Finite Group Databasebeta

← C3×D3×D5⋊C8 #13088633

Subgroups — C3×D3×D5⋊C8 #13088633

Order 1440.

326 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C3×C4×D3×D5C211yesmaximal, characteristic
2C3×D5⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C32×D5⋊C8C211yesmaximal, characteristic, complemented
4C3×#6738C212yesmaximal, complemented
5C3×D3×#170C212yesmaximal, complemented
6C2×C3×D5⋊C8—31nomaximal
7D3×D5⋊C8C311yesmaximal, characteristic, direct product factor
8C2×C3×D3×D5C411yescharacteristic
9C3×C4×D15C411yescharacteristic
10C3×C4×C5×D3C411yescharacteristic
11C32×C4×D5C2211yescharacteristic
12C3×#1200C2211yescharacteristic
13C3×D3×Dic5C2211yescharacteristic
14C3×D5×Dic3C411yescharacteristic
15C3×C3⋊#170C2212yescomplemented
16C32×#170C2212yescomplemented
17C2×C3×D3×C8—51nomaximal, Hall
18C2×C3×C4×D5—31no—
19C4×D3×D5C2×C311yescharacteristic
20D5⋊(C3⋊C8)C2×C311yescharacteristic, complemented
21C2×C3×#170—32no—
22C3×D5⋊C8—21no—
23C3×D5⋊C8—31no—
24C3×D5⋊C8—32no—
25C3×D5⋊C8D311yescharacteristic, direct product factor
26C3×D5⋊C8C2×C311yescharacteristic, complemented
27#6738C2×C312yescomplemented
28D3×#170C2×C312yescomplemented
29C2×C3×D15C2×C411yescharacteristic
30C2×C3×C5×D3C2×C411yescharacteristic
31C2×C32×D5C2×C411yescharacteristic
32C3×D3×D5C814yescomplemented
33C32×C4×C5C2×C411yescharacteristic
34C3×Dic15C2×C411yescharacteristic
35C3×C5×Dic3C2×C411yescharacteristic
36C32×Dic5C2311yescharacteristic
37C2×D5⋊C8—31noHall
38C2×C3×C4×D3—51no—
39C2×C32×C8—51no—
40C2×C3×C3⋊C8—51no—
41C3×D3×C8—52no—
42C3×D3×C8—52no—
43C22×C3×D5—31no—
44C2×D3×D5C3×C411yescharacteristic
45C2×C3×C4×C5—31no—
46C4×D15C3×C411yescharacteristic
47C4×C5×D3C3×C411yescharacteristic
48C2×C3×Dic5—31no—
49C3×C4×D5—21no—
50C3×C4×D5—31no—
51C3×C4×D5—31no—
52C3×C4×D5—31no—
53C3×C4×D5C2×D311yescharacteristic
54C3×C4×D5C22×C311yescharacteristic
55#1200C22×C311yescharacteristic
56D3×Dic5C22×C311yescharacteristic
57D5×Dic3C3×C411yescharacteristic
58C3⋊#170C22×C312yescomplemented
59C3×#170—22no—
60C3×#170—32no—
61C3×#170C2×D312yescomplemented
62C3×#170C22×C312yescomplemented
63C22×C3×C8—151no—
64C2×D3×C8—51no—
65C2×C32×C5C22×C411yescharacteristic
66C3×D15C2×C812yescomplemented
67C3×C5×D3C2×C812yescomplemented
68C32×D5C2×C812yescomplemented
69C2×C4×D5—31no—
70C2×#170—32no—
71D5⋊C8—31no—
72D5⋊C8—32no—
73D5⋊C8C3×D311yescharacteristic, direct product factor
74C22×C3×D3—51no—
75C2×C32×C4—51no—
76C2×C3×Dic3—51no—
77C3×C4×D3—51no—
78C3×C4×D3—51no—
79C3×C4×D3—51no—
80C3×C4×D3AGL(1,𝔽5)11yescharacteristic
81C32×C8—52no—
82C3×C3⋊C8—52no—
83C22×C3×C5—31no—
84C2×D15C2×C3×C411yescharacteristic
85C2×C5×D3C2×C3×C411yescharacteristic
86C2×C3×D5—21no—
87C2×C3×D5—31no—
88C2×C3×D5—34no—
89C2×C3×D5C4×D311yescharacteristic
90C2×C3×D5C2×C3×C411yescharacteristic
91D3×D5C3×C814yescomplemented
92C3×C4×C5—21no—
93C3×C4×C5—31no—
94C3×C4×C5C4×D311yescharacteristic
95C3×C4×C5C2×C3×C411yescharacteristic
96Dic15C2×C3×C411yescharacteristic
97C3×Dic5—21no—
98C3×Dic5—31no—
99C3×Dic5C22×D311yescharacteristic
100C3×Dic5C23×C311yescharacteristic
101C5×Dic3C2×C3×C411yescharacteristic
102C22×C3×C4—151no—
103C2×C4×D3—51no—
104C2×C3×C8—51no—
105C2×C3×C8—51no—
106C2×C3×C8—101no—
107C2×C3×C8—152no—
108C2×C3×C8—152no—
109C2×C3×C8—151no—
110C2×C3⋊C8—51no—
111D3×C8—52no—
112D3×C8—52no—
113C32×C5C22×C811yescharacteristic, complemented, Hall
114C22×D5—31no—
115C2×C4×C5—31no—
116C2×Dic5—31no—
117C4×D5—31no—
118C4×D5—31no—
119C4×D5—31no—
120C4×D5C2×C3×D311yescharacteristic
121#170—32no—
122#170C2×C3×D312yescomplemented
123C22×C32—51no—
124C2×C3×D3—51no—
125C2×C3×D3—54no—
126C2×C3×D3C2×AGL(1,𝔽5)11yescharacteristic
127C32×C4—51no—
128C32×C4C2×AGL(1,𝔽5)11yescharacteristic
129C3×Dic3—51no—
130C3×Dic3C2×AGL(1,𝔽5)11yescharacteristic
131C22×C8—151noSylow
132C2×C3×C5—21no—
133C2×C3×C5—32no—
134C2×C3×C5C2×C4×D311yescharacteristic
135C2×C3×C5C22×C3×C411yescharacteristic
136D15C2×C3×C812yescomplemented
137C3×D5—22no—
138C3×D5—32no—
139C3×D5D3×C812yescomplemented
140C3×D5C2×C3×C812yescomplemented
141C5×D3C2×C3×C812yescomplemented
142C23×C3—151no—
143C22×D3—51no—
144C2×C3×C4—31no—
145C2×C3×C4—51no—
146C2×C3×C4—51no—
147C2×C3×C4—101no—
148C2×C3×C4—151no—
149C2×C3×C4—151no—
150C2×C3×C4—151no—
151C2×C3×C4—151no—
152C2×Dic3—51no—
153C4×D3—51no—
154C4×D3—51no—
155C4×D3—51no—
156C4×D3C3×AGL(1,𝔽5)11yescharacteristic
157C3×C8—52no—
158C3×C8—52no—
159C3×C8—102no—
160C3×C8—152no—
161C3⋊C8—52no—
162C22×C5—31no—
163C2×D5—31no—
164C2×D5—34no—
165C2×D5C3×C4×D311yescharacteristic
166C4×C5—31no—
167C4×C5C3×C4×D311yescharacteristic
168Dic5—31no—
169Dic5C22×C3×D311yescharacteristic
170C2×C32—52no—
171C2×C32C22×AGL(1,𝔽5)11yescharacteristic
172C3×D3—52no—
173C3×D3D5⋊C812yesdirect product factor
174C22×C4—151no—
175C2×C8—51no—
176C2×C8—152no—
177C2×C8—152no—
178C2×C8—151no—
179C3×C5—21no—
180C3×C5C2×D3×C811yescharacteristic, complemented
181C3×C5C22×C3×C811yescharacteristic, complemented
182C22×C3—31no—
183C22×C3—51no—
184C22×C3—51no—
185C22×C3—101no—
186C22×C3—154no—
187C22×C3—151no—
188C2×D3—51no—
189C2×D3—54no—
190C2×D3C2×C3×AGL(1,𝔽5)11yescharacteristic
191C3×C4—21no—
192C3×C4—31no—
193C3×C4—51no—
194C3×C4—51no—
195C3×C4—101no—
196C3×C4—151no—
197C3×C4D3×AGL(1,𝔽5)11yescharacteristic
198C3×C4C2×C3×AGL(1,𝔽5)11yescharacteristic
199Dic3—51no—
200Dic3C2×C3×AGL(1,𝔽5)11yescharacteristic
201C2×C5—32no—
202C2×C5C2×C3×C4×D311yescharacteristic
203D5—32no—
204D5C3×D3×C812yescomplemented
205C32C2×D5⋊C811yescharacteristic, complemented, Sylow
206C23—151no—
207C2×C4—31no—
208C2×C4—51no—
209C2×C4—151no—
210C2×C4—151no—
211C2×C4—151no—
212C2×C4—151no—
213C8—52no—
214C8—152no—
215C2×C3—21no—
216C2×C3—32no—
217C2×C3—52no—
218C2×C3—52no—
219C2×C3—102no—
220C2×C3—152no—
221C2×C3C2×D3×AGL(1,𝔽5)11yescharacteristic
222C2×C3C22×C3×AGL(1,𝔽5)11yescharacteristic
223D3—52no—
224D3C3×D5⋊C812yesdirect product factor
225C5C2×C3×D3×C811yescharacteristic, complemented, Sylow
226C22—31no—
227C22—51no—
228C22—154no—
229C22—151no—
230C4—31no—
231C4—51no—
232C4—151no—
233C4C3×D3×AGL(1,𝔽5)11yescharacteristic
234C3—21no—
235C3D3×D5⋊C811yescharacteristic, direct product factor
236C3C2×C3×D5⋊C811yescharacteristic, complemented
237C2—32no—
238C2—52no—
239C2—152no—
240C2C2×C3×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, hypercenterC3×C4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C22×C3×C8
FrattiniC2C2×C3×D3×AGL(1,𝔽5)
FittingC32×C4×C5C2×C4
socleC2×C32×C5C22×C4
prime radicalC2×C3×D3×D5C4
cosocleC3×Dic5C23×C3
LCSG ▷ C3×C5
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×D5⋊(C3⋊C8)C2semidirect
3. C32×D5⋊C8C2semidirect
4. C3×#6738C2semidirect
5. C3×D3×#170C2semidirect
7. D3×D5⋊C8C3direct (N × H)
15. C3×C3⋊#170C22semidirect
16. C32×#170C22semidirect
20. D5⋊(C3⋊C8)C2×C3semidirect
25. C3×D5⋊C8D3direct (N × H)
26. C3×D5⋊C8C2×C3semidirect
27. #6738C2×C3semidirect
28. D3×#170C2×C3semidirect
32. C3×D3×D5C8semidirect
58. C3⋊#170C22×C3semidirect
61. C3×#170C2×D3semidirect
62. C3×#170C22×C3semidirect
66. C3×D15C2×C8semidirect
67. C3×C5×D3C2×C8semidirect
68. C32×D5C2×C8semidirect
73. D5⋊C8C3×D3direct (N × H)
91. D3×D5C3×C8semidirect
113. C32×C5C22×C8semidirect
122. #170C2×C3×D3semidirect
136. D15C2×C3×C8semidirect
139. C3×D5D3×C8semidirect
140. C3×D5C2×C3×C8semidirect
141. C5×D3C2×C3×C8semidirect
173. C3×D3D5⋊C8direct (N × H)
180. C3×C5C2×D3×C8semidirect
181. C3×C5C22×C3×C8semidirect
204. D5C3×D3×C8semidirect
205. C32C2×D5⋊C8semidirect
224. D3C3×D5⋊C8direct (N × H)
225. C5C2×C3×D3×C8semidirect
235. C3D3×D5⋊C8direct (N × H)
236. C3C2×C3×D5⋊C8semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D52
C3×D5⋊(C3⋊C8)2
C32×D5⋊C82
C3×#67382
C3×D3×#1702
C2×C3×D5⋊C83
D3×D5⋊C83
C2×C3×D3×C85