Finite Group Databasebeta

← #14279091

Subgroups — #14279091

Order 1920.

332 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 72 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
1#11752404C211yesmaximal, characteristic
2C3×#65745C211yesmaximal, characteristic
3#11748343C211yesmaximal, characteristic
4#10598790—31nomaximal, Hall
5C2×C3×#709C2211yescharacteristic
6#91989—21no—
7C3×#4130—21no—
8C22×C3⋊#168C411yescharacteristic, complemented
9C2×C5×#208C411yescharacteristic, complemented
10#91240C412yescomplemented
11#91228—21no—
12C3×#4011C412yescomplemented
13C3×#3999—21no—
14#90955—21no—
15#90955—21no—
16#67696—51nomaximal, Hall
17#65745—31no—
18#65745D311yescharacteristic
19#65418—31no—
20C22×C3×C4×C5C2×C411yescharacteristic
21C2×C3×C22⋊D5C2×C411yescharacteristic
22C2×C3×C22⋊D5C2×C411yescharacteristic
23C3×#709—41no—
24C3×#709—41no—
25C2×C3×D20D411yescharacteristic
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×Dic10Q811yescharacteristic
29#6763—22no—
30C4⋊ΓL(1,𝔽16)—41no—
31C4×ΓL(1,𝔽16)—41no—
32C3×C22⋊AGL(1,𝔽5)—22no—
33C3×C4⋊AGL(1,𝔽5)—41no—
34C3×C4×AGL(1,𝔽5)—41no—
35C2×C3⋊#168—21no—
36C2×C3⋊#168—41no—
37C5×#208—41no—
38C2×C5×C3⋊C8—21no—
39C3×#410—51no—
40#5240—51no—
41#5234—51no—
42C2×#709C2×D311yescharacteristic
43#4130—21no—
44#4130—61no—
45C2×C5×M16—31no—
46C22×#168—31no—
47#4011—32no—
48#4011Dic312yescomplemented
49#3999—21no—
50#3999—61no—
51#3952—61no—
52#3952—61no—
53#1391—151noSylow
54C23×C3×C5C4211yescharacteristic
55C22×C3×D5C22⋊C411yescharacteristic
56C22×C3×D5C22⋊C411yescharacteristic
57C2×ΓL(1,𝔽16)—42no—
58C2×C3×AGL(1,𝔽5)—42no—
59C2×C3×C4×C5—21no—
60C2×C3×C4×C5—21no—
61C2×C3×C4×C5C22⋊C411yescharacteristic
62C2×C3×C4×C5C4⋊C411yescharacteristic
63C3×C22⋊D5—41no—
64C3×C22⋊D5—41no—
65C2×C3×Dic5C4⋊C411yescharacteristic
66C2×C3×Dic5C4⋊C411yescharacteristic
67C3×D20—41no—
68C3×C4×D5—21no—
69C3×C4×D5—21no—
70C3×C4×D5—21no—
71C3×C4×D5—21no—
72C3×Dic10—41no—
73C3⋊#168—41no—
74C5×C3⋊C8—41no—
75C2×C3×#41—51no—
76C3×#117—101no—
77#926—101no—
78C2×#208AGL(1,𝔽5)11yescharacteristic, complemented
79C22×C3⋊C8—51no—
80C3×#99—52no—
81C3×#99—101no—
82#834—52no—
83#834—101no—
84#830—101no—
85#830—101no—
86C22×C4×C5C4×D311yescharacteristic
87C2×C22⋊D5C4×D311yescharacteristic
88C2×C22⋊D5C2×Dic311yescharacteristic
89#709—41no—
90#709—41no—
91C2×D20#6711yescharacteristic
92C2×C4×D5D1211yescharacteristic
93C2×C4×D5#6711yescharacteristic
94C2×Dic10Dic611yescharacteristic
95C22⋊AGL(1,𝔽5)—22no—
96C22⋊AGL(1,𝔽5)—62no—
97C4⋊AGL(1,𝔽5)—41no—
98C4⋊AGL(1,𝔽5)—121no—
99C4×AGL(1,𝔽5)—41no—
100C4×AGL(1,𝔽5)—121no—
101C5×M16—121no—
102C2×C5×C8—61no—
103C2×#168—61no—
104C2×#168—121no—
105#410—51no—
106#410—151no—
107#408—151no—
108C22×C3×C5—21no—
109C22×C3×C5—41no—
110C22×C3×C5#9511yescharacteristic
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5—41no—
114C2×C3×D5—41no—
115ΓL(1,𝔽16)—82no—
116C3×AGL(1,𝔽5)—82no—
117C3×C4×C5—21no—
118C3×C4×C5#9911yescharacteristic
119C3×C4×C5#9911yescharacteristic
120C3×Dic5—21no—
121C3×Dic5—21no—
122C3×#41—201no—
123C3×#41—201no—
124C2×C3×Q8—51no—
125C2×C3×D4—51no—
126C2×C3×D4—51no—
127C2×C3×D4—51no—
128C22×C3×C4—51no—
129C22×C3×C4—51no—
130C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
131C3×C4⋊C4—201no—
132C3×C22⋊C4—102no—
133C3×C42—201no—
134#217—102no—
135C4⋊Dic3—201no—
136C4×Dic3—201no—
137#208—41no—
138C2×C3⋊C8—21no—
139C2×C3⋊C8—101no—
140C2×C3⋊C8—201no—
141C23×C5C4×Dic311yescharacteristic
142C22×D5(C2×D3)⋊C411yescharacteristic
143C22×D5#21711yescharacteristic
144C2×AGL(1,𝔽5)—42no—
145C2×AGL(1,𝔽5)—122no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5Dic3⋊C411yescharacteristic
149C2×C4×C5(C2×D3)⋊C411yescharacteristic
150C22⋊D5—41no—
151C22⋊D5—41no—
152C2×Dic5Dic3⋊C411yescharacteristic
153C2×Dic5C4⋊Dic311yescharacteristic
154D20—41no—
155C4×D5—21no—
156C4×D5—21no—
157C4×D5—21no—
158C4×D5—21no—
159Dic10—41no—
160C5×C8—121no—
161#168—121no—
162C2×#41—51no—
163C2×M16—31no—
164C22×C8—151no—
165#117—101no—
166#117—301no—
167#99—52no—
168#99—101no—
169#99—152no—
170#99—301no—
171C22⋊C8—301no—
172C22⋊C8—301no—
173C2×C3×C5—21no—
174C2×C3×C5—41no—
175C2×C3×C5#34211yescharacteristic
176C3×D5—41no—
177C3×D5—41no—
178C23×C3—51no—
179C23×C3—51no—
180C23×C3C4×AGL(1,𝔽5)11yescharacteristic
181C3×Q8—201no—
182C3×D4—201no—
183C3×D4—201no—
184C3×D4—201no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—51no—
188C2×C3×C4—51no—
189C2×C3×C4—101no—
190C2×C3×C4—101no—
191C2×C3×C4—101no—
192C2×C3×C4—101no—
193C2×C3×C4—202no—
194C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
195C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C2×Dic3—202no—
197C3⋊C8—41no—
198C3⋊C8—201no—
199C22×C5—21no—
200C22×C5—41no—
201C22×C5C3⋊#9511yescharacteristic
202C2×D5—21no—
203C2×D5—21no—
204C2×D5—41no—
205C2×D5—41no—
206AGL(1,𝔽5)—82no—
207AGL(1,𝔽5)—242no—
208C4×C5—21no—
209C4×C5#80611yescharacteristic
210C4×C5#80611yescharacteristic
211Dic5—21no—
212Dic5—21no—
213#41—201no—
214#41—201no—
215C2×Q8—51no—
216C2×D4—51no—
217C2×D4—51no—
218C2×D4—51no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4D3×AGL(1,𝔽5)11yescharacteristic
222M16—121no—
223C2×C8—61no—
224C2×C8—301no—
225C2×C8—601no—
226C4⋊C4—201no—
227C4⋊C4—601no—
228C22⋊C4—102no—
229C22⋊C4—302no—
230C42—201no—
231C42—601no—
232C3×C5#139111yescharacteristic, complemented, Hall
233C22×C3—21no—
234C22×C3—41no—
235C22×C3—101no—
236C22×C3—101no—
237C22×C3—201no—
238C22×C3—201no—
239C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
240C3×C4—21no—
241C3×C4—101no—
242C3×C4—101no—
243C3×C4—402no—
244C3×C4#399911yescharacteristic
245C3×C4#401111yescharacteristic
246Dic3—402no—
247C2×C5—21no—
248C2×C5—41no—
249C2×C5#452711yescharacteristic
250D5—41no—
251D5—41no—
252C23—51no—
253C23—51no—
254C23Dic3×AGL(1,𝔽5)11yescharacteristic
255Q8—201no—
256D4—201no—
257D4—201no—
258D4—201no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—51no—
262C2×C4—51no—
263C2×C4—101no—
264C2×C4—101no—
265C2×C4—101no—
266C2×C4—101no—
267C2×C4—202no—
268C2×C4—602no—
269C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
270C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
271C8—121no—
272C8—601no—
273C2×C3—21no—
274C2×C3—41no—
275C2×C3—201no—
276C2×C3—201no—
277C2×C3#6491711yescharacteristic
278C5#6769611yescharacteristic, complemented, Sylow
279C22—21no—
280C22—41no—
281C22—101no—
282C22—101no—
283C22—201no—
284C22—201no—
285C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
286C4—21no—
287C4—101no—
288C4—101no—
289C4—402no—
290C4—1202no—
291C4#9117211yescharacteristic
292C4#9117311yescharacteristic
293C3#1059879011yescharacteristic, complemented, Sylow
294C2—21no—
295C2—41no—
296C2—201no—
297C2—201no—
298C2#1174657311yescharacteristic
subgroupG/H
centerC4#91173
commutatorC23×C3×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#709C22
hypocenterC3×C5#1391
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C22×C3⋊#168C4semidirect
9. C2×C5×#208C4semidirect
10. #91240C4semidirect
12. C3×#4011C4semidirect
48. #4011Dic3semidirect
78. C2×#208AGL(1,𝔽5)semidirect
232. C3×C5#1391semidirect
278. C5#67696semidirect
293. C3#10598790semidirect

Maximal subgroups

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

subgroupindex
#117524042
C3×#657452
#117483432
#105987903
#676965