Finite Group Databasebeta

← #14512480

Subgroups — #14512480

Order 1920.

382 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 42 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×A4×Dic10C211yesmaximal, characteristic
2#11756728C212yesmaximal
3#10604905—31nomaximal, Hall
4C2×C4×C5×A4C411yescharacteristic
5C2×A4×Dic5C411yescharacteristic
6C2×A4×Dic5C2211yescharacteristic
7A4×Dic10—22no—
8A4⋊#170—22no—
9#91234—41nomaximal
10#73146—51nomaximal, Hall
11C23×Dic10D311yescharacteristic
12#65798—32no—
13C2×#4005—32no—
14C2×#4005—31no—
15C2×#4005—31no—
16C22×C5×A4C2×C411yescharacteristic
17C2×C3×Dic10—41no—
18C4×C5×A4—21no—
19#6762—42no—
20A4×Dic5—21no—
21A4×Dic5D412yes—
22C2×Q8×A4—51no—
23#5409—52no—
24C23×C4×C5Dic311yescharacteristic
25C23×Dic5Dic311yescharacteristic
26C23×Dic5C2×D311yescharacteristic
27C22×Dic10—22no—
28C22×Dic10—31no—
29C22×Dic10—31no—
30C22×Dic10—31no—
31C22×Dic10—31no—
32C22×Dic10—62no—
33C2×#704—32no—
34C2×#704—32no—
35C22⋊#170—62no—
36C22⋊#170—62no—
37#4005—64no—
38#4005—61no—
39#4005—61no—
40#4005—61no—
41#4005—61no—
42#1784—151noSylow
43C2×C5×A4—21no—
44C2×C5×A4C22⋊C411yescharacteristic
45C2×C3×C4×C5—41no—
46C2×C3×Dic5—41no—
47C2×C3×Dic5—41no—
48C3×Dic10—82no—
49C3⋊#170—82no—
50Q8×A4—102no—
51C2×C4×A4—51no—
52C2×C4×A4—51no—
53C2×C4×A4AGL(1,𝔽5)11yescharacteristic
54A4⋊C8—102no—
55#836—201no—
56C24×C5C2×Dic311yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—31no—
59C22×C4×C5—31no—
60C22×C4×C5—61no—
61C22×Dic5—21no—
62C22×Dic5—31no—
63C22×Dic5—31no—
64C22×Dic5—31no—
65C22×Dic5—32no—
66C22×Dic5—31no—
67C22×Dic5—61no—
68C22×Dic5#6712yes—
69C2×Dic10—34no—
70C2×Dic10—31no—
71C2×Dic10—31no—
72C2×Dic10—31no—
73C2×Dic10—62no—
74C2×Dic10—62no—
75C2×Dic10—61no—
76C2×Dic10—62no—
77C2×Dic10—62no—
78C2×Dic10—62no—
79C2×Dic10—62no—
80C2×Dic10—62no—
81C2×Dic10S411yescharacteristic
82#704—62no—
83#704—62no—
84#704—62no—
85#704—62no—
86C2×#170—62no—
87C2×#170—62no—
88C23×Q8—51no—
89C2×#101—151no—
90C2×#101—151no—
91C2×#101—152no—
92#407—152no—
93C22×C3×C5—41no—
94C5×A4#10111yescharacteristic, complemented
95C3×C4×C5—81no—
96C3×Dic5—42no—
97C3×Dic5—81no—
98C22×A4C2×AGL(1,𝔽5)11yescharacteristic
99C2×C3×Q8—201no—
100C4×A4—21no—
101C4×A4—52no—
102C4×A4—101no—
103#208—202no—
104C23×C5—21no—
105C23×C5—31no—
106C23×C5—31no—
107C23×C5—61no—
108C23×C5#21711yescharacteristic
109C2×C4×C5—32no—
110C2×C4×C5—31no—
111C2×C4×C5—61no—
112C2×C4×C5—61no—
113C2×C4×C5—61no—
114C2×C4×C5SL(2,ℤ/4)11yescharacteristic
115C2×Dic5—31no—
116C2×Dic5—32no—
117C2×Dic5—32no—
118C2×Dic5—32no—
119C2×Dic5—32no—
120C2×Dic5—31no—
121C2×Dic5—61no—
122C2×Dic5—61no—
123C2×Dic5—61no—
124C2×Dic5—61no—
125C2×Dic5SL(2,ℤ/4)11yescharacteristic
126C2×Dic5C2×S411yescharacteristic
127Dic10—22no—
128Dic10—62no—
129Dic10—62no—
130Dic10—64no—
131Dic10—62no—
132#170—122no—
133#170—122no—
134C22×Q8—102no—
135C22×Q8—151no—
136C22×Q8—151no—
137C22×Q8—151no—
138C22×Q8—151no—
139C22×Q8—302no—
140C23×C4—51no—
141C23×C4—51no—
142C23×C4ΓL(1,𝔽16)11yescharacteristic
143C2×M16—152no—
144C2×M16—152no—
145#101—301no—
146#101—301no—
147#101—301no—
148#101—304no—
149#101—301no—
150C22⋊C8—302no—
151C22⋊C8—302no—
152C2×C3×C5—41no—
153C2×C3×C5—81no—
154C2×A4—21no—
155C2×A4C22⋊AGL(1,𝔽5)11yescharacteristic
156C3×Q8—402no—
157C2×C3×C4—41no—
158C2×C3×C4—201no—
159C2×C3×C4—201no—
160C3⋊C8—402no—
161C22×C5—31no—
162C22×C5—31no—
163C22×C5—32no—
164C22×C5—31no—
165C22×C5—61no—
166C22×C5—61no—
167C22×C5—61no—
168C22×C5#83611yescharacteristic, complemented
169C22×C5C2×SL(2,ℤ/4)11yescharacteristic
170C4×C5—21no—
171C4×C5—61no—
172Dic5—21no—
173Dic5—32no—
174Dic5—61no—
175Dic5GL(2,ℤ/4)12yes—
176C24C2×ΓL(1,𝔽16)11yescharacteristic
177C2×Q8—51no—
178C2×Q8—151no—
179C2×Q8—151no—
180C2×Q8—154no—
181C2×Q8—151no—
182C2×Q8—301no—
183C2×Q8—302no—
184C2×Q8—302no—
185C2×Q8—302no—
186C2×Q8—302no—
187C2×Q8—302no—
188C2×Q8—302no—
189C2×Q8—302no—
190C22×C4—21no—
191C22×C4—31no—
192C22×C4—31no—
193C22×C4—52no—
194C22×C4—61no—
195C22×C4—101no—
196C22×C4—151no—
197C22×C4—151no—
198C22×C4—152no—
199C22×C4—151no—
200C22×C4—151no—
201C22×C4—301no—
202M16—302no—
203M16—302no—
204M16—302no—
205M16—302no—
206C2×C8—302no—
207C2×C8—302no—
208C3×C5—41noHall
209C22×C3—41no—
210A4#400511yescharacteristic, complemented
211C3×C4—81no—
212C3×C4—202no—
213C3×C4—401no—
214C2×C5—21no—
215C2×C5—31no—
216C2×C5—31no—
217C2×C5—61no—
218C2×C5#543211yescharacteristic
219C23—21no—
220C23—31no—
221C23—31no—
222C23—61no—
223C23#676311yescharacteristic
224Q8—102no—
225Q8—302no—
226Q8—302no—
227Q8—302no—
228Q8—304no—
229C2×C4—32no—
230C2×C4—31no—
231C2×C4—51no—
232C2×C4—51no—
233C2×C4—61no—
234C2×C4—61no—
235C2×C4—61no—
236C2×C4—152no—
237C2×C4—152no—
238C2×C4—151no—
239C2×C4—152no—
240C2×C4—152no—
241C2×C4—151no—
242C2×C4—301no—
243C2×C4—301no—
244C2×C4—301no—
245C2×C4—301no—
246C2×C4A4⋊AGL(1,𝔽5)11yescharacteristic
247C8—602no—
248C8—602no—
249C2×C3—41no—
250C2×C3—81no—
251C5#7314611yescharacteristic, complemented, Sylow
252C22—31no—
253C22—31no—
254C22—32no—
255C22—31no—
256C22—61no—
257C22—61no—
258C22—61no—
259C22#9123411yescharacteristic, complemented
260C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
261C4—21no—
262C4—52no—
263C4—61no—
264C4—101no—
265C4—152no—
266C4—301no—
267C3—41noSylow
268C2—21no—
269C2—31no—
270C2—31no—
271C2—61no—
272C2#1175672911yescharacteristic
subgroupG/H
centerC2#11756729
commutator, prime radicalC22×C5×A4C2×C4
FrattiniC22C2×A4⋊AGL(1,𝔽5)
FittingC23×C4×C5Dic3
socleC23×C5#217
cosocleC2×A4×Dic5C22
hypercenterC2×C4A4⋊AGL(1,𝔽5)
hypocenterC5×A4#101
LCSG ▷ C22×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
94. C5×A4#101semidirect
168. C22×C5#836semidirect
210. A4#4005semidirect
251. C5#73146semidirect
259. C22#91234semidirect

Maximal subgroups

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

subgroupindex
C2×A4×Dic102
#117567282
#106049053
#912344
#731465