Finite Group Databasebeta

← C2×#11748320 #14411348

Subgroups — C2×#11748320 #14411348

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊#168C211yesmaximal, characteristic
2C22×C5×#208C211yesmaximal, characteristic
3C2×C3×#4072C211yesmaximal, characteristic
4C2×#90952C212yesmaximal, complemented
5#11748320C218yesmaximal, direct product factor
6C2×Dic5×C3⋊C8C212yesmaximal, complemented
7C2×#65411—31nomaximal, Hall
8C23×C3×C4×C5C2211yescharacteristic
9C22×C3⋊#168C418yescomplemented
10C22×C3⋊#168C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C22×C3⋊#168C2214yes—
13C2×C5×#208C418yescomplemented
14C2×C5×#208C2214yes—
15C22×C5×C3⋊C8C2212yes—
16C2×C3×C22⋊Dic5C412yes—
17C3×#4072C414yes—
18C3×#4072C2214yes—
19C2×C3×C4⋊Dic5C412yes—
20C2×C3×C4×Dic5C2212yes—
21#90952C2218yescomplemented
22Dic5×C3⋊C8C2218yescomplemented
23C2×#4997—51nomaximal, Hall
24C22×C5×M16—31no—
25C2×#4072D311yescharacteristic
26C23×#168—31no—
27#65411—38no—
28C2×#3947—32no—
29C2×C8×Dic5—32no—
30C24×C3×C5C2×C411yescharacteristic
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C3×C4×C5C2×C412yes—
33C22×C3×C4×C5C2×C414yes—
34C22×C3×C4×C5C2×C414yes—
35C22×C3×C4×C5C2311yescharacteristic
36C22×C3×C4×C5C2312yes—
37C22×C3×Dic5C2×C414yes—
38C2×C3⋊#168C2×C414yes—
39C2×C3⋊#168C2×C414yes—
40C2×C3⋊#168C2×C4116yescomplemented
41C2×C3⋊#168C2312yes—
42C2×C3⋊#168C2312yes—
43C5×#208C2×C4116yescomplemented
44C2×C5×C3⋊C8C2×C418yes—
45C2×C5×C3⋊C8C2314yes—
46C3×C22⋊Dic5C2×C418yes—
47C3×C4⋊Dic5C2×C418yes—
48C3×C4×Dic5C2×C414yes—
49C3×C4×Dic5C2314yes—
50C2×C3×#117—51no—
51C22×#208D511yescharacteristic
52C23×C3⋊C8—51no—
53#4997—58no—
54C2×#803—52no—
55C2×C4×C3⋊C8—52no—
56C23×C4×C5C2×D311yescharacteristic
57C2×C5×M16—38no—
58C2×C5×M16—34no—
59C22×C5×C8—32no—
60C2×C22⋊Dic5Dic312yes—
61#4072Dic314yes—
62#4072C2×D314yes—
63C2×C4⋊Dic5Dic312yes—
64C2×C4×Dic5C2×D312yes—
65C22×#168—38no—
66C22×#168—31no—
67C22×#168—31no—
68C22×#168—34no—
69#3947—38no—
70C8×Dic5—38no—
71C2×#405—151noSylow
72C23×C3×C5—24no—
73C23×C3×C5C4214yes—
74C23×C3×C5C22×C412yes—
75C23×C3×C5C22×C411yescharacteristic
76C2×C3×C4×C5C4218yes—
77C2×C3×C4×C5C4214yes—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×C4×C5C22×C412yes—
80C2×C3×C4×C5C22×C412yes—
81C2×C3×C4×C5C22×C414yes—
82C2×C3×C4×C5C22×C412yes—
83C2×C3×C4×C5C22×C414yes—
84C2×C3×C4×C5C2411yescharacteristic
85C2×C3×Dic5—28no—
86C2×C3×Dic5C22×C418yes—
87C3⋊#168C22×C414yes—
88C3⋊#168C22×C414yes—
89C5×C3⋊C8C22×C418yes—
90C23×C3×C4C2×D511yescharacteristic
91C3×#117—54no—
92C3×#117—54no—
93C2×C3×C4⋊C4—52no—
94C2×C3×C22⋊C4—52no—
95C2×C3×C42—52no—
96C2×#208Dic518yescomplemented
97C2×#208C2×D514yes—
98C22×C3⋊C8—58no—
99C22×C3⋊C8—51no—
100C22×C3⋊C8—51no—
101C22×C3⋊C8—54no—
102C22×C3⋊C8C2×D512yes—
103#803—58no—
104C4×C3⋊C8—58no—
105C24×C5C2×Dic311yescharacteristic
106C22×C4×C5C4×D314yes—
107C22×C4×C5C4×D314yes—
108C22×C4×C5C2×Dic311yescharacteristic
109C22×C4×C5C2×Dic312yes—
110C22×C4×C5C22×D312yes—
111C22×C4×C5C22×D311yescharacteristic
112C22×Dic5C2×Dic314yes—
113C5×M16—316no—
114C2×C5×C8—38no—
115C2×C5×C8—34no—
116C22⋊Dic5C2×Dic318yes—
117C4⋊Dic5C2×Dic318yes—
118C4×Dic5C2×Dic314yes—
119C4×Dic5C22×D314yes—
120C2×#168—34no—
121C2×#168—34no—
122C2×#168—316no—
123C2×#168—32no—
124C2×#168—32no—
125C22×M16—31no—
126C23×C8—151no—
127C2×#117—51no—
128#405—158no—
129C2×#97—152no—
130C2×C4×C8—152no—
131C22×C3×C5—24no—
132C22×C3×C5—28no—
133C22×C3×C5C2×C4214yes—
134C22×C3×C5C2×C4212yes—
135C22×C3×C5#13114yes—
136C22×C3×C5C23×C411yescharacteristic
137C3×C4×C5C2×C4212yes—
138C3×C4×C5C2×C4214yes—
139C3×C4×C5C23×C411yescharacteristic
140C3×C4×C5C23×C411yescharacteristic
141C3×Dic5—28no—
142C24×C3C4×D511yescharacteristic
143C22×C3×C4—54no—
144C22×C3×C4C4×D511yescharacteristic
145C22×C3×C4C4×D512yes—
146C22×C3×C4C4×D514yes—
147C22×C3×C4C2×Dic514yes—
148C22×C3×C4C22×D512yes—
149C22×C3×C4C22×D511yescharacteristic
150C3×C4⋊C4—58no—
151C3×C22⋊C4—58no—
152C3×C42—54no—
153C3×C42—54no—
154#208C2×Dic5116yescomplemented
155C2×C3⋊C8—54no—
156C2×C3⋊C8—54no—
157C2×C3⋊C8—516no—
158C2×C3⋊C8—52no—
159C2×C3⋊C8—52no—
160C2×C3⋊C8C2×Dic518yes—
161C2×C3⋊C8C22×D514yes—
162C23×C5—24no—
163C23×C5C4×Dic314yes—
164C23×C5C22×Dic312yes—
165C23×C5C22×Dic311yescharacteristic
166C2×C4×C5C4×Dic318yes—
167C2×C4×C5C4×Dic314yes—
168C2×C4×C5C2×C4×D312yes—
169C2×C4×C5C2×C4×D314yes—
170C2×C4×C5C2×C4×D314yes—
171C2×C4×C5C2×C4×D312yes—
172C2×C4×C5C22×Dic311yescharacteristic
173C2×C4×C5C22×Dic312yes—
174C2×C4×C5C23×D311yescharacteristic
175C2×Dic5—28no—
176C2×Dic5C22×Dic318yes—
177C5×C8—38no—
178#168—34no—
179#168—34no—
180C23×C4D3×D511yescharacteristic
181C2×M16—38no—
182C2×M16—34no—
183C22×C8—32no—
184C22×C8—158no—
185C22×C8—154no—
186C22×C8—151no—
187C22×C8—151no—
188#117—54no—
189#117—54no—
190C2×C4⋊C4—52no—
191C2×C22⋊C4—52no—
192C2×C42—52no—
193#97—158no—
194C4×C8—158no—
195C2×C3×C5—24no—
196C2×C3×C5#40514yescomplemented
197C2×C3×C5C22×C4211yescharacteristic
198C2×C3×C5C2×#13112yes—
199C23×C3—24no—
200C23×C3C4×Dic514yes—
201C23×C3C2×C4×D512yes—
202C23×C3C2×C4×D511yescharacteristic
203C2×C3×C4—58no—
204C2×C3×C4—108no—
205C2×C3×C4C4×Dic518yes—
206C2×C3×C4C4×Dic514yes—
207C2×C3×C4C2×C4×D511yescharacteristic
208C2×C3×C4C2×C4×D512yes—
209C2×C3×C4C2×C4×D514yes—
210C2×C3×C4C2×C4×D512yes—
211C2×C3×C4C22×Dic512yes—
212C2×C3×C4C22×Dic514yes—
213C2×C3×C4C23×D511yescharacteristic
214C3⋊C8—54no—
215C3⋊C8—54no—
216C3⋊C8C22×Dic518yes—
217C22×C5—28no—
218C22×C5—24no—
219C22×C5C2×C4×Dic314yes—
220C22×C5C2×C4×Dic312yes—
221C22×C5#94814yes—
222C22×C5C23×Dic311yescharacteristic
223C4×C5C2×C4×Dic312yes—
224C4×C5C2×C4×Dic314yes—
225C4×C5C22×C4×D311yescharacteristic
226C4×C5C22×C4×D311yescharacteristic
227Dic5—28no—
228C24D5×Dic311yescharacteristic
229C22×C4—54no—
230C22×C4D5×Dic311yescharacteristic
231C22×C4D5×Dic312yes—
232C22×C4D3×Dic514yes—
233C22×C4#120014yes—
234C22×C4C2×D3×D512yes—
235C22×C4C2×D3×D511yescharacteristic
236M16—316no—
237C2×C8—38no—
238C2×C8—34no—
239C2×C8—1516no—
240C2×C8—154no—
241C2×C8—154no—
242C2×C8—152no—
243C2×C8—152no—
244C4⋊C4—58no—
245C22⋊C4—58no—
246C42—54no—
247C42—54no—
248C3×C5C2×#40511yescharacteristic, complemented, Hall
249C22×C3—24no—
250C22×C3—28no—
251C22×C3#405314yes—
252C22×C3C2×C4×Dic514yes—
253C22×C3C2×C4×Dic512yes—
254C22×C3C22×C4×D511yescharacteristic
255C3×C4—108no—
256C3×C4C2×C4×Dic512yes—
257C3×C4C2×C4×Dic514yes—
258C3×C4C22×C4×D511yescharacteristic
259C3×C4C23×Dic511yescharacteristic
260C2×C5—24no—
261C2×C5#499714yescomplemented
262C2×C5C22×C4×Dic311yescharacteristic
263C2×C5C2×#94812yes—
264C23—24no—
265C23Dic3×Dic514yes—
266C23C2×D5×Dic312yes—
267C23C2×D5×Dic311yescharacteristic
268C2×C4—58no—
269C2×C4—108no—
270C2×C4Dic3×Dic518yes—
271C2×C4Dic3×Dic514yes—
272C2×C4C2×D5×Dic311yescharacteristic
273C2×C4C2×D5×Dic312yes—
274C2×C4C2×D3×Dic512yes—
275C2×C4C2×D3×Dic514yes—
276C2×C4C2×#120014yes—
277C2×C4C2×#120012yes—
278C2×C4C22×D3×D511yescharacteristic
279C8—38no—
280C8—154no—
281C8—154no—
282C2×C3—24no—
283C2×C3#6541114yescomplemented
284C2×C3C2×#405312yes—
285C2×C3C22×C4×Dic511yescharacteristic
286C5C2×#499711yescharacteristic, complemented, Sylow
287C22—24no—
288C22—28no—
289C22#9128414yes—
290C22C2×Dic3×Dic514yes—
291C22C2×Dic3×Dic512yes—
292C22C22×D5×Dic311yescharacteristic
293C4—108no—
294C4C2×Dic3×Dic512yes—
295C4C2×Dic3×Dic514yes—
296C4C22×D3×Dic511yescharacteristic
297C4C22×#120011yescharacteristic
298C3C2×#6541111yescharacteristic, complemented, Sylow
299C2—24no—
300C2#1174832014yesdirect product factor
301C2C2×#9128412yes—
302C2C22×Dic3×Dic511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C22×C42
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC2×C3×C4×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#405
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#90952C2semidirect
5. #11748320C2direct (N × H)
6. C2×Dic5×C3⋊C8C2semidirect
9. C22×C3⋊#168C4semidirect
13. C2×C5×#208C4semidirect
21. #90952C22semidirect
22. Dic5×C3⋊C8C22semidirect
40. C2×C3⋊#168C2×C4semidirect
43. C5×#208C2×C4semidirect
96. C2×#208Dic5semidirect
154. #208C2×Dic5semidirect
196. C2×C3×C5#405semidirect
248. C3×C5C2×#405semidirect
261. C2×C5#4997semidirect
283. C2×C3#65411semidirect
286. C5C2×#4997semidirect
298. C3C2×#65411semidirect
300. C2#11748320direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊#1682
C22×C5×#2082
C2×C3×#40722
C2×#909522
#117483202
C2×Dic5×C3⋊C82
C2×#654113
C2×#49975