132833

Subgroups — C3×C5×#1157 #13132833

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
1C2×C3×C4×C5×C7C211yesmaximal, characteristic, complemented
2C3×C5×C22⋊D7C212yesmaximal, complemented
3C3×C5×D28C211yesmaximal, characteristic, complemented
4C3×C4×C5×D7C212yesmaximal, complemented
5C3×C5×Dic14C211yesmaximal, characteristic, complemented
6C5×#1157C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C7C2211yescharacteristic
8C2×C3×C5×D7C2212yes—
9C3×C4×C5×C7C2211yescharacteristic
10C3×C4×C5×C7C2211yescharacteristic
11C3×C5×Dic7C2212yes—
12C3×#1157C511yesmaximal, characteristic, direct product factor, Hall
13C2×C4×C5×C7C2×C311yescharacteristic, complemented
14C5×C22⋊D7C2×C312yescomplemented
15C5×D28C2×C311yescharacteristic, complemented
16C4×C5×D7C2×C312yescomplemented
17C5×Dic14C2×C311yescharacteristic, complemented
18C3×C5×#41—71nomaximal, Hall
19C2×C3×C5×C7—21no—
20C2×C3×C5×C7C2311yescharacteristic
21C3×C5×D7—22no—
22C2×C3×C4×C7C2×C511yescharacteristic, complemented
23C3×C22⋊D7C2×C512yescomplemented
24C3×D28C2×C511yescharacteristic, complemented
25C3×C4×D7C2×C512yescomplemented
26C3×Dic14C2×C511yescharacteristic, complemented
27C22×C5×C7C22×C311yescharacteristic
28C2×C5×D7C22×C312yes—
29C4×C5×C7C22×C311yescharacteristic
30C4×C5×C7C22×C311yescharacteristic
31C5×Dic7C22×C312yes—
32C3×C5×Q8—71no—
33C3×C5×D4—72no—
34C3×C5×D4—71no—
35C2×C3×C4×C5—72no—
36C2×C3×C4×C5D711yescharacteristic, complemented
37#1157C3×C511yescharacteristic, direct product factor, Hall
38C3×C5×C7#4111yescharacteristic, complemented, Hall
39C22×C3×C7C22×C511yescharacteristic
40C2×C3×D7C22×C512yes—
41C3×C4×C7C22×C511yescharacteristic
42C3×C4×C7C22×C511yescharacteristic
43C3×Dic7C22×C512yes—
44C5×#41—71noHall
45C2×C5×C7—21no—
46C2×C5×C7C23×C311yescharacteristic
47C5×D7—22no—
48C22×C3×C5—72no—
49C22×C3×C5C2×D711yescharacteristic
50C3×C4×C5—72no—
51C3×C4×C5C2×D711yescharacteristic
52C3×C4×C5C2×D711yescharacteristic
53C2×C4×C7C2×C3×C511yescharacteristic, complemented
54C22⋊D7C2×C3×C512yescomplemented
55D28C2×C3×C511yescharacteristic, complemented
56C4×D7C2×C3×C512yescomplemented
57Dic14C2×C3×C511yescharacteristic, complemented
58C3×#41—71noHall
59C2×C3×C7—21no—
60C2×C3×C7C23×C511yescharacteristic
61C3×D7—22no—
62C5×Q8—71no—
63C5×D4—72no—
64C5×D4—71no—
65C2×C4×C5—72no—
66C2×C4×C5C3×D711yescharacteristic, complemented
67C5×C7C3×#4111yescharacteristic, complemented, Hall
68C2×C3×C5—21no—
69C2×C3×C5—142no—
70C2×C3×C5C22×D711yescharacteristic
71C22×C7C22×C3×C511yescharacteristic
72C2×D7C22×C3×C512yes—
73C4×C7C22×C3×C511yescharacteristic
74C4×C7C22×C3×C511yescharacteristic
75Dic7C22×C3×C512yes—
76C3×Q8—71no—
77C3×D4—72no—
78C3×D4—71no—
79C2×C3×C4—72no—
80C2×C3×C4C5×D711yescharacteristic, complemented
81C3×C7C5×#4111yescharacteristic, complemented, Hall
82C22×C5—72no—
83C22×C5C2×C3×D711yescharacteristic
84C4×C5—72no—
85C4×C5C2×C3×D711yescharacteristic
86C4×C5C2×C3×D711yescharacteristic
87#41—71noSylow
88C3×C5#115711yescharacteristic, direct product factor, Hall
89C2×C7—21no—
90C2×C7C23×C3×C511yescharacteristic
91D7—22no—
92C22×C3—72no—
93C22×C3C2×C5×D711yescharacteristic
94C3×C4—72no—
95C3×C4C2×C5×D711yescharacteristic
96C3×C4C2×C5×D711yescharacteristic
97C2×C5—21no—
98C2×C5—142no—
99C2×C5C22×C3×D711yescharacteristic
100Q8—71no—
101D4—72no—
102D4—71no—
103C2×C4—72no—
104C2×C4C3×C5×D711yescharacteristic, complemented
105C7C3×C5×#4111yescharacteristic, complemented, Sylow
106C2×C3—21no—
107C2×C3—142no—
108C2×C3C22×C5×D711yescharacteristic
109C5C3×#115711yescharacteristic, direct product factor, Sylow
110C22—72no—
111C22C2×C3×C5×D711yescharacteristic
112C4—72no—
113C4C2×C3×C5×D711yescharacteristic
114C4C2×C3×C5×D711yescharacteristic
115C3C5×#115711yescharacteristic, direct product factor, Sylow
116C2—21no—
117C2—142no—
118C2C22×C3×C5×D711yescharacteristic
subgroupG/H
centerC3×C4×C5C2×D7
commutator, cosocleC2×C7C23×C3×C5
FrattiniC2C22×C3×C5×D7
FittingC2×C3×C4×C5×C7C2
socleC2×C3×C5×C7C23
hypercenterC2×C3×C4×C5D7
hypocenterC7C3×C5×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C3×C4×C5 ◁ C2×C3×C4×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×C7C2semidirect
2. C3×C5×C22⋊D7C2semidirect
3. C3×C5×D28C2semidirect
4. C3×C4×C5×D7C2semidirect
5. C3×C5×Dic14C2semidirect
6. C5×#1157C3direct (N × H)
12. C3×#1157C5direct (N × H)
13. C2×C4×C5×C7C2×C3semidirect
14. C5×C22⋊D7C2×C3semidirect
15. C5×D28C2×C3semidirect
16. C4×C5×D7C2×C3semidirect
17. C5×Dic14C2×C3semidirect
22. C2×C3×C4×C7C2×C5semidirect
23. C3×C22⋊D7C2×C5semidirect
24. C3×D28C2×C5semidirect
25. C3×C4×D7C2×C5semidirect
26. C3×Dic14C2×C5semidirect
36. C2×C3×C4×C5D7semidirect
37. #1157C3×C5direct (N × H)
38. C3×C5×C7#41semidirect
53. C2×C4×C7C2×C3×C5semidirect
54. C22⋊D7C2×C3×C5semidirect
55. D28C2×C3×C5semidirect
56. C4×D7C2×C3×C5semidirect
57. Dic14C2×C3×C5semidirect
66. C2×C4×C5C3×D7semidirect
67. C5×C7C3×#41semidirect
80. C2×C3×C4C5×D7semidirect
81. C3×C7C5×#41semidirect
88. C3×C5#1157direct (N × H)
104. C2×C4C3×C5×D7semidirect
105. C7C3×C5×#41semidirect
109. C5C3×#1157direct (N × H)
115. C3C5×#1157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×C72
C3×C5×C22⋊D72
C3×C5×D282
C3×C4×C5×D72
C3×C5×Dic142
C5×#11573
C3×#11575
C3×C5×#417