Finite Group Databasebeta

← C32×#4149 #13089454

Subgroups — C32×#4149 #13089454

Order 1440.

996 conjugacy classes of subgroups; only the 510 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 510 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
1C32×C5×#41C211yesmaximal, characteristic, complemented
2C32×#713C212yesmaximal, complemented
3C32×D4×D5C216yesmaximal, complemented
4C32×#709C213yesmaximal, complemented
5C2×C32×D20C213yesmaximal, complemented
6C3×#4149C314yesmaximal, direct product factor
7C22×C32×D5C2216yescomplemented
8C32×C5×Q8C2211yescharacteristic, complemented
9C32×C5×D4C2213yescomplemented
10C2×C32×C4×C5C2213yescomplemented
11C32×C22⋊D5C2216yescomplemented
12C32×D20C2213yescomplemented
13C32×D20C2216yescomplemented
14C32×C4×D5C2216yescomplemented
15C32×Dic10C2211yescharacteristic, complemented
16C32×H(5,𝔽2)—51nomaximal, Hall
17C3×C5×#41C2×C314yescomplemented
18C3×#713C2×C318yescomplemented
19C3×D4×D5C2×C3124yescomplemented
20C3×#709C2×C3112yescomplemented
21C2×C3×D20C2×C3112yescomplemented
22C22×C32×C5C2313yes—
23C2×C32×D5—46no—
24C2×C32×D5C2316yes—
25C32×C4×C5C2311yescharacteristic
26C32×C4×C5C2313yes—
27C32×Dic5C2312yes—
28#4149C3211yescharacteristic, direct product factor, Hall
29C32×#41—52no—
30C32×#41—53no—
31C32×#41D511yescharacteristic, complemented
32C2×C32×D4—56no—
33C2×C32×D4—53no—
34C22×C3×D5C22×C3124yescomplemented
35C3×C5×Q8C22×C314yescomplemented
36C3×C5×D4C22×C3112yescomplemented
37C2×C3×C4×C5C22×C3112yescomplemented
38C3×C22⋊D5C22×C3124yescomplemented
39C3×D20C22×C3112yescomplemented
40C3×D20C22×C3124yescomplemented
41C3×C4×D5C22×C3124yescomplemented
42C3×Dic10C22×C314yescomplemented
43C3×H(5,𝔽2)—54no—
44C2×C32×C5—23no—
45C2×C32×C5C2411yescharacteristic
46C32×D5—26no—
47C5×#41C2×C3211yescharacteristic, complemented
48#713C2×C3212yescomplemented
49D4×D5C2×C3216yescomplemented
50#709C2×C3213yescomplemented
51C2×D20C2×C3213yescomplemented
52C23×C32—56no—
53C32×Q8—51no—
54C32×Q8C2×D511yescharacteristic, complemented
55C32×D4—56no—
56C32×D4—56no—
57C32×D4—53no—
58C32×D4C2×D513yescomplemented
59C2×C32×C4—56no—
60C2×C32×C4C2×D513yescomplemented
61C22×C3×C5C23×C3112yes—
62C2×C3×D5—424no—
63C2×C3×D5C23×C3124yes—
64C3×C4×C5C23×C314yes—
65C3×C4×C5C23×C3112yes—
66C3×Dic5C23×C318yes—
67C3×#41—58no—
68C3×#41—512no—
69C3×#41C3×D514yescomplemented
70C2×C3×D4—524no—
71C2×C3×D4—512no—
72C32×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
73C22×D5C22×C3216yescomplemented
74C5×Q8C22×C3211yescharacteristic, complemented
75C5×D4C22×C3213yescomplemented
76C2×C4×C5C22×C3213yescomplemented
77C22⋊D5C22×C3216yescomplemented
78D20C22×C3213yescomplemented
79D20C22×C3216yescomplemented
80C4×D5C22×C3216yescomplemented
81Dic10C22×C3211yescharacteristic, complemented
82C22×C32—56no—
83C22×C32—206no—
84C22×C32C22×D513yes—
85C32×C4—52no—
86C32×C4C22×D513yes—
87C32×C4C22×D511yescharacteristic
88H(5,𝔽2)—51noSylow
89C2×C3×C5—212no—
90C2×C3×C5C24×C314yes—
91C3×D5—224no—
92C23×C3—524no—
93C3×Q8—54no—
94C3×Q8C2×C3×D514yescomplemented
95C3×D4—524no—
96C3×D4—524no—
97C3×D4—512no—
98C3×D4C2×C3×D5112yescomplemented
99C2×C3×C4—524no—
100C2×C3×C4C2×C3×D5112yescomplemented
101C22×C5C23×C3213yes—
102C2×D5—46no—
103C2×D5C23×C3216yes—
104C4×C5C23×C3211yescharacteristic
105C4×C5C23×C3213yes—
106Dic5C23×C3212yes—
107C2×C32—23no—
108C2×C32—106no—
109C2×C32C23×D511yescharacteristic
110#41—52no—
111#41—53no—
112#41C32×D511yescharacteristic, complemented
113C2×D4—56no—
114C2×D4—53no—
115C3×C5C3×H(5,𝔽2)14yescomplemented
116C22×C3—524no—
117C22×C3—2024no—
118C22×C3C22×C3×D5112yes—
119C3×C4—58no—
120C3×C4C22×C3×D5112yes—
121C3×C4C22×C3×D514yes—
122C2×C5—23no—
123C2×C5C24×C3211yescharacteristic
124D5—26no—
125C32#414911yescharacteristic, direct product factor, Sylow
126C23—56no—
127Q8—51no—
128Q8C2×C32×D511yescharacteristic, complemented
129D4—56no—
130D4—56no—
131D4—53no—
132D4C2×C32×D513yescomplemented
133C2×C4—56no—
134C2×C4C2×C32×D513yescomplemented
135C2×C3—212no—
136C2×C3—1024no—
137C2×C3C23×C3×D514yes—
138C5C32×H(5,𝔽2)11yescharacteristic, complemented, Sylow
139C22—56no—
140C22—206no—
141C22C22×C32×D513yes—
142C4—52no—
143C4C22×C32×D513yes—
144C4C22×C32×D511yescharacteristic
145C3C3×#414914yesdirect product factor
146C2—23no—
147C2—106no—
148C2C23×C32×D511yescharacteristic
subgroupG/H
centerC2×C32C23×D5
commutator, cosocleC2×C5C24×C32
FrattiniC2C23×C32×D5
FittingC32×C5×#41C2
socleC2×C32×C5C24
hypercenterC32×#41D5
hypocenterC5C32×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C32 ◁ C32×#41

Complements

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

NH ≅ G/Ntype
1. C32×C5×#41C2semidirect
2. C32×#713C2semidirect
3. C32×D4×D5C2semidirect
4. C32×#709C2semidirect
5. C2×C32×D20C2semidirect
6. C3×#4149C3direct (N × H)
7. C22×C32×D5C22semidirect
8. C32×C5×Q8C22semidirect
9. C32×C5×D4C22semidirect
10. C2×C32×C4×C5C22semidirect
11. C32×C22⋊D5C22semidirect
12. C32×D20C22semidirect
13. C32×D20C22semidirect
14. C32×C4×D5C22semidirect
15. C32×Dic10C22semidirect
17. C3×C5×#41C2×C3semidirect
18. C3×#713C2×C3semidirect
19. C3×D4×D5C2×C3semidirect
20. C3×#709C2×C3semidirect
21. C2×C3×D20C2×C3semidirect
28. #4149C32direct (N × H)
31. C32×#41D5semidirect
34. C22×C3×D5C22×C3semidirect
35. C3×C5×Q8C22×C3semidirect
36. C3×C5×D4C22×C3semidirect
37. C2×C3×C4×C5C22×C3semidirect
38. C3×C22⋊D5C22×C3semidirect
39. C3×D20C22×C3semidirect
40. C3×D20C22×C3semidirect
41. C3×C4×D5C22×C3semidirect
42. C3×Dic10C22×C3semidirect
47. C5×#41C2×C32semidirect
48. #713C2×C32semidirect
49. D4×D5C2×C32semidirect
50. #709C2×C32semidirect
51. C2×D20C2×C32semidirect
54. C32×Q8C2×D5semidirect
58. C32×D4C2×D5semidirect
60. C2×C32×C4C2×D5semidirect
69. C3×#41C3×D5semidirect
72. C32×C5H(5,𝔽2)semidirect
73. C22×D5C22×C32semidirect
74. C5×Q8C22×C32semidirect
75. C5×D4C22×C32semidirect
76. C2×C4×C5C22×C32semidirect
77. C22⋊D5C22×C32semidirect
78. D20C22×C32semidirect
79. D20C22×C32semidirect
80. C4×D5C22×C32semidirect
81. Dic10C22×C32semidirect
94. C3×Q8C2×C3×D5semidirect
98. C3×D4C2×C3×D5semidirect
100. C2×C3×C4C2×C3×D5semidirect
112. #41C32×D5semidirect
115. C3×C5C3×H(5,𝔽2)semidirect
125. C32#4149direct (N × H)
128. Q8C2×C32×D5semidirect
132. D4C2×C32×D5semidirect
134. C2×C4C2×C32×D5semidirect
138. C5C32×H(5,𝔽2)semidirect
145. C3C3×#4149direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×#412
C32×#7132
C32×D4×D52
C32×#7092
C2×C32×D202
C3×#41493
C32×H(5,𝔽2)5