Finite Group Databasebeta

← D3×D120 #13087266

Subgroups — D3×D120 #13087266

Order 1440.

326 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D3×D60C212yesmaximal, complemented
2#10623901C211yesmaximal, characteristic, complemented
3C3×D120C211yesmaximal, characteristic, complemented
4C3×C5×D3×C8C211yesmaximal, characteristic, complemented
5#10623799C212yesmaximal, complemented
6C2×D120—31nomaximal
7D3×D40—31nomaximal
8C2×D3×D15—22no—
9C4⋊(C3⋊D15)C2212yescomplemented
10C3×D60C2212yescomplemented
11C3×C4×C5×D3C2211yescharacteristic
12#67151—22no—
13C32×C5×C8C2211yescharacteristic, complemented
14C3×C5×C3⋊C8C2211yescharacteristic, complemented
15D3×D24—51nomaximal, Hall
16C2×D60—32no—
17D3×D20—32no—
18C2×C3×C5×C8—31no—
19D120—32no—
20D120—31no—
21D120—31no—
22D120—61no—
23D120D311yescharacteristic, direct product factor
24C5×D3×C8D311yescharacteristic, complemented
25C3×D40—31no—
26#6653—32no—
27C2×C3⋊D15—22no—
28C2×C3×D15—22no—
29C2×C3×C5×D3D411yescharacteristic
30D3×D15—44no—
31C32×C4×C5C2311yescharacteristic
32C3×C5×Dic3D411yescharacteristic
33C2×D40—91noHall
34D3×D12—52no—
35#3745—51no—
36C3×D24—51no—
37C3×D3×C8D511yescharacteristic, complemented
38#3714—52no—
39C22×D15—62no—
40C2×D3×D5—62no—
41C2×C3×C4×C5—31no—
42D60—32no—
43D60—32no—
44D60—62no—
45D60—62no—
46D60C2×D312yescomplemented
47C4×C5×D3C2×D311yescharacteristic
48C3×D20—32no—
49#1202—62no—
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—151no—
56C2×D24—151no—
57C2×C32×C5C2×D411yescharacteristic
58C3⋊D15—42no—
59C3×D15—42no—
60C3×C5×D3D812yescomplemented
61C2×D20—92no—
62C2×C5×C8—31no—
63D40—31no—
64D40—92no—
65D40—91no—
66C2×D32—102no—
67C4⋊(C3⋊D3)—52no—
68C3×D12—52no—
69C3×C4×D3C2×D511yescharacteristic
70#626—102no—
71C32×C8C2×D511yescharacteristic, complemented
72C3×C3⋊C8C2×D511yescharacteristic, complemented
73C22×C3×C5—31no—
74C2×D15—22no—
75C2×D15—62no—
76C2×D15—62no—
77C2×D15—122no—
78C2×D15—124no—
79C2×C5×D3D1211yescharacteristic
80C2×C3×D5—62no—
81D3×D5—124no—
82C3×C4×C5—21no—
83C3×C4×C5—31no—
84C3×C4×C5C22×D311yescharacteristic
85C3×C4×C5C22×D311yescharacteristic
86C5×Dic3D1211yescharacteristic
87D3×D4—152no—
88C2×D12—152no—
89C3×D8—151no—
90C2×C3×C8—31no—
91#213—152no—
92D24—51no—
93D24—152no—
94D24—151no—
95D24—151no—
96D24—301no—
97D3×C8D1511yescharacteristic, complemented
98C32×C5C2×D811yescharacteristic, complemented, Hall
99C22×D5—182no—
100C2×C4×C5—31no—
101D20—32no—
102D20—92no—
103D20—182no—
104C5×C8—31no—
105C5×C8D3211yescharacteristic, complemented
106C2×C3⋊D3—102no—
107C2×C3×D3—102no—
108C2×C3×D3D2011yescharacteristic
109D32—204no—
110C32×C4C22×D511yescharacteristic
111C3×Dic3D2011yescharacteristic
112C2×D8—451noSylow
113C2×C3×C5—21no—
114C2×C3×C5—32no—
115C2×C3×C5C2×D1211yescharacteristic
116C2×C3×C5D3×D411yescharacteristic
117D15—42no—
118D15—122no—
119D15—122no—
120D15—242no—
121C3×D5—122no—
122C5×D3D2412yescomplemented
123C22×D3—302no—
124C22×D3—302no—
125C3×D4—152no—
126C2×C3×C4—31no—
127#67—302no—
128D12—52no—
129D12—152no—
130D12—152no—
131D12—302no—
132D12—302no—
133C4×D3C2×D1511yescharacteristic
134C3×C8—21no—
135C3×C8—31no—
136C3×C8D3×D511yescharacteristic, complemented
137C3×C8C2×D1511yescharacteristic, complemented
138C3⋊C8C2×D1511yescharacteristic, complemented
139C22×C5—31no—
140C2×D5—62no—
141C2×D5—182no—
142C2×D5—364no—
143C4×C5—31no—
144C4×C5C2×D3211yescharacteristic
145C2×C32C2×D2011yescharacteristic
146C3⋊D3—202no—
147C3×D3—202no—
148C3×D3D4012yescomplemented
149C2×D4—452no—
150D8—151no—
151D8—452no—
152D8—451no—
153C2×C8—31no—
154C3×C5—21no—
155C3×C5C2×D2411yescharacteristic, complemented
156C3×C5D3×D811yescharacteristic, complemented
157C22×C3—31no—
158C22×C3—302no—
159C2×D3—102no—
160C2×D3—302no—
161C2×D3—302no—
162C2×D3—602no—
163C2×D3—604no—
164C2×D3—604no—
165C2×D3D6011yescharacteristic
166C3×C4—21no—
167C3×C4—31no—
168C3×C4C2×D3×D511yescharacteristic
169C3×C4C22×D1511yescharacteristic
170Dic3D6011yescharacteristic
171C2×C5—32no—
172C2×C5D3×D1211yescharacteristic
173D5—122no—
174D5—362no—
175C32C2×D4011yescharacteristic, complemented, Sylow
176C23—902no—
177D4—152no—
178D4—452no—
179D4—902no—
180C2×C4—31no—
181C8—31no—
182C8D3×D1511yescharacteristic, complemented
183C2×C3—21no—
184C2×C3—32no—
185C2×C3—602no—
186C2×C3D3×D2011yescharacteristic
187C2×C3C2×D6011yescharacteristic
188D3—202no—
189D3—602no—
190D3—602no—
191D3—1202no—
192D3D12012yesdirect product factor
193C5D3×D2411yescharacteristic, complemented, Sylow
194C22—31no—
195C22—302no—
196C22—902no—
197C22—1804no—
198C4—31no—
199C4C2×D3×D1511yescharacteristic
200C3—21no—
201C3D3×D4011yescharacteristic, complemented
202C3C2×D12011yescharacteristic, complemented
203C2—32no—
204C2—602no—
205C2—1802no—
206C2D3×D6011yescharacteristic
subgroupG/H
centerC2D3×D60
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
hypercenterC8D3×D15
hypocenterC32×C5C2×D8
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. D3×D60C2semidirect
2. #10623901C2semidirect
3. C3×D120C2semidirect
4. C3×C5×D3×C8C2semidirect
5. #10623799C2semidirect
9. C4⋊(C3⋊D15)C22semidirect
10. C3×D60C22semidirect
13. C32×C5×C8C22semidirect
14. C3×C5×C3⋊C8C22semidirect
23. D120D3direct (N × H)
24. C5×D3×C8D3semidirect
37. C3×D3×C8D5semidirect
46. D60C2×D3semidirect
52. C3×C5×C8C2×D3semidirect
53. C3×C5×C8C2×D3semidirect
54. C5×C3⋊C8C2×D3semidirect
60. C3×C5×D3D8semidirect
71. C32×C8C2×D5semidirect
72. C3×C3⋊C8C2×D5semidirect
97. D3×C8D15semidirect
98. C32×C5C2×D8semidirect
105. C5×C8D32semidirect
122. C5×D3D24semidirect
136. C3×C8D3×D5semidirect
137. C3×C8C2×D15semidirect
138. C3⋊C8C2×D15semidirect
148. C3×D3D40semidirect
155. C3×C5C2×D24semidirect
156. C3×C5D3×D8semidirect
175. C32C2×D40semidirect
182. C8D3×D15semidirect
192. D3D120direct (N × H)
193. C5D3×D24semidirect
201. C3D3×D40semidirect
202. C3C2×D120semidirect

Maximal subgroups

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

subgroupindex
D3×D602
#106239012
C3×D1202
C3×C5×D3×C82
#106237992
C2×D1203
D3×D403
D3×D245