Finite Group Databasebeta

← C5×D3×D24 #13087065

Subgroups — C5×D3×D24 #13087065

Order 1440.

326 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C5×D3×D12C212yesmaximal, complemented
2C5×#3745C211yesmaximal, characteristic, complemented
3C3×C5×D24C211yesmaximal, characteristic, complemented
4C3×C5×D3×C8C211yesmaximal, characteristic, complemented
5C5×#3714C212yesmaximal, complemented
6C5×D3×D8—31nomaximal
7C2×C5×D24—31nomaximal
8C2×C5×D32—22no—
9C5×C4⋊(C3⋊D3)C2212yescomplemented
10C3×C5×D12C2212yescomplemented
11C3×C4×C5×D3C2211yescharacteristic
12C5×#626—22no—
13C32×C5×C8C2211yescharacteristic, complemented
14C3×C5×C3⋊C8C2211yescharacteristic, complemented
15D3×D24C511yesmaximal, characteristic, direct product factor, Hall
16C5×D3×D4—32no—
17C2×C5×D12—32no—
18C3×C5×D8—31no—
19C2×C3×C5×C8—31no—
20C5×#213—32no—
21C5×D24—32no—
22C5×D24—31no—
23C5×D24—31no—
24C5×D24—61no—
25C5×D24D311yescharacteristic, direct product factor
26C5×D3×C8D311yescharacteristic, complemented
27C2×C5×C3⋊D3—22no—
28C2×C3×C5×D3—22no—
29C2×C3×C5×D3D411yescharacteristic
30C5×D32—44no—
31C32×C4×C5C2311yescharacteristic
32C3×C5×Dic3D411yescharacteristic
33C2×C5×D8—91noHall
34D3×D12C2×C512yescomplemented
35#3745C2×C511yescharacteristic, complemented
36C3×D24C2×C511yescharacteristic, complemented
37C3×D3×C8C2×C511yescharacteristic, complemented
38#3714C2×C512yescomplemented
39C22×C5×D3—62no—
40C22×C5×D3—62no—
41C3×C5×D4—32no—
42C2×C3×C4×C5—31no—
43C5×#67—62no—
44C5×D12—32no—
45C5×D12—32no—
46C5×D12—62no—
47C5×D12—62no—
48C5×D12C2×D312yescomplemented
49C4×C5×D3C2×D311yescharacteristic
50C3×C5×C8—21no—
51C3×C5×C8—31no—
52C3×C5×C8C2×D311yescharacteristic, complemented
53C3×C5×C8C2×D311yescharacteristic, complemented
54C5×C3⋊C8C2×D311yescharacteristic, complemented
55D3×D8—31no—
56C2×D24—31no—
57C2×C32×C5C2×D411yescharacteristic
58C5×C3⋊D3—42no—
59C3×C5×D3—42no—
60C3×C5×D3D812yescomplemented
61C2×C5×D4—92no—
62C5×D8—31no—
63C5×D8—92no—
64C5×D8—91no—
65C2×C5×C8—31no—
66C2×D32—22no—
67C4⋊(C3⋊D3)C22×C512yescomplemented
68C3×D12C22×C512yescomplemented
69C3×C4×D3C22×C511yescharacteristic
70#626—22no—
71C32×C8C22×C511yescharacteristic, complemented
72C3×C3⋊C8C22×C511yescharacteristic, complemented
73C22×C3×C5—31no—
74C22×C3×C5—62no—
75C2×C5×D3—22no—
76C2×C5×D3—62no—
77C2×C5×D3—62no—
78C2×C5×D3—122no—
79C2×C5×D3—124no—
80C2×C5×D3—124no—
81C2×C5×D3D1211yescharacteristic
82C3×C4×C5—21no—
83C3×C4×C5—31no—
84C3×C4×C5C22×D311yescharacteristic
85C3×C4×C5C22×D311yescharacteristic
86C5×Dic3D1211yescharacteristic
87D3×D4—32no—
88C2×D12—32no—
89C3×D8—31no—
90C2×C3×C8—31no—
91#213—32no—
92D24—32no—
93D24—31no—
94D24—31no—
95D24—61no—
96D24C5×D311yescharacteristic, direct product factor
97D3×C8C5×D311yescharacteristic, complemented
98C32×C5C2×D811yescharacteristic, complemented, Hall
99C23×C5—182no—
100C5×D4—32no—
101C5×D4—92no—
102C5×D4—182no—
103C2×C4×C5—31no—
104C5×C8—31no—
105C5×C8D3211yescharacteristic, complemented
106C2×C3⋊D3—22no—
107C2×C3×D3—22no—
108C2×C3×D3C5×D411yescharacteristic
109D32—44no—
110C32×C4C23×C511yescharacteristic
111C3×Dic3C5×D411yescharacteristic
112C2×D8—91noSylow
113C2×C3×C5—21no—
114C2×C3×C5—32no—
115C2×C3×C5—122no—
116C2×C3×C5C2×D1211yescharacteristic
117C2×C3×C5D3×D411yescharacteristic
118C5×D3—42no—
119C5×D3—122no—
120C5×D3—122no—
121C5×D3—242no—
122C5×D3D2412yesdirect product factor
123C22×D3—62no—
124C22×D3—62no—
125C3×D4—32no—
126C2×C3×C4—31no—
127#67—62no—
128D12—32no—
129D12—32no—
130D12—62no—
131D12—62no—
132D12C2×C5×D312yescomplemented
133C4×D3C2×C5×D311yescharacteristic
134C3×C8—21no—
135C3×C8—31no—
136C3×C8C2×C5×D311yescharacteristic, complemented
137C3×C8C2×C5×D311yescharacteristic, complemented
138C3⋊C8C2×C5×D311yescharacteristic, complemented
139C22×C5—31no—
140C22×C5—62no—
141C22×C5—182no—
142C22×C5—364no—
143C4×C5—31no—
144C4×C5C2×D3211yescharacteristic
145C2×C32C2×C5×D411yescharacteristic
146C3⋊D3—42no—
147C3×D3—42no—
148C3×D3C5×D812yescomplemented
149C2×D4—92no—
150D8—31no—
151D8—92no—
152D8—91no—
153C2×C8—31no—
154C3×C5—21no—
155C3×C5C2×D2411yescharacteristic, complemented
156C3×C5D3×D811yescharacteristic, complemented
157C22×C3—31no—
158C22×C3—62no—
159C2×D3—22no—
160C2×D3—62no—
161C2×D3—62no—
162C2×D3—122no—
163C2×D3—124no—
164C2×D3—124no—
165C2×D3C5×D1211yescharacteristic
166C3×C4—21no—
167C3×C4—31no—
168C3×C4C22×C5×D311yescharacteristic
169C3×C4C22×C5×D311yescharacteristic
170Dic3C5×D1211yescharacteristic
171C2×C5—32no—
172C2×C5—122no—
173C2×C5—362no—
174C2×C5D3×D1211yescharacteristic
175C32C2×C5×D811yescharacteristic, complemented, Sylow
176C23—182no—
177D4—32no—
178D4—92no—
179D4—182no—
180C2×C4—31no—
181C8—31no—
182C8C5×D3211yescharacteristic, complemented
183C2×C3—21no—
184C2×C3—32no—
185C2×C3—122no—
186C2×C3C2×C5×D1211yescharacteristic
187C2×C3C5×D3×D411yescharacteristic
188D3—42no—
189D3—122no—
190D3—122no—
191D3—242no—
192D3C5×D2412yesdirect product factor
193C5D3×D2411yescharacteristic, direct product factor, Sylow
194C22—31no—
195C22—62no—
196C22—182no—
197C22—364no—
198C4—31no—
199C4C2×C5×D3211yescharacteristic
200C3—21no—
201C3C2×C5×D2411yescharacteristic, complemented
202C3C5×D3×D811yescharacteristic, complemented
203C2—32no—
204C2—122no—
205C2—362no—
206C2C5×D3×D1211yescharacteristic
subgroupG/H
centerC2×C5D3×D12
commutator, cosocleC32×C4C23×C5
FrattiniC4C2×C5×D32
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
hypercenterC5×C8D32
hypocenterC32C2×C5×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8

Complements

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

NH ≅ G/Ntype
1. C5×D3×D12C2semidirect
2. C5×#3745C2semidirect
3. C3×C5×D24C2semidirect
4. C3×C5×D3×C8C2semidirect
5. C5×#3714C2semidirect
9. C5×C4⋊(C3⋊D3)C22semidirect
10. C3×C5×D12C22semidirect
13. C32×C5×C8C22semidirect
14. C3×C5×C3⋊C8C22semidirect
15. D3×D24C5direct (N × H)
25. C5×D24D3direct (N × H)
26. C5×D3×C8D3semidirect
34. D3×D12C2×C5semidirect
35. #3745C2×C5semidirect
36. C3×D24C2×C5semidirect
37. C3×D3×C8C2×C5semidirect
38. #3714C2×C5semidirect
48. C5×D12C2×D3semidirect
52. C3×C5×C8C2×D3semidirect
53. C3×C5×C8C2×D3semidirect
54. C5×C3⋊C8C2×D3semidirect
60. C3×C5×D3D8semidirect
67. C4⋊(C3⋊D3)C22×C5semidirect
68. C3×D12C22×C5semidirect
71. C32×C8C22×C5semidirect
72. C3×C3⋊C8C22×C5semidirect
96. D24C5×D3direct (N × H)
97. D3×C8C5×D3semidirect
98. C32×C5C2×D8semidirect
105. C5×C8D32semidirect
122. C5×D3D24direct (N × H)
132. D12C2×C5×D3semidirect
136. C3×C8C2×C5×D3semidirect
137. C3×C8C2×C5×D3semidirect
138. C3⋊C8C2×C5×D3semidirect
148. C3×D3C5×D8semidirect
155. C3×C5C2×D24semidirect
156. C3×C5D3×D8semidirect
175. C32C2×C5×D8semidirect
182. C8C5×D32semidirect
192. D3C5×D24direct (N × H)
193. C5D3×D24direct (N × H)
201. C3C2×C5×D24semidirect
202. C3C5×D3×D8semidirect

Maximal subgroups

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

subgroupindex
C5×D3×D122
C5×#37452
C3×C5×D242
C3×C5×D3×C82
C5×#37142
C5×D3×D83
C2×C5×D243
D3×D245