Finite Group Databasebeta

← C32×D5×#41 #13089453

Subgroups — C32×D5×#41 #13089453

Order 1440.

984 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×#41C211yesmaximal, characteristic, complemented
2C32×#713C211yesmaximal, characteristic, complemented
3C32×Q8×D5C211yesmaximal, characteristic, complemented
4C32×#711C213yesmaximal, complemented
5C32×D4×D5C213yesmaximal, complemented
6C32×#709C213yesmaximal, complemented
7C2×C32×C4×D5C213yesmaximal, complemented
8C3×D5×#41C314yesmaximal, direct product factor
9C22×C32×D5C2213yes—
10C32×C5×Q8C2211yescharacteristic, complemented
11C32×C5×D4C2213yescomplemented
12C2×C32×C4×C5C2213yescomplemented
13C32×C22⋊D5C2216yescomplemented
14C2×C32×Dic5C2213yescomplemented
15C32×D20C2213yescomplemented
16C32×C4×D5C2211yescharacteristic
17C32×C4×D5C2213yes—
18C32×C4×D5C2213yescomplemented
19C32×C4×D5C2213yescomplemented
20C32×Dic10C2213yescomplemented
21C2×C32×#41—51nomaximal, Hall
22C3×C5×#41C2×C314yescomplemented
23C3×#713C2×C314yescomplemented
24C3×Q8×D5C2×C314yescomplemented
25C3×#711C2×C3112yescomplemented
26C3×D4×D5C2×C3112yescomplemented
27C3×#709C2×C3112yescomplemented
28C2×C3×C4×D5C2×C3112yescomplemented
29C22×C32×C5C2313yes—
30C2×C32×D5—26no—
31C2×C32×D5C2313yes—
32C2×C32×D5C2311yescharacteristic
33C32×C4×C5C2313yes—
34C32×C4×C5C2311yescharacteristic
35C32×Dic5C2313yes—
36C32×Dic5C2311yescharacteristic
37D5×#41C3211yescharacteristic, direct product factor, Hall
38C32×#41—51no—
39C32×#41—53no—
40C32×#41—53no—
41C32×#41D511yescharacteristic, direct product factor
42C2×C32×Q8—51no—
43C2×C32×D4—53no—
44C22×C32×C4—53no—
45C22×C3×D5C22×C3112yes—
46C3×C5×Q8C22×C314yescomplemented
47C3×C5×D4C22×C3112yescomplemented
48C2×C3×C4×C5C22×C3112yescomplemented
49C3×C22⋊D5C22×C3124yescomplemented
50C2×C3×Dic5C22×C3112yescomplemented
51C3×D20C22×C3112yescomplemented
52C3×C4×D5C22×C314yes—
53C3×C4×D5C22×C3112yes—
54C3×C4×D5C22×C3112yescomplemented
55C3×C4×D5C22×C3112yescomplemented
56C3×Dic10C22×C3112yescomplemented
57C2×C3×#41—54no—
58C2×C32×C5—23no—
59C2×C32×C5C2411yescharacteristic
60C32×D5—23no—
61C32×D5#4112yesdirect product factor
62C5×#41C2×C3211yescharacteristic, complemented
63#713C2×C3211yescharacteristic, complemented
64Q8×D5C2×C3211yescharacteristic, complemented
65#711C2×C3213yescomplemented
66D4×D5C2×C3213yescomplemented
67#709C2×C3213yescomplemented
68C2×C4×D5C2×C3213yescomplemented
69C23×C32—53no—
70C32×Q8—53no—
71C32×Q8C2×D511yescharacteristic, complemented
72C32×D4—56no—
73C32×D4—53no—
74C32×D4C2×D513yescomplemented
75C2×C32×C4—53no—
76C2×C32×C4—53no—
77C2×C32×C4—53no—
78C2×C32×C4—51no—
79C2×C32×C4—53no—
80C2×C32×C4C2×D513yescomplemented
81C22×C3×C5C23×C3112yes—
82C2×C3×D5—224no—
83C2×C3×D5C23×C3112yes—
84C2×C3×D5C23×C314yes—
85C3×C4×C5C23×C3112yes—
86C3×C4×C5C23×C314yes—
87C3×Dic5C23×C3112yes—
88C3×Dic5C23×C314yes—
89C3×#41—54no—
90C3×#41—512no—
91C3×#41—512no—
92C3×#41C3×D514yesdirect product factor
93C2×C3×Q8—54no—
94C2×C3×D4—512no—
95C22×C3×C4—512no—
96C32×C5C2×#4111yescharacteristic, complemented, Hall
97C22×D5C22×C3213yes—
98C5×Q8C22×C3211yescharacteristic, complemented
99C5×D4C22×C3213yescomplemented
100C2×C4×C5C22×C3213yescomplemented
101C22⋊D5C22×C3216yescomplemented
102C2×Dic5C22×C3213yescomplemented
103D20C22×C3213yescomplemented
104C4×D5C22×C3211yescharacteristic
105C4×D5C22×C3213yes—
106C4×D5C22×C3213yescomplemented
107C4×D5C22×C3213yescomplemented
108Dic10C22×C3213yescomplemented
109C22×C32—51no—
110C22×C32—53no—
111C22×C32—106no—
112C22×C32C22×D513yes—
113C32×C4—51no—
114C32×C4—53no—
115C32×C4C22×D513yes—
116C32×C4C22×D511yescharacteristic
117C2×#41—51noSylow
118C2×C3×C5—212no—
119C2×C3×C5C24×C314yes—
120C3×D5—212no—
121C3×D5C3×#4118yesdirect product factor
122C23×C3—512no—
123C3×Q8—512no—
124C3×Q8C2×C3×D514yescomplemented
125C3×D4—524no—
126C3×D4—512no—
127C3×D4C2×C3×D5112yescomplemented
128C2×C3×C4—512no—
129C2×C3×C4—54no—
130C2×C3×C4—512no—
131C2×C3×C4—512no—
132C2×C3×C4—512no—
133C2×C3×C4C2×C3×D5112yescomplemented
134C22×C5C23×C3213yes—
135C2×D5—26no—
136C2×D5C23×C3213yes—
137C2×D5C23×C3211yescharacteristic
138C4×C5C23×C3213yes—
139C4×C5C23×C3211yescharacteristic
140Dic5C23×C3213yes—
141Dic5C23×C3211yescharacteristic
142C2×C32—23no—
143C2×C32—52no—
144C2×C32—103no—
145C2×C32C23×D511yescharacteristic
146#41—51no—
147#41—53no—
148#41—53no—
149#41C32×D511yescharacteristic, direct product factor
150C2×Q8—51no—
151C2×D4—53no—
152C22×C4—53no—
153C3×C5C2×C3×#4114yescomplemented
154C22×C3—54no—
155C22×C3—512no—
156C22×C3—1024no—
157C22×C3C22×C3×D5112yes—
158C3×C4—54no—
159C3×C4—512no—
160C3×C4C22×C3×D514yes—
161C3×C4C22×C3×D5112yes—
162C2×C5—23no—
163C2×C5C24×C3211yescharacteristic
164D5—23no—
165D5C32×#4112yesdirect product factor
166C32D5×#4111yescharacteristic, direct product factor, Sylow
167C23—53no—
168Q8—53no—
169Q8C2×C32×D511yescharacteristic, complemented
170D4—56no—
171D4—53no—
172D4C2×C32×D513yescomplemented
173C2×C4—53no—
174C2×C4—51no—
175C2×C4—53no—
176C2×C4—53no—
177C2×C4—53no—
178C2×C4C2×C32×D513yescomplemented
179C2×C3—212no—
180C2×C3—58no—
181C2×C3—1012no—
182C2×C3C23×C3×D514yes—
183C5C2×C32×#4111yescharacteristic, complemented, Sylow
184C22—51no—
185C22—53no—
186C22—106no—
187C22C22×C32×D513yes—
188C4—51no—
189C4—53no—
190C4C22×C32×D511yescharacteristic
191C4C22×C32×D513yes—
192C3C3×D5×#4114yesdirect product factor
193C2—23no—
194C2—52no—
195C2—103no—
196C2C23×C32×D511yescharacteristic
subgroupG/H
centerC32×C4C22×D5
commutator, cosocleC2×C5C24×C32
FrattiniC2C23×C32×D5
FittingC32×C5×#41C2
socleC2×C32×C5C24
hypercenterC32×#41D5
hypocenterC5C2×C32×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C32×C4 ◁ 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×Q8×D5C2semidirect
4. C32×#711C2semidirect
5. C32×D4×D5C2semidirect
6. C32×#709C2semidirect
7. C2×C32×C4×D5C2semidirect
8. C3×D5×#41C3direct (N × H)
10. C32×C5×Q8C22semidirect
11. C32×C5×D4C22semidirect
12. C2×C32×C4×C5C22semidirect
13. C32×C22⋊D5C22semidirect
14. C2×C32×Dic5C22semidirect
15. C32×D20C22semidirect
18. C32×C4×D5C22semidirect
19. C32×C4×D5C22semidirect
20. C32×Dic10C22semidirect
22. C3×C5×#41C2×C3semidirect
23. C3×#713C2×C3semidirect
24. C3×Q8×D5C2×C3semidirect
25. C3×#711C2×C3semidirect
26. C3×D4×D5C2×C3semidirect
27. C3×#709C2×C3semidirect
28. C2×C3×C4×D5C2×C3semidirect
37. D5×#41C32direct (N × H)
41. C32×#41D5direct (N × H)
46. C3×C5×Q8C22×C3semidirect
47. C3×C5×D4C22×C3semidirect
48. C2×C3×C4×C5C22×C3semidirect
49. C3×C22⋊D5C22×C3semidirect
50. C2×C3×Dic5C22×C3semidirect
51. C3×D20C22×C3semidirect
54. C3×C4×D5C22×C3semidirect
55. C3×C4×D5C22×C3semidirect
56. C3×Dic10C22×C3semidirect
61. C32×D5#41direct (N × H)
62. C5×#41C2×C32semidirect
63. #713C2×C32semidirect
64. Q8×D5C2×C32semidirect
65. #711C2×C32semidirect
66. D4×D5C2×C32semidirect
67. #709C2×C32semidirect
68. C2×C4×D5C2×C32semidirect
71. C32×Q8C2×D5semidirect
74. C32×D4C2×D5semidirect
80. C2×C32×C4C2×D5semidirect
92. C3×#41C3×D5direct (N × H)
96. C32×C5C2×#41semidirect
98. C5×Q8C22×C32semidirect
99. C5×D4C22×C32semidirect
100. C2×C4×C5C22×C32semidirect
101. C22⋊D5C22×C32semidirect
102. C2×Dic5C22×C32semidirect
103. D20C22×C32semidirect
106. C4×D5C22×C32semidirect
107. C4×D5C22×C32semidirect
108. Dic10C22×C32semidirect
121. C3×D5C3×#41direct (N × H)
124. C3×Q8C2×C3×D5semidirect
127. C3×D4C2×C3×D5semidirect
133. C2×C3×C4C2×C3×D5semidirect
149. #41C32×D5direct (N × H)
153. C3×C5C2×C3×#41semidirect
165. D5C32×#41direct (N × H)
166. C32D5×#41direct (N × H)
169. Q8C2×C32×D5semidirect
172. D4C2×C32×D5semidirect
178. C2×C4C2×C32×D5semidirect
183. C5C2×C32×#41semidirect
192. C3C3×D5×#41direct (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×Q8×D52
C32×#7112
C32×D4×D52
C32×#7092
C2×C32×C4×D52
C3×D5×#413
C2×C32×#415