Finite Group Databasebeta

← #14293452

Subgroups — #14293452

Order 1920.

448 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 106 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#11751174C211yesmaximal, characteristic
2C5×#5070C211yesmaximal, characteristic, complemented
3C3×#65365C211yesmaximal, characteristic, complemented
4#11747067C211yesmaximal, characteristic, complemented
5#11746962C211yesmaximal, characteristic, complemented
6#11746910C211yesmaximal, characteristic, complemented
7C3⋊C8×#168C211yesmaximal, characteristic, complemented
8#10601973—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6715—22no—
11#91763C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C2×C3×#687—22no—
14C3×#4015C2211yescharacteristic
15C2×#6660—22no—
16C4×C3⋊#168C2211yescharacteristic
17C5×#832—22no—
18C4×C5×C3⋊C8C2211yescharacteristic
19C3×C4×#168C2211yescharacteristic
20#90989—22no—
21#90968—22no—
22#71255—51nomaximal, Hall
23C5×#486—31no—
24#65374—31no—
25#65367—31no—
26#65365D311yescharacteristic, complemented
27#65362—31no—
28#64983—31no—
29C8×#168—31no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×C5×Dic6—21no—
37C2×C3×Dic10—21no—
38C3×C42×C5C2311yescharacteristic
39#6715—44no—
40C2×C3⋊#168D412yes—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C2×C5×C3⋊C8D412yes—
44C3×#687—44no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168D412yes—
48#6660—44no—
49C3×#492—51no—
50#5088—51no—
51#5078—51no—
52#5073—51no—
53#5070D511yescharacteristic, complemented
54#4693—51no—
55C8×C3⋊C8—51no—
56C5×C4⋊Q8—31no—
57C5×#127C2×D311yescharacteristic
58C2×#688—62no—
59C2×#687—22no—
60C2×#686—62no—
61#4020—31no—
62#4015C2×D311yescharacteristic
63C5×#102—62no—
64C4×C5×C8—31no—
65#3953—62no—
66#3939—62no—
67C4×#168—31no—
68C4×#168C2×D311yescharacteristic
69#1706—151noSylow
70C23×C3×C5—41no—
71C22×D15—41no—
72C3×C5×D4—42no—
73C3×C5×D4—42no—
74C3×C5×D4—42no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78D60—42no—
79D60—42no—
80D60—42no—
81C2×C5×Dic3—41no—
82C5×Dic6—42no—
83C2×C3×Dic5—41no—
84C3×Dic10—42no—
85C3⋊#168SD1614yescomplemented
86C3×#168D814yescomplemented
87C5×C3⋊C8—22no—
88C2×C3×SD16—102no—
89C3×C4⋊Q8—51no—
90C3×#127C2×D511yescharacteristic
91C2×#213—102no—
92C2×#204—102no—
93#874—51no—
94#869C2×D511yescharacteristic
95C3×C4×C8—51no—
96#832—22no—
97#809—102no—
98#807—102no—
99C4×C3⋊C8—51no—
100C4×C3⋊C8C2×D511yescharacteristic
101C2×C5×Q8—61no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×D20—61no—
106C2×D20—61no—
107C2×D20—61no—
108C2×Dic10—21no—
109C2×C5×C8—32no—
110C5×C4⋊C4—61no—
111C5×C4⋊C4—61no—
112C42×C5C22×D311yescharacteristic
113#688—124no—
114#687—44no—
115#686—124no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118C2×#168—32no—
119C2×#168#6712yes—
120#500—151no—
121#493—151no—
122#492—51no—
123#492—151no—
124#486—31no—
125#486—151no—
126C82—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×C5C2×D812yes—
135C3×C4×C5C2×SD1612yes—
136C3×C4×C5#13512yes—
137C3×Dic5—81no—
138C5×Dic3—81no—
139C2×C3×Q8—101no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×D12—101no—
144C2×D12—101no—
145C2×D12—101no—
146C2×Dic6—21no—
147C3×SD16—204no—
148C2×C3×C8—52no—
149C3×C4⋊C4—101no—
150C3×C4⋊C4—101no—
151C3×C42C22×D511yescharacteristic
152#213—204no—
153C4⋊Dic3—21no—
154C4⋊Dic3—21no—
155C2×C3⋊C8—52no—
156C2×C3⋊C8C22⋊D512yes—
157#204—204no—
158C23×C5—41no—
159C22×D5—121no—
160C5×Q8—122no—
161C5×D4—42no—
162C5×D4—42no—
163C5×D4—42no—
164C2×C4×C5—121no—
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—41no—
169D20—122no—
170D20—122no—
171D20—122no—
172Dic10—42no—
173C5×C8—62no—
174#168—34no—
175#168#21314yescomplemented
176C2×SD16—102no—
177C2×SD16—302no—
178C2×D8—302no—
179C4⋊Q8—31no—
180C4⋊Q8—51no—
181#127—151no—
182#127D3×D511yescharacteristic
183#107—302no—
184#102—62no—
185#102—302no—
186C4×C8—31no—
187C4×C8—51no—
188C4×C8—151no—
189C2×C3×C5—161no—
190C2×C3×C5#49211yescharacteristic
191C2×C3×C5#49311yescharacteristic
192C2×C3×C5#49511yescharacteristic
193D15—161no—
194C23×C3—41no—
195C22×D3—201no—
196C3×Q8—202no—
197C3×D4—42no—
198C3×D4—42no—
199C3×D4—42no—
200C2×C3×C4—201no—
201C2×C3×C4D4×D511yescharacteristic
202C2×C3×C4D4×D511yescharacteristic
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—41no—
205D12—202no—
206D12—202no—
207D12—202no—
208Dic6—42no—
209C3×C8—54no—
210C3⋊C8—22no—
211C3⋊C8—54no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5#94011yescharacteristic
216C2×D5—241no—
217C2×D5—241no—
218C2×D5—241no—
219C4×C5—241no—
220C4×C5D3×SD1612yes—
221C4×C5#91612yes—
222C4×C5C2×#21312yes—
223Dic5—81no—
224C2×Q8—61no—
225C2×Q8—101no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—301no—
230C2×D4—301no—
231C2×D4—301no—
232SD16—204no—
233SD16—604no—
234D8—604no—
235C2×C8—32no—
236C2×C8—52no—
237C2×C8—152no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—101no—
241C4⋊C4—101no—
242C42C2×D3×D511yescharacteristic
243C3×C5#170611yescharacteristic, 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—401no—
252C3×C4D5×D812yes—
253C3×C4D5×SD1612yes—
254C3×C4#409612yes—
255Dic3—81no—
256C2×C5—161no—
257C2×C5#507311yescharacteristic
258C2×C5#516811yescharacteristic
259C2×C5#517511yescharacteristic
260D5—481no—
261C23—41no—
262C23—601no—
263Q8—122no—
264Q8—202no—
265D4—42no—
266D4—42no—
267D4—42no—
268D4—602no—
269D4—602no—
270D4—602no—
271C2×C4—121no—
272C2×C4—201no—
273C2×C4D5×#6711yescharacteristic
274C2×C4D3×C22⋊D511yescharacteristic
275C2×C4#679011yescharacteristic
276C8—54no—
277C8—62no—
278C8—154no—
279C2×C3—161no—
280C2×C3#6534811yescharacteristic
281C2×C3#6544011yescharacteristic
282C2×C3#6546411yescharacteristic
283D3—801no—
284C5#7125511yescharacteristic, complemented, Sylow
285C22—81no—
286C22—81no—
287C22—81no—
288C22—1201no—
289C22—1201no—
290C22—1201no—
291C22#9156711yescharacteristic
292C4—241no—
293C4—401no—
294C4D5×#21312yes—
295C4#9148712yes—
296C4#9149512yes—
297C3#1060197311yescharacteristic, complemented, Sylow
298C2—161no—
299C2—2401no—
300C2#1174907811yescharacteristic
301C2#1174909311yescharacteristic
302C2#1174910911yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#127
prime radical#11751174C2
hypercenter#127D3×D5
hypocenterC3×C5#1706
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C5×#5070C2semidirect
3. C3×#65365C2semidirect
4. #11747067C2semidirect
5. #11746962C2semidirect
6. #11746910C2semidirect
7. C3⋊C8×#168C2semidirect
26. #65365D3semidirect
53. #5070D5semidirect
85. C3⋊#168SD16semidirect
86. C3×#168D8semidirect
175. #168#213semidirect
243. C3×C5#1706semidirect
284. C5#71255semidirect
297. C3#10601973semidirect

Maximal subgroups

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

subgroupindex
#117511742
C5×#50702
C3×#653652
#117470672
#117469622
#117469102
C3⋊C8×#1682
#106019733
#712555