Finite Group Databasebeta

← #14293725

Subgroups — #14293725

Order 1920.

440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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×C5×#486C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11751181C211yesmaximal, characteristic, complemented
4#11751174C211yesmaximal, characteristic
5#11751171C211yesmaximal, characteristic, complemented
6#11750794C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10601978—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#127C2211yescharacteristic
11C2×#6717—22no—
12C2×#6715—22no—
13C2×#6706—22no—
14#91763C2211yescharacteristic
15#91758C2211yescharacteristic
16C3×C5×#102—22no—
17C3×C4×C5×C8C2211yescharacteristic
18#91116—22no—
19#91092—22no—
20C4×C3⋊#168C2211yescharacteristic
21C4×C3⋊#168C2211yescharacteristic
22#71185—51nomaximal, Hall
23C5×#486D311yescharacteristic, complemented
24#65374—31no—
25#65368—31no—
26#65362—31no—
27#65359—31no—
28#64982—31no—
29#64674—31no—
30C2×C3×C5×Q8—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30—21no—
38C2×C3×C5×C8D412yes—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6717—44no—
43#6715—44no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C2×C3⋊#168D412yes—
47C2×C3⋊#168D412yes—
48#6706—44no—
49C3×#486D511yescharacteristic, complemented
50#5085—51no—
51#5080—51no—
52#5073—51no—
53#5070—51no—
54#4693—51no—
55#4454—51no—
56C5×C4⋊Q8C2×D311yescharacteristic
57C5×#127C2×D311yescharacteristic
58C2×#688—62no—
59C2×#686—62no—
60C2×#677—62no—
61#4020—31no—
62#4015—31no—
63C5×#102—22no—
64C4×C5×C8C2×D311yescharacteristic
65#3964—62no—
66#3940—62no—
67C4×#168—31no—
68C4×#168—31no—
69#1715—151noSylow
70C23×C3×C5—41no—
71C22×D15—41no—
72C3×C5×Q8—42no—
73C3×C5×D4—42no—
74C3×C5×D4—42no—
75C3×C5×D4—42no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×Dic15—41no—
81D60—42no—
82D60—42no—
83D60—42no—
84Dic30—42no—
85C3×C5×C8—22no—
86C3⋊#168—22no—
87C3⋊#168SD1614yescomplemented
88C3×C4⋊Q8C2×D511yescharacteristic
89C3×#127C2×D511yescharacteristic
90C2×#215—102no—
91C2×#213—102no—
92C2×#204—102no—
93#874—51no—
94#869—51no—
95C3×#102—22no—
96C3×C4×C8C2×D511yescharacteristic
97#832—102no—
98#808—102no—
99C4×C3⋊C8—51no—
100C4×C3⋊C8—51no—
101C2×C5×Q8—21no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×D20—61no—
106C2×D20—61no—
107C2×D20—61no—
108C2×Dic10—61no—
109C2×C5×C8#6712yes—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C42×C5C22×D311yescharacteristic
113#688—124no—
114#686—124no—
115C4⋊Dic5—61no—
116C4⋊Dic5—61no—
117C2×#168—32no—
118C2×#168—32no—
119#677—124no—
120#498—151no—
121#493—151no—
122#492—151no—
123#492—151no—
124#486—151no—
125#486D1511yescharacteristic, complemented
126#322—151no—
127C22×C3×C5—81no—
128C22×C3×C5—81no—
129C22×C3×C5—81no—
130C22×C3×C5#12711yescharacteristic
131C2×D15—81no—
132C2×D15—81no—
133C2×D15—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—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×D12—101no—
144C2×D12—101no—
145C2×D12—101no—
146C2×Dic6—101no—
147C2×C3×C8C22⋊D512yes—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C42C22×D511yescharacteristic
151#215—204no—
152#213—204no—
153C4⋊Dic3—101no—
154C4⋊Dic3—101no—
155C2×C3⋊C8—52no—
156C2×C3⋊C8—52no—
157#204—204no—
158C23×C5—41no—
159C22×D5—121no—
160C5×Q8—42no—
161C5×D4—42no—
162C5×D4—42no—
163C5×D4—42no—
164C2×C4×C5—41no—
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—121no—
169D20—122no—
170D20—122no—
171D20—122no—
172Dic10—122no—
173C5×C8—22no—
174#168—34no—
175#168—62no—
176C2×SD16—302no—
177C2×SD16—302no—
178C2×D8—302no—
179C4⋊Q8—151no—
180C4⋊Q8C2×D1511yescharacteristic
181#127—151no—
182#127C2×D1511yescharacteristic
183#106—302no—
184#102—22no—
185#102—302no—
186C4×C8—151no—
187C4×C8—151no—
188C4×C8C2×D1511yescharacteristic
189C2×C3×C5—161no—
190C2×C3×C5#49211yescharacteristic
191C2×C3×C5#49611yescharacteristic
192C2×C3×C5#49611yescharacteristic
193D15—161no—
194C23×C3—41no—
195C22×D3—201no—
196C3×Q8—42no—
197C3×D4—42no—
198C3×D4—42no—
199C3×D4—42no—
200C2×C3×C4—41no—
201C2×C3×C4D4×D511yescharacteristic
202C2×C3×C4D4×D511yescharacteristic
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—201no—
205D12—202no—
206D12—202no—
207D12—202no—
208Dic6—202no—
209C3×C8—22no—
210C3⋊C8—54no—
211C3⋊C8—102no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5#94011yescharacteristic
216C2×D5—241no—
217C2×D5—241no—
218C2×D5—241no—
219C4×C5—81no—
220C4×C5#91112yes—
221C4×C5D3×SD1612yes—
222C4×C5#94912yes—
223Dic5—241no—
224C2×Q8—21no—
225C2×Q8—301no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—301no—
230C2×D4—301no—
231C2×D4—301no—
232SD16—604no—
233SD16—604no—
234D8—604no—
235C2×C8—152no—
236C2×C8—152no—
237C2×C8#122012yes—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—301no—
241C4⋊C4—301no—
242C42C22×D1511yescharacteristic
243C3×C5#171511yescharacteristic, complemented, Hall
244C22×C3—81no—
245C22×C3—81no—
246C22×C3—81no—
247C22×C3#408611yescharacteristic
248C2×D3—401no—
249C2×D3—401no—
250C2×D3—401no—
251C3×C4—81no—
252C3×C4#405712yes—
253C3×C4D5×SD1612yes—
254C3×C4#409512yes—
255Dic3—401no—
256C2×C5—161no—
257C2×C5#505811yescharacteristic
258C2×C5#515411yescharacteristic
259C2×C5#517511yescharacteristic
260D5—481no—
261C23—41no—
262C23—601no—
263Q8—42no—
264Q8—602no—
265D4—42no—
266D4—42no—
267D4—42no—
268D4—602no—
269D4—602no—
270D4—602no—
271C2×C4—41no—
272C2×C4—601no—
273C2×C4D4×D1511yescharacteristic
274C2×C4D4×D1511yescharacteristic
275C2×C4C2×#122011yescharacteristic
276C8—22no—
277C8—154no—
278C8—302no—
279C2×C3—161no—
280C2×C3#6534711yescharacteristic
281C2×C3#6544311yescharacteristic
282C2×C3#6546411yescharacteristic
283D3—801no—
284C5#7118511yescharacteristic, complemented, Sylow
285C22—81no—
286C22—81no—
287C22—81no—
288C22—1201no—
289C22—1201no—
290C22—1201no—
291C22#9182911yescharacteristic
292C4—81no—
293C4—1201no—
294C4#9180012yes—
295C4SD16×D1512yes—
296C4#9183812yes—
297C3#1060197811yescharacteristic, complemented, Sylow
298C2—161no—
299C2—2401no—
300C2#1175115911yescharacteristic
301C2#1175125511yescharacteristic
302C2#1175127611yescharacteristic
subgroupG/H
centerC22#91829
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#486C2
socleC22×C3×C5#127
prime radical#11751174C2
hypercenter#486D15
hypocenterC3×C5#1715
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C3×C5×#486C2semidirect
2. #11751186C2semidirect
3. #11751181C2semidirect
5. #11751171C2semidirect
6. #11750794C2semidirect
7. #11746275C2semidirect
23. C5×#486D3semidirect
49. C3×#486D5semidirect
87. C3⋊#168SD16semidirect
125. #486D15semidirect
243. C3×C5#1715semidirect
284. C5#71185semidirect
297. C3#10601978semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4862
#117511862
#117511812
#117511742
#117511712
#117507942
#117462752
#106019783
#711855