Finite Group Databasebeta

← #14292672

Subgroups — #14292672

Order 1920.

320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65130C211yesmaximal, characteristic
2#11747010C211yesmaximal, characteristic
3#11746948C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic
5#11746302C211yesmaximal, characteristic, complemented
6C5×#4479C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599376—31nomaximal, Hall
9#91758C2211yescharacteristic
10C2×C3×#677—21no—
11C3×C4×D20C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6649—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15C4⋊(C3⋊#168)C2211yescharacteristic
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3948—21no—
19#90987—21no—
20#90987—21no—
21#90987—21no—
22#90965—21no—
23#90955—21no—
24#71040—51nomaximal, Hall
25#65131—31no—
26#65130D311yescharacteristic
27#64977—31no—
28#64969—31no—
29C5×#335—31no—
30#64702—31no—
31#64701—31no—
32C2×Dic30—21no—
33C2×C3×D20D411yescharacteristic
34C2×C3×C4×D5—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C2×C3⋊#168—21no—
41C2×C5×C3⋊C8—21no—
42C2×C5×C3⋊C8D411yescharacteristic
43C2×C5×C3⋊C8D411yescharacteristic
44C3×#685—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5D411yescharacteristic
48C3×#677—42no—
49#6649—42no—
50C3×#461—51no—
51#5080—51no—
52#5012—51no—
53#5008—51no—
54#4547—51no—
55#4481—51no—
56#4479D511yescharacteristic, complemented
57C2×#677—21no—
58C2×#676—61no—
59C4×D20C2×D311yescharacteristic
60#4015—31no—
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8—31no—
65#3953—61no—
66#3952—61no—
67#3949—61no—
68#3949—61no—
69#3949—61no—
70#3948—21no—
71C4⋊#168—31no—
72#1691—151noSylow
73C22×C3×D5—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—41no—
78Dic30—81no—
79C2×C3×Dic5—21no—
80C2×C3×Dic5—41no—
81C3×D20—21no—
82C3×D20—21no—
83C3×C4×D5—41no—
84C3×C4×D5—41no—
85C3×Dic10—41no—
86C3×Dic10—41no—
87C3×C5×C8—41no—
88C3⋊#168—41no—
89C5×C3⋊C8—21no—
90C5×C3⋊C8—41no—
91C5×C3⋊C8SD1612yescomplemented
92C2×C3×SD16—101no—
93C3×C4⋊Q8—51no—
94C3×C4×D4—51no—
95C2×#208—101no—
96#869—51no—
97C3×C4⋊C8C2×D511yescharacteristic
98C3×#103—101no—
99#832—101no—
100#830—101no—
101#808—101no—
102#808—101no—
103#808—101no—
104C4⋊(C3⋊C8)—51no—
105C4⋊(C3⋊C8)C2×D511yescharacteristic
106C4×C3⋊C8C2×D511yescharacteristic
107C2×D20#6711yescharacteristic
108C2×C4×D5—21no—
109C2×Dic10—21no—
110C2×Dic10—61no—
111C2×C5×C8—21no—
112C2×C5×C8—31no—
113C2×C5×C8—31no—
114C2×C5×C8—61no—
115C42×C5C22×D311yescharacteristic
116#685—21no—
117C4⋊Dic5—21no—
118C4⋊Dic5—21no—
119C4⋊Dic5—61no—
120C4⋊Dic5—61no—
121C4⋊Dic5#6711yescharacteristic
122C2×#168—61no—
123#677—42no—
124#676—122no—
125#498—151no—
126#476—151no—
127#461—51no—
128#436—151no—
129#335—31no—
130#333—151no—
131#332—151no—
132C22×C3×C5#12111yescharacteristic
133C2×C3×D5—41no—
134C2×C3×D5—41no—
135C2×C3×D5—41no—
136C3×C4×C5—21no—
137C3×C4×C5C2×SD1611yescharacteristic
138C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
139C3×C4×C5#13711yescharacteristic
140C3×C4×C5#13711yescharacteristic
141Dic15—81no—
142C3×Dic5—41no—
143C3×Dic5—81no—
144C2×C3×Q8—101no—
145C2×C3×D4—51no—
146C22×C3×C4—101no—
147C2×Dic6—101no—
148C3×SD16—202no—
149C2×C3×C8—21no—
150C3×C4⋊C4—51no—
151C3×C4⋊C4—101no—
152C3×C4⋊C4—101no—
153C3×C22⋊C4—101no—
154C3×C42C22×D511yescharacteristic
155C4⋊Dic3—101no—
156C4⋊Dic3—101no—
157#208—202no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—101no—
160C2×C3⋊C8D2011yescharacteristic
161C2×C3⋊C8D2011yescharacteristic
162C22×D5—21no—
163C2×C4×C5D3×D411yescharacteristic
164C2×C4×C5#23711yescharacteristic
165C2×C4×C5C2×#6711yescharacteristic
166C2×Dic5—21no—
167C2×Dic5—41no—
168C2×Dic5—121no—
169D20—21no—
170D20—21no—
171C4×D5—41no—
172C4×D5—41no—
173Dic10—41no—
174Dic10—41no—
175Dic10—241no—
176C5×C8—32no—
177C5×C8—41no—
178C5×C8—61no—
179C5×C8—121no—
180#168—121no—
181C2×SD16—101no—
182C2×M16—301no—
183C4⋊Q8—51no—
184C4⋊Q8—151no—
185C4×D4—51no—
186#106—301no—
187#106—301no—
188#106—301no—
189C4⋊C8—31no—
190C4⋊C8—151no—
191C4⋊C8D3×D511yescharacteristic
192#103—101no—
193#102—301no—
194C22⋊C8—301no—
195C4×C8—31no—
196C2×C3×C5#46111yescharacteristic
197C2×C3×C5#46811yescharacteristic
198C2×C3×C5#47111yescharacteristic
199C3×D5—81no—
200C23×C3—101no—
201C3×Q8—201no—
202C3×Q8—201no—
203C3×D4—101no—
204C3×D4—101no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4—201no—
209C2×C3×C4C2×D2011yescharacteristic
210C2×C3×C4D4×D511yescharacteristic
211C2×C3×C4#71311yescharacteristic
212C2×Dic3—201no—
213Dic6—401no—
214C3×C8—41no—
215C3⋊C8—21no—
216C3⋊C8—41no—
217C3⋊C8—201no—
218C3⋊C8#67712yescomplemented
219C22×C5#93911yescharacteristic
220C2×D5—41no—
221C2×D5—41no—
222C2×D5—41no—
223C4×C5—21no—
224C4×C5D3×SD1611yescharacteristic
225C4×C5#91511yescharacteristic
226C4×C5#93211yescharacteristic
227C4×C5#95111yescharacteristic
228Dic5—41no—
229Dic5—81no—
230Dic5—241no—
231C2×Q8—101no—
232C2×Q8—301no—
233C2×D4—51no—
234C22×C4—101no—
235SD16—202no—
236M16—602no—
237C2×C8—21no—
238C2×C8—31no—
239C2×C8—31no—
240C2×C8—61no—
241C2×C8—301no—
242C4⋊C4—51no—
243C4⋊C4—101no—
244C4⋊C4—101no—
245C4⋊C4—301no—
246C4⋊C4—301no—
247C22⋊C4—101no—
248C42C2×D3×D511yescharacteristic
249C3×C5#169111yescharacteristic, complemented, Hall
250C22×C3—201no—
251C22×C3—201no—
252C22×C3—201no—
253C22×C3#404111yescharacteristic
254C3×C4—21no—
255C3×C4—201no—
256C3×C4—401no—
257C3×C4C2×#67711yescharacteristic
258C3×C4#405511yescharacteristic
259C3×C4#405711yescharacteristic
260C3×C4#406411yescharacteristic
261Dic3—401no—
262C2×C5#504211yescharacteristic
263C2×C5#516211yescharacteristic
264C2×C5#520311yescharacteristic
265D5—81no—
266C23—101no—
267Q8—201no—
268Q8—201no—
269Q8—1201no—
270D4—101no—
271D4—101no—
272C2×C4—101no—
273C2×C4—201no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—601no—
277C2×C4#676611yescharacteristic
278C2×C4D3×D2011yescharacteristic
279C2×C4D5×#6711yescharacteristic
280C8—32no—
281C8—41no—
282C8—61no—
283C8—121no—
284C8—601no—
285C2×C3—401no—
286C2×C3#6513011yescharacteristic
287C2×C3#6517511yescharacteristic
288C2×C3#6518711yescharacteristic
289C5#7104011yescharacteristic, complemented, Sylow
290C22—201no—
291C22—201no—
292C22—201no—
293C22#9140911yescharacteristic
294C4—21no—
295C4—201no—
296C4—401no—
297C4—1201no—
298C4D3×#67711yescharacteristic
299C4#9127411yescharacteristic
300C4#9148911yescharacteristic
301C4#9150811yescharacteristic
302C3#1059937611yescharacteristic, complemented, Sylow
303C2—401no—
304C2#1174746311yescharacteristic
305C2#1174775311yescharacteristic
306C2#1174818411yescharacteristic
subgroupG/H
centerC22#91409
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1691
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11746948C2semidirect
5. #11746302C2semidirect
6. C5×#4479C2semidirect
7. #11745856C2semidirect
56. #4479D5semidirect
91. C5×C3⋊C8SD16semidirect
218. C3⋊C8#677semidirect
249. C3×C5#1691semidirect
289. C5#71040semidirect
302. C3#10599376semidirect

Maximal subgroups

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

subgroupindex
C3×#651302
#117470102
#117469482
#117468812
#117463022
C5×#44792
#117458562
#105993763
#710405