Finite Group Databasebeta

← C2×D3×Dic30 #13089349

Subgroups — C2×D3×Dic30 #13089349

Order 1440.

662 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 202 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×#67180C211yesmaximal, characteristic, complemented
2C2×C3×Dic30C211yesmaximal, characteristic, complemented
3C2×C3×C4×C5×D3C211yesmaximal, characteristic
4C2×#67153C212yesmaximal, complemented
5C2×D3×Dic15C212yesmaximal
6D3×Dic30C218yesmaximal, direct product factor
7C22×Dic30—31nomaximal
8C2×D3×Dic10—31nomaximal
9C22×C3×C5×D3C2211yescharacteristic
10C2×C32×C4×C5C2211yescharacteristic
11C2×C3⋊Dic15C2212yes—
12#67180C2214yescomplemented
13C2×C3×Dic15C2212yes—
14C3×Dic30C2214yescomplemented
15C2×C3×C5×Dic3C2211yescharacteristic
16C3×C4×C5×D3C2214yes—
17#67153C2218yescomplemented
18D3×Dic15C2218yes—
19C2×D3×Dic6—51nomaximal, Hall
20C22×C3×C4×C5—31no—
21C22×Dic15—32no—
22C2×Dic30—31no—
23C2×Dic30—31no—
24C2×Dic30—32no—
25C2×Dic30—38no—
26C2×Dic30—61no—
27C2×Dic30D311yescharacteristic, direct product factor
28C2×C4×C5×D3D311yescharacteristic
29C2×C3×Dic10—31no—
30C2×#1204—32no—
31C2×D3×Dic5—32no—
32D3×Dic10—38no—
33C22×C32×C5C2311yescharacteristic
34C2×C3×C5×D3Q814yescomplemented
35C2×C3×C5×D3C2312yes—
36C32×C4×C5C2312yes—
37C3⋊Dic15C2314yes—
38C3×Dic15C2314yes—
39C3×C5×Dic3C2312yes—
40C22×Dic10—91noHall
41C2×#634—51no—
42C2×C3×C4×D3D511yescharacteristic
43C2×C3×Dic6—51no—
44C2×#627—52no—
45C2×D3×Dic3—52no—
46D3×Dic6—58no—
47C23×C3×C5—31no—
48C22×C5×D3C2×D311yescharacteristic
49C2×C3×C4×C5—21no—
50C2×C3×C4×C5—31no—
51C2×C3×C4×C5—34no—
52C2×C3×C4×C5C2×D311yescharacteristic
53C2×C3×C4×C5C2×D311yescharacteristic
54C2×Dic15—32no—
55C2×Dic15—32no—
56C2×Dic15—38no—
57C2×Dic15—62no—
58C2×Dic15C2×D312yes—
59Dic30—34no—
60Dic30—34no—
61Dic30—38no—
62Dic30—64no—
63Dic30C2×D314yesdirect product factor
64C2×C5×Dic3C2×D311yescharacteristic
65C4×C5×D3C2×D314yes—
66C2×C3×Dic5—32no—
67C3×Dic10—34no—
68#1204—38no—
69D3×Dic5—38no—
70C2×D3×Q8—151no—
71C22×Dic6—151no—
72C2×C32×C5C2×Q812yescomplemented
73C2×C32×C5C2411yescharacteristic
74C3×C5×D3C2×Q814yescomplemented
75C22×C4×C5—31no—
76C22×Dic5—92no—
77C2×Dic10—31no—
78C2×Dic10—98no—
79C2×Dic10—92no—
80C2×Dic10—91no—
81C22×C3×D3C2×D511yescharacteristic
82C2×C32×C4C2×D511yescharacteristic
83C2×C3⋊Dic3—52no—
84#634—54no—
85C2×C3×Dic3—52no—
86C2×C3×Dic3C2×D511yescharacteristic
87C3×C4×D3C2×D514yes—
88C3×Dic6—54no—
89#627—58no—
90D3×Dic3—58no—
91C22×C3×C5—21no—
92C22×C3×C5—34no—
93C22×C3×C5—32no—
94C22×C3×C5C22×D311yescharacteristic
95C22×C3×C5C22×D311yescharacteristic
96C2×C5×D3Dic614yescomplemented
97C2×C5×D3C22×D312yes—
98C3×C4×C5—22no—
99C3×C4×C5—32no—
100C3×C4×C5C22×D312yes—
101C3×C4×C5C22×D312yes—
102Dic15—34no—
103Dic15—34no—
104Dic15—64no—
105Dic15C22×D314yes—
106C3×Dic5—34no—
107C5×Dic3C22×D312yes—
108C2×C3×Q8—151no—
109C22×C3×C4—31no—
110C22×Dic3—152no—
111D3×Q8—158no—
112C2×C4×D3—152no—
113C2×C4×D3D1511yescharacteristic
114C2×Dic6—51no—
115C2×Dic6—158no—
116C2×Dic6—152no—
117C2×Dic6—151no—
118C2×Dic6—151no—
119C2×Dic6—152no—
120C2×Dic6—301no—
121C32×C5C22×Q811yescharacteristic, complemented, Hall
122C23×C5—31no—
123C2×C4×C5—31no—
124C2×C4×C5—34no—
125C2×C4×C5D3211yescharacteristic
126C2×Dic5—32no—
127C2×Dic5—98no—
128C2×Dic5—92no—
129Dic10—34no—
130Dic10—98no—
131Dic10—94no—
132C22×C32C22×D511yescharacteristic
133C2×C3×D3Dic1014yescomplemented
134C2×C3×D3C22×D512yes—
135C32×C4C22×D512yes—
136C3⋊Dic3—54no—
137C3×Dic3—54no—
138C3×Dic3C22×D512yes—
139C22×Q8—451noSylow
140C2×C3×C5—21no—
141C2×C3×C5—22no—
142C2×C3×C5—34no—
143C2×C3×C5C2×Dic612yescomplemented
144C2×C3×C5D3×Q812yescomplemented
145C2×C3×C5C23×D311yescharacteristic
146C2×C3×C5C23×D311yescharacteristic
147C5×D3C2×Dic614yescomplemented
148C23×C3—31no—
149C22×D3C2×D1511yescharacteristic
150C3×Q8—154no—
151C2×C3×C4—21no—
152C2×C3×C4—31no—
153C2×C3×C4—34no—
154C2×C3×C4—152no—
155C2×C3×C4D3×D511yescharacteristic
156C2×C3×C4C2×D1511yescharacteristic
157C2×Dic3—52no—
158C2×Dic3—158no—
159C2×Dic3—152no—
160C2×Dic3—152no—
161C2×Dic3—302no—
162C2×Dic3C2×D1511yescharacteristic
163C4×D3—158no—
164C4×D3C2×D1514yes—
165Dic6—54no—
166Dic6—158no—
167Dic6—154no—
168Dic6—154no—
169Dic6—158no—
170Dic6—304no—
171C22×C5—32no—
172C22×C5—34no—
173C22×C5C2×D3211yescharacteristic
174C4×C5—32no—
175C4×C5C2×D3212yes—
176Dic5—34no—
177Dic5—94no—
178C2×C32C2×Dic1012yescomplemented
179C2×C32C23×D511yescharacteristic
180C3×D3C2×Dic1014yescomplemented
181C2×Q8—151no—
182C2×Q8—452no—
183C2×Q8—458no—
184C2×Q8—451no—
185C22×C4—31no—
186C22×C4—452no—
187C3×C5—21no—
188C3×C5C22×Dic611yescharacteristic, complemented
189C3×C5C2×D3×Q811yescharacteristic, complemented
190C22×C3—21no—
191C22×C3—34no—
192C22×C3—32no—
193C22×C3C2×D3×D511yescharacteristic
194C22×C3C22×D1511yescharacteristic
195C2×D3Dic3014yesdirect product factor
196C2×D3C22×D1512yes—
197C3×C4—22no—
198C3×C4—32no—
199C3×C4—154no—
200C3×C4C2×D3×D512yes—
201C3×C4C22×D1512yes—
202Dic3—54no—
203Dic3—154no—
204Dic3—154no—
205Dic3—304no—
206Dic3C22×D1512yes—
207C2×C5—34no—
208C2×C5D3×Dic612yescomplemented
209C2×C5C22×D3211yescharacteristic
210C32C22×Dic1011yescharacteristic, complemented, Sylow
211C23—31no—
212Q8—154no—
213Q8—458no—
214Q8—454no—
215C2×C4—31no—
216C2×C4—34no—
217C2×C4—152no—
218C2×C4—458no—
219C2×C4—452no—
220C2×C4D3×D1511yescharacteristic
221C2×C3—21no—
222C2×C3—22no—
223C2×C3—34no—
224C2×C3D3×Dic1012yescomplemented
225C2×C3C2×Dic3012yescomplemented
226C2×C3C22×D3×D511yescharacteristic
227C2×C3C23×D1511yescharacteristic
228D3C2×Dic3014yesdirect product factor
229C5C2×D3×Dic611yescharacteristic, complemented, Sylow
230C22—32no—
231C22—34no—
232C22C2×D3×D1511yescharacteristic
233C4—32no—
234C4—154no—
235C4—454no—
236C4C2×D3×D1512yes—
237C3—21no—
238C3C2×D3×Dic1011yescharacteristic, complemented
239C3C22×Dic3011yescharacteristic, complemented
240C2—34no—
241C2D3×Dic3012yesdirect product factor
242C2C22×D3×D1511yescharacteristic
subgroupG/H
centerC22C2×D3×D15
commutator, cosocleC2×C32×C5C24
FrattiniC2C22×D3×D15
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C3×C5×D3C22
hypercenterC2×C4D3×D15
hypocenterC32×C5C22×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#67180C2semidirect
2. C2×C3×Dic30C2semidirect
4. C2×#67153C2semidirect
6. D3×Dic30C2direct (N × H)
12. #67180C22semidirect
14. C3×Dic30C22semidirect
17. #67153C22semidirect
27. C2×Dic30D3direct (N × H)
34. C2×C3×C5×D3Q8semidirect
63. Dic30C2×D3direct (N × H)
72. C2×C32×C5C2×Q8semidirect
74. C3×C5×D3C2×Q8semidirect
96. C2×C5×D3Dic6semidirect
121. C32×C5C22×Q8semidirect
133. C2×C3×D3Dic10semidirect
143. C2×C3×C5C2×Dic6semidirect
144. C2×C3×C5D3×Q8semidirect
147. C5×D3C2×Dic6semidirect
178. C2×C32C2×Dic10semidirect
180. C3×D3C2×Dic10semidirect
188. C3×C5C22×Dic6semidirect
189. C3×C5C2×D3×Q8semidirect
195. C2×D3Dic30direct (N × H)
208. C2×C5D3×Dic6semidirect
210. C32C22×Dic10semidirect
224. C2×C3D3×Dic10semidirect
225. C2×C3C2×Dic30semidirect
228. D3C2×Dic30direct (N × H)
229. C5C2×D3×Dic6semidirect
238. C3C2×D3×Dic10semidirect
239. C3C22×Dic30semidirect
241. C2D3×Dic30direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#671802
C2×C3×Dic302
C2×C3×C4×C5×D32
C2×#671532
C2×D3×Dic152
D3×Dic302
C22×Dic303
C2×D3×Dic103
C2×D3×Dic65