Finite Group Databasebeta

← C2×C32×#713 #13089451

Subgroups — C2×C32×#713 #13089451

Order 1440.

984 conjugacy classes of subgroups; only the 534 normal subgroups are shown.

normal subgroups only

This group has 984 conjugacy classes of subgroups — too many to draw. Only its 534 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×C32×C5×Q8C211yesmaximal, characteristic, complemented
2C32×#713C218yesmaximal, direct product factor
3C2×C32×D20C213yesmaximal, complemented
4C2×C32×C4×D5C213yesmaximal, complemented
5C2×C3×#713C314yesmaximal, direct product factor
6C22×C32×D5C2213yes—
7C32×C5×Q8C2214yescomplemented
8C2×C32×C4×C5C2213yes—
9C2×C32×Dic5C2211yescharacteristic
10C32×D20C22112yescomplemented
11C32×C4×D5C22112yescomplemented
12C2×C32×#41—51nomaximal, Hall
13C2×C3×C5×Q8C2×C314yescomplemented
14C3×#713C2×C3132yesdirect product factor
15C2×C3×D20C2×C3112yescomplemented
16C2×C3×C4×D5C2×C3112yescomplemented
17C22×C32×C5C2311yescharacteristic
18C2×C32×D5—26no—
19C2×C32×D5C2316yes—
20C32×C4×C5C2316yes—
21C32×Dic5C2312yes—
22C2×#713C3211yescharacteristic, direct product factor, Hall
23C32×#41—58no—
24C2×C32×Q8D511yescharacteristic, complemented
25C2×C32×D4—53no—
26C22×C32×C4—53no—
27C22×C3×D5C22×C3112yes—
28C3×C5×Q8C22×C3116yescomplemented
29C2×C3×C4×C5C22×C3112yes—
30C2×C3×Dic5C22×C314yes—
31C3×D20C22×C3148yescomplemented
32C3×C4×D5C22×C3148yescomplemented
33C2×C3×#41—54no—
34C2×C32×C5#4112yescomplemented
35C2×C32×C5C2411yescharacteristic
36C32×D5—26no—
37C2×C5×Q8C2×C3211yescharacteristic, complemented
38#713C2×C3218yesdirect product factor
39C2×D20C2×C3213yescomplemented
40C2×C4×D5C2×C3213yescomplemented
41C23×C32—53no—
42C32×Q8C2×D514yescomplemented
43C32×D4—512no—
44C2×C32×C4—51no—
45C2×C32×C4—512no—
46C2×C32×C4C2×D513yes—
47C22×C3×C5C23×C314yes—
48C2×C3×D5—224no—
49C2×C3×D5C23×C3124yes—
50C3×C4×C5C23×C3124yes—
51C3×Dic5C23×C318yes—
52C3×#41—532no—
53C2×C3×Q8C3×D514yescomplemented
54C2×C3×D4—512no—
55C22×C3×C4—512no—
56C32×C5C2×#4111yescharacteristic, complemented, Hall
57C22×D5C22×C3213yes—
58C5×Q8C22×C3214yescomplemented
59C2×C4×C5C22×C3213yes—
60C2×Dic5C22×C3211yescharacteristic
61D20C22×C32112yescomplemented
62C4×D5C22×C32112yescomplemented
63C22×C32—56no—
64C22×C32—106no—
65C22×C32C22×D511yescharacteristic
66C32×C4—52no—
67C32×C4C22×D516yes—
68C2×#41—51noSylow
69C2×C3×C5C3×#4118yescomplemented
70C2×C3×C5C24×C314yes—
71C3×D5—224no—
72C23×C3—512no—
73C3×Q8C2×C3×D5116yescomplemented
74C3×D4—548no—
75C2×C3×C4—54no—
76C2×C3×C4—548no—
77C2×C3×C4C2×C3×D5112yes—
78C22×C5C23×C3211yescharacteristic
79C2×D5—26no—
80C2×D5C23×C3216yes—
81C4×C5C23×C3216yes—
82Dic5C23×C3212yes—
83C2×C32—106no—
84C2×C32#71312yesdirect product factor
85C2×C32C23×D511yescharacteristic
86#41—58no—
87C2×Q8C32×D511yescharacteristic, complemented
88C2×D4—53no—
89C22×C4—53no—
90C3×C5C2×C3×#4114yescomplemented
91C22×C3—524no—
92C22×C3—1024no—
93C22×C3C22×C3×D514yes—
94C3×C4—58no—
95C3×C4C22×C3×D5124yes—
96C2×C5C32×#4112yescomplemented
97C2×C5C24×C3211yescharacteristic
98D5—26no—
99C32C2×#71311yescharacteristic, direct product factor, Sylow
100C23—53no—
101Q8C2×C32×D514yescomplemented
102D4—512no—
103C2×C4—51no—
104C2×C4—512no—
105C2×C4C2×C32×D513yes—
106C2×C3—1024no—
107C2×C3C3×#71318yesdirect product factor
108C2×C3C23×C3×D514yes—
109C5C2×C32×#4111yescharacteristic, complemented, Sylow
110C22—56no—
111C22—106no—
112C22C22×C32×D511yescharacteristic
113C4—52no—
114C4C22×C32×D516yes—
115C3C2×C3×#71314yesdirect product factor
116C2—106no—
117C2C32×#71312yesdirect product factor
118C2C23×C32×D511yescharacteristic
subgroupG/H
centerC22×C32C22×D5
commutator, cosocleC2×C5C24×C32
FrattiniC2C23×C32×D5
FittingC2×C32×C5×Q8C2
socleC22×C32×C5C23
hypercenterC2×C32×Q8D5
hypocenterC5C2×C32×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C32 ◁ C2×C32×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×Q8C2semidirect
2. C32×#713C2direct (N × H)
3. C2×C32×D20C2semidirect
4. C2×C32×C4×D5C2semidirect
5. C2×C3×#713C3direct (N × H)
7. C32×C5×Q8C22semidirect
10. C32×D20C22semidirect
11. C32×C4×D5C22semidirect
13. C2×C3×C5×Q8C2×C3semidirect
14. C3×#713C2×C3direct (N × H)
15. C2×C3×D20C2×C3semidirect
16. C2×C3×C4×D5C2×C3semidirect
22. C2×#713C32direct (N × H)
24. C2×C32×Q8D5semidirect
28. C3×C5×Q8C22×C3semidirect
31. C3×D20C22×C3semidirect
32. C3×C4×D5C22×C3semidirect
34. C2×C32×C5#41semidirect
37. C2×C5×Q8C2×C32semidirect
38. #713C2×C32direct (N × H)
39. C2×D20C2×C32semidirect
40. C2×C4×D5C2×C32semidirect
42. C32×Q8C2×D5semidirect
53. C2×C3×Q8C3×D5semidirect
56. C32×C5C2×#41semidirect
58. C5×Q8C22×C32semidirect
61. D20C22×C32semidirect
62. C4×D5C22×C32semidirect
69. C2×C3×C5C3×#41semidirect
73. C3×Q8C2×C3×D5semidirect
84. C2×C32#713direct (N × H)
87. C2×Q8C32×D5semidirect
90. C3×C5C2×C3×#41semidirect
96. C2×C5C32×#41semidirect
99. C32C2×#713direct (N × H)
101. Q8C2×C32×D5semidirect
107. C2×C3C3×#713direct (N × H)
109. C5C2×C32×#41semidirect
115. C3C2×C3×#713direct (N × H)
117. C2C32×#713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×Q82
C32×#7132
C2×C32×D202
C2×C32×C4×D52
C2×C3×#7133
C2×C32×#415