Finite Group Databasebeta

← #14293682

Subgroups — #14293682

Order 1920.

396 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C5×#4693C211yesmaximal, characteristic
2C3×#64970C211yesmaximal, characteristic, complemented
3#11747081C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic, complemented
5#11746947C211yesmaximal, characteristic, complemented
6#11746901C211yesmaximal, characteristic
7#11746275C211yesmaximal, characteristic, complemented
8#10602050—31nomaximal, Hall
9C2×C5×#204—22no—
10C5×#874C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C2×#6656—22no—
15C3×C4×C5×C8C2211yescharacteristic
16C4×C3⋊#168C2211yescharacteristic
17C4×C3⋊#168C2211yescharacteristic
18C3×#3948—22no—
19#90989—22no—
20#90986—22no—
21#90966—22no—
22#71216—51nomaximal, Hall
23C5×#492—31no—
24#65368—31no—
25#65367—31no—
26#65365—31no—
27#65359—31no—
28#64970D311yescharacteristic, complemented
29#64674—31no—
30C2×C5×D12—21no—
31C2×C5×D12—21no—
32C2×C5×D12—21no—
33C2×C5×Dic6—21no—
34C2×C3×Dic10—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8D412yes—
37C3×C42×C5C2311yescharacteristic
38C2×C3⋊#168D412yes—
39C2×C3⋊#168D412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C5×#204—44no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47#6656—44no—
48C3×#487—51no—
49#5088—51no—
50#5085—51no—
51#5080—51no—
52#5078—51no—
53#4693D511yescharacteristic
54#4454—51no—
55C2×C5×SD16—62no—
56C5×C4⋊Q8—31no—
57C5×#127—31no—
58C2×#687—62no—
59#4015C2×D311yescharacteristic
60#4015C2×D311yescharacteristic
61C4×C5×C8C2×D311yescharacteristic
62#3964—62no—
63#3948—22no—
64#3940—62no—
65#3939—62no—
66C4×#168—31no—
67C4×#168—31no—
68#1714—151noSylow
69C22×C5×D3—41no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C5×Dic3—41no—
74C5×D12—42no—
75C5×D12—42no—
76C5×D12—42no—
77C5×Dic6—42no—
78C2×C3×Dic5—41no—
79C2×C3×Dic5—41no—
80C3×Dic10—42no—
81C3×Dic10—42no—
82C3×C5×C8—22no—
83C3⋊#168—22no—
84C3⋊#168SD1614yescomplemented
85C3×C4⋊Q8—51no—
86C3×C4⋊Q8—51no—
87C2×#215—102no—
88C2×#204—22no—
89#874C2×D511yescharacteristic
90#869C2×D511yescharacteristic
91C3×#103—102no—
92C3×C4×C8C2×D511yescharacteristic
93#809—102no—
94#808—102no—
95#807—102no—
96C4×C3⋊C8—51no—
97C4×C3⋊C8—51no—
98C2×C5×Q8—61no—
99C2×C5×D4—61no—
100C2×C5×D4—61no—
101C2×C5×D4—61no—
102C2×Dic10—21no—
103C2×Dic10—21no—
104C5×SD16—124no—
105C2×C5×C8#6712yes—
106C5×C4⋊C4—61no—
107C5×C4⋊C4—61no—
108C42×C5C22×D311yescharacteristic
109#687—124no—
110C4⋊Dic5—21no—
111C4⋊Dic5—21no—
112C4⋊Dic5—21no—
113C4⋊Dic5—21no—
114C2×#168—32no—
115C2×#168—32no—
116#500—151no—
117#498—151no—
118#492—31no—
119#492—151no—
120#487—51no—
121#486—151no—
122#322—151no—
123C22×C3×C5#12711yescharacteristic
124C2×C5×D3—81no—
125C2×C5×D3—81no—
126C2×C5×D3—81no—
127C3×C4×C5C2×SD1612yes—
128C3×C4×C5AGL(1,ℤ/8)12yes—
129C3×C4×C5#13712yes—
130C3×Dic5—81no—
131C3×Dic5—81no—
132C5×Dic3—81no—
133C2×C3×Q8—101no—
134C2×C3×Q8—101no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×Dic6—21no—
139C2×C3×C8C22⋊D512yes—
140C3×C4⋊C4—101no—
141C3×C4⋊C4—101no—
142C3×C4⋊C4—101no—
143C3×C4⋊C4—101no—
144C3×C42C22×D511yescharacteristic
145#215—204no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C2×C3⋊C8—52no—
149C2×C3⋊C8—52no—
150#204—44no—
151C23×C5—121no—
152C5×Q8—122no—
153C5×D4—122no—
154C5×D4—122no—
155C5×D4—122no—
156C2×C4×C5—121no—
157C2×C4×C5D3×D411yescharacteristic
158C2×C4×C5D3×D411yescharacteristic
159C2×C4×C5C2×#6711yescharacteristic
160C2×Dic5—41no—
161C2×Dic5—41no—
162Dic10—42no—
163Dic10—42no—
164C5×C8—22no—
165#168—34no—
166#168—62no—
167C2×SD16—62no—
168C2×SD16—302no—
169C4⋊Q8—31no—
170C4⋊Q8—51no—
171C4⋊Q8—51no—
172#127—31no—
173#107—302no—
174#106—302no—
175#103—102no—
176#102—302no—
177C4×C8—151no—
178C4×C8—151no—
179C4×C8D3×D511yescharacteristic
180C2×C3×C5#49211yescharacteristic
181C2×C3×C5#49611yescharacteristic
182C2×C3×C5#49711yescharacteristic
183C5×D3—161no—
184C22×D3—41no—
185C3×Q8—202no—
186C3×Q8—202no—
187C2×C3×C4—201no—
188C2×C3×C4—201no—
189C2×C3×C4D4×D511yescharacteristic
190C2×C3×C4D4×D511yescharacteristic
191C2×C3×C4C2×C22⋊D511yescharacteristic
192C2×Dic3—41no—
193D12—42no—
194D12—42no—
195D12—42no—
196Dic6—42no—
197C3×C8—22no—
198C3⋊C8—54no—
199C3⋊C8—102no—
200C22×C5—241no—
201C22×C5—241no—
202C22×C5—241no—
203C22×C5#94011yescharacteristic
204C4×C5—241no—
205C4×C5D3×SD1612yes—
206C4×C5#91812yes—
207C4×C5#94912yes—
208Dic5—81no—
209Dic5—81no—
210C2×Q8—61no—
211C2×Q8—101no—
212C2×Q8—101no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216SD16—124no—
217SD16—604no—
218C2×C8—152no—
219C2×C8—152no—
220C2×C8#120112yes—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—101no—
224C4⋊C4—101no—
225C4⋊C4—101no—
226C4⋊C4—101no—
227C42C2×D3×D511yescharacteristic
228C3×C5#171411yescharacteristic, complemented, Hall
229C22×C3#408611yescharacteristic
230C2×D3—81no—
231C2×D3—81no—
232C2×D3—81no—
233C3×C4—401no—
234C3×C4—401no—
235C3×C4D5×SD1612yes—
236C3×C4#406112yes—
237C3×C4#407812yes—
238Dic3—81no—
239C2×C5—481no—
240C2×C5#505811yescharacteristic
241C2×C5#517511yescharacteristic
242C2×C5#519011yescharacteristic
243C23—121no—
244Q8—122no—
245Q8—202no—
246Q8—202no—
247D4—122no—
248D4—122no—
249D4—122no—
250C2×C4—121no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4#677711yescharacteristic
254C2×C4#677711yescharacteristic
255C2×C4C2×#120111yescharacteristic
256C8—22no—
257C8—154no—
258C8—302no—
259C2×C3#6536311yescharacteristic
260C2×C3#6545611yescharacteristic
261C2×C3#6546411yescharacteristic
262D3—161no—
263C5#7121611yescharacteristic, complemented, Sylow
264C22—241no—
265C22—241no—
266C22—241no—
267C22#9146311yescharacteristic
268C4—241no—
269C4—401no—
270C4—401no—
271C4#9125512yes—
272C4#9128012yes—
273C4#9129912yes—
274C3#1060205011yescharacteristic, complemented, Sylow
275C2—481no—
276C2#1174704211yescharacteristic
277C2#1174798311yescharacteristic
278C2#1174801011yescharacteristic
subgroupG/H
centerC22#91463
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radicalC5×#874C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1714
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
2. C3×#64970C2semidirect
4. #11746962C2semidirect
5. #11746947C2semidirect
7. #11746275C2semidirect
28. #64970D3semidirect
84. C3⋊#168SD16semidirect
228. C3×C5#1714semidirect
263. C5#71216semidirect
274. C3#10602050semidirect

Maximal subgroups

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

subgroupindex
C5×#46932
C3×#649702
#117470812
#117469622
#117469472
#117469012
#117462752
#106020503
#712165