Finite Group Databasebeta

← #14293749

Subgroups — #14293749

Order 1920.

440 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 98 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#11751181C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic, complemented
3C3×#65374C211yesmaximal, characteristic, complemented
4#11747071C211yesmaximal, characteristic, complemented
5#11747039C211yesmaximal, characteristic
6#11746906C211yesmaximal, characteristic, complemented
7#11745833C211yesmaximal, characteristic, complemented
8#10601978—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#874C2211yescharacteristic
12C2×C3×#688—22no—
13C3×#4020C2211yescharacteristic
14C2×#6657—22no—
15C2×#6652—22no—
16#91092—22no—
17C4×C3⋊#168C2211yescharacteristic
18C5×#809—22no—
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×C4×#168C2211yescharacteristic
21#90967—22no—
22#71259—51nomaximal, Hall
23C5×#486—31no—
24#65374D311yescharacteristic, complemented
25#65368—31no—
26#65362—31no—
27#65359—31no—
28#64982—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×Dic30—21no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C3×D20—21no—
36C2×C3×D20—21no—
37C2×C3×D20—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C2×C3⋊#168D412yes—
44C2×C5×C3⋊C8D412yes—
45C3×#688—44no—
46C2×C3×#168D412yes—
47#6657—44no—
48#6652—44no—
49C3×#492—51no—
50#5088D511yescharacteristic, complemented
51#5080—51no—
52#5076—51no—
53#5073—51no—
54#4694—51no—
55#4454—51no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C5×#127—31no—
58C2×#688—22no—
59C2×#686—62no—
60C2×#677—62no—
61#4020C2×D311yescharacteristic
62#4015—31no—
63C5×#102—62no—
64C4×C5×C8—31no—
65#3964—62no—
66#3940—62no—
67C4×#168—31no—
68C4×#168C2×D311yescharacteristic
69#1715—151noSylow
70C22×C5×D3—41no—
71C22×C3×D5—41no—
72C3×C5×Q8—42no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×Dic15—41no—
78Dic30—42no—
79C5×D12—42no—
80C5×D12—42no—
81C5×D12—42no—
82C3×D20—42no—
83C3×D20—42no—
84C3×D20—42no—
85C3⋊#168SD1614yescomplemented
86C3×#168—22no—
87C5×C3⋊C8—22no—
88C2×C3×SD16—102no—
89C3×C4⋊Q8C2×D511yescharacteristic
90C3×#127—51no—
91C2×#214—102no—
92C2×#213—102no—
93#874C2×D511yescharacteristic
94#869—51no—
95C3×C4×C8—51no—
96#821—102no—
97#809—22no—
98#808—102no—
99C4×C3⋊C8—51no—
100C4×C3⋊C8C2×D511yescharacteristic
101C2×C5×Q8—21no—
102C2×C5×D4—61no—
103C2×C5×D4—61no—
104C2×C5×D4—61no—
105C2×D20—21no—
106C2×D20—21no—
107C2×D20—21no—
108C2×Dic10—61no—
109C2×C5×C8—32no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C42×C5C22×D311yescharacteristic
113#688—44no—
114#686—124no—
115C4⋊Dic5—61no—
116C4⋊Dic5—61no—
117C2×#168—32no—
118C2×#168#6712yes—
119#677—124no—
120#498—151no—
121#493—151no—
122#492—51no—
123#492—151no—
124#486—31no—
125#486—151no—
126#322—151no—
127C22×C3×C5#12711yescharacteristic
128C2×C5×D3—81no—
129C2×C5×D3—81no—
130C2×C5×D3—81no—
131C2×C3×D5—81no—
132C2×C3×D5—81no—
133C2×C3×D5—81no—
134C3×C4×C5—81no—
135C3×C4×C5C2×SD1612yes—
136C3×C4×C5AGL(1,ℤ/8)12yes—
137C3×C4×C5AGL(1,ℤ/8)12yes—
138Dic15—81no—
139C2×C3×Q8—21no—
140C2×C3×D4—101no—
141C2×C3×D4—101no—
142C2×C3×D4—101no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12—21no—
146C2×Dic6—101no—
147C3×SD16—204no—
148C2×C3×C8—52no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C42C22×D511yescharacteristic
152#214—204no—
153#213—204no—
154C4⋊Dic3—101no—
155C4⋊Dic3—101no—
156C2×C3⋊C8—52no—
157C2×C3⋊C8C22⋊D512yes—
158C23×C5—121no—
159C22×D5—41no—
160C5×Q8—42no—
161C5×D4—122no—
162C5×D4—122no—
163C5×D4—122no—
164C2×C4×C5—41no—
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—121no—
169D20—42no—
170D20—42no—
171D20—42no—
172Dic10—122no—
173C5×C8—62no—
174#168—22no—
175#168—34no—
176C2×SD16—102no—
177C2×SD16—302no—
178C2×D8—302no—
179C4⋊Q8—151no—
180C4⋊Q8D3×D511yescharacteristic
181#127—31no—
182#127—51no—
183#106—302no—
184#102—62no—
185#102—302no—
186C4×C8—31no—
187C4×C8—51no—
188C4×C8—151no—
189C2×C3×C5#49211yescharacteristic
190C2×C3×C5#49611yescharacteristic
191C2×C3×C5#49611yescharacteristic
192C3×D5—161no—
193C5×D3—161no—
194C23×C3—201no—
195C22×D3—41no—
196C3×Q8—42no—
197C3×D4—202no—
198C3×D4—202no—
199C3×D4—202no—
200C2×C3×C4—41no—
201C2×C3×C4D4×D511yescharacteristic
202C2×C3×C4D4×D511yescharacteristic
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—201no—
205D12—42no—
206D12—42no—
207D12—42no—
208Dic6—202no—
209C3×C8—102no—
210C3⋊C8—22no—
211C3⋊C8—54no—
212C22×C5—241no—
213C22×C5—241no—
214C22×C5—241no—
215C22×C5#94011yescharacteristic
216C2×D5—81no—
217C2×D5—81no—
218C2×D5—81no—
219C4×C5—81no—
220C4×C5D3×SD1612yes—
221C4×C5#91412yes—
222C4×C5#93212yes—
223Dic5—241no—
224C2×Q8—21no—
225C2×Q8—301no—
226C2×D4—61no—
227C2×D4—61no—
228C2×D4—61no—
229C2×D4—101no—
230C2×D4—101no—
231C2×D4—101no—
232SD16—204no—
233SD16—604no—
234D8—604no—
235C2×C8—32no—
236C2×C8—52no—
237C2×C8—152no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—301no—
241C4⋊C4—301no—
242C42C2×D3×D511yescharacteristic
243C3×C5#171511yescharacteristic, complemented, Hall
244C22×C3—401no—
245C22×C3—401no—
246C22×C3—401no—
247C22×C3#408611yescharacteristic
248C2×D3—81no—
249C2×D3—81no—
250C2×D3—81no—
251C3×C4—81no—
252C3×C4#405712yes—
253C3×C4D5×SD1612yes—
254C3×C4#409512yes—
255Dic3—401no—
256C2×C5—481no—
257C2×C5#507411yescharacteristic
258C2×C5#517511yescharacteristic
259C2×C5#517611yescharacteristic
260D5—161no—
261C23—121no—
262C23—201no—
263Q8—42no—
264Q8—602no—
265D4—122no—
266D4—122no—
267D4—122no—
268D4—202no—
269D4—202no—
270D4—202no—
271C2×C4—41no—
272C2×C4—601no—
273C2×C4D5×#6711yescharacteristic
274C2×C4D3×C22⋊D511yescharacteristic
275C2×C4#679011yescharacteristic
276C8—62no—
277C8—102no—
278C8—154no—
279C2×C3—801no—
280C2×C3#6534711yescharacteristic
281C2×C3#6544311yescharacteristic
282C2×C3#6546411yescharacteristic
283D3—161no—
284C5#7125911yescharacteristic, complemented, Sylow
285C22—241no—
286C22—241no—
287C22—241no—
288C22—401no—
289C22—401no—
290C22—401no—
291C22#9156711yescharacteristic
292C4—81no—
293C4—1201no—
294C4#9148912yes—
295C4#9150412yes—
296C4#9150512yes—
297C3#1060197811yescharacteristic, complemented, Sylow
298C2—481no—
299C2—801no—
300C2#1174906611yescharacteristic
301C2#1174934111yescharacteristic
302C2#1174934211yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#127
prime radical#11747039C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1715
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11751181C2semidirect
2. C5×#5088C2semidirect
3. C3×#65374C2semidirect
4. #11747071C2semidirect
6. #11746906C2semidirect
7. #11745833C2semidirect
24. #65374D3semidirect
50. #5088D5semidirect
85. C3⋊#168SD16semidirect
243. C3×C5#1715semidirect
284. C5#71259semidirect
297. C3#10601978semidirect

Maximal subgroups

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

subgroupindex
#117511812
C5×#50882
C3×#653742
#117470712
#117470392
#117469062
#117458332
#106019783
#712595