Finite Group Databasebeta

← #14293617

Subgroups — #14293617

Order 1920.

356 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 94 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#11751189C211yesmaximal, characteristic
2C5×#5079C211yesmaximal, characteristic, complemented
3C3×#65382C211yesmaximal, characteristic, complemented
4#11746923C211yesmaximal, characteristic, complemented
5#11746912C211yesmaximal, characteristic
6#11746910C211yesmaximal, characteristic
7C3⋊C8×#168C211yesmaximal, characteristic, complemented
8#10602008—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91763C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91093—22no—
14C4×C3⋊#168C2211yescharacteristic
15C5×#835—22no—
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3942—22no—
18C3×C4×#168C2211yescharacteristic
19#90972—22no—
20#90969—22no—
21#90968—22no—
22#71215—51nomaximal, Hall
23C5×#487—31no—
24#65382D311yescharacteristic, complemented
25#65377—31no—
26#65377—31no—
27#65370—31no—
28#64983—31no—
29C8×#168—31no—
30C2×C3×C5×Q8—21no—
31C2×D60—21no—
32C2×D60—21no—
33C2×D60—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C42×C5C2311yescharacteristic
39C2×C3⋊#168D412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C2×C5×C3⋊C8D412yes—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C2×C3×#168D412yes—
46C3×#487—51no—
47#5093—51no—
48#5088—51no—
49#5088—51no—
50#5079D511yescharacteristic, complemented
51#4694—51no—
52C8×C3⋊C8—51no—
53C5×C4⋊Q8—31no—
54C5×C4⋊Q8C2×D311yescharacteristic
55#4020—31no—
56#4015C2×D311yescharacteristic
57C5×#103—62no—
58C4×C5×C8—31no—
59#3967—62no—
60#3953—62no—
61#3942—22no—
62#3941—62no—
63#3941—62no—
64C4×#168—31no—
65C4×#168C2×D311yescharacteristic
66#1711—151noSylow
67C22×D15—41no—
68C3×C5×Q8—42no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73D60—42no—
74D60—42no—
75D60—42no—
76C2×C5×Dic3—41no—
77C5×Dic6—42no—
78C2×C3×Dic5—41no—
79C3×Dic10—42no—
80C3⋊#168—22no—
81C3×#168—22no—
82C5×C3⋊C8—22no—
83C3×C4⋊Q8—51no—
84C3×C4⋊Q8C2×D511yescharacteristic
85#874—51no—
86#869C2×D511yescharacteristic
87C3×#103—102no—
88C3×C4×C8—51no—
89#835—22no—
90#821—102no—
91#810—102no—
92#809—102no—
93#809—102no—
94C4×C3⋊C8—51no—
95C4×C3⋊C8C2×D511yescharacteristic
96C2×C5×Q8—21no—
97C2×C5×Q8—61no—
98C2×D20—61no—
99C2×D20—61no—
100C2×D20—61no—
101C2×Dic10—21no—
102C2×C5×C8—32no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—61no—
106C5×C4⋊C4—61no—
107C42×C5C22×D311yescharacteristic
108C4⋊Dic5—21no—
109C4⋊Dic5—21no—
110C2×#168—32no—
111C2×#168#6712yes—
112#487—31no—
113#487—51no—
114#487—151no—
115#486—151no—
116#486—151no—
117#486—151no—
118C82—151no—
119C22×C3×C5#12711yescharacteristic
120C2×D15—81no—
121C2×D15—81no—
122C2×D15—81no—
123C3×C4×C5—81no—
124C3×C4×C5#13512yes—
125C3×C4×C5#13512yes—
126C3×C4×C5#13512yes—
127C3×Dic5—81no—
128C5×Dic3—81no—
129C2×C3×Q8—21no—
130C2×C3×Q8—101no—
131C2×D12—101no—
132C2×D12—101no—
133C2×D12—101no—
134C2×Dic6—21no—
135C2×C3×C8—52no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—101no—
139C3×C4⋊C4—101no—
140C3×C42C22×D511yescharacteristic
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C2×C3⋊C8—52no—
144C2×C3⋊C8C22⋊D512yes—
145C22×D5—121no—
146C5×Q8—42no—
147C5×Q8—122no—
148C2×C4×C5—41no—
149C2×C4×C5—121no—
150C2×C4×C5D3×D411yescharacteristic
151C2×C4×C5D3×D411yescharacteristic
152C2×C4×C5C2×#6711yescharacteristic
153C2×Dic5—41no—
154D20—122no—
155D20—122no—
156D20—122no—
157Dic10—42no—
158C5×C8—62no—
159#168—22no—
160#168—62no—
161C4⋊Q8—31no—
162C4⋊Q8—51no—
163C4⋊Q8D3×D511yescharacteristic
164#127—151no—
165#103—62no—
166#103—102no—
167#103—302no—
168#102—302no—
169#102—302no—
170#102—302no—
171C4×C8—31no—
172C4×C8—51no—
173C4×C8—151no—
174C2×C3×C5#49511yescharacteristic
175C2×C3×C5#49511yescharacteristic
176C2×C3×C5#49511yescharacteristic
177D15—161no—
178C22×D3—201no—
179C3×Q8—42no—
180C3×Q8—202no—
181C2×C3×C4—41no—
182C2×C3×C4—201no—
183C2×C3×C4D4×D511yescharacteristic
184C2×C3×C4D4×D511yescharacteristic
185C2×C3×C4C2×C22⋊D511yescharacteristic
186C2×Dic3—41no—
187D12—202no—
188D12—202no—
189D12—202no—
190Dic6—42no—
191C3×C8—102no—
192C3⋊C8—22no—
193C3⋊C8—102no—
194C22×C5#94011yescharacteristic
195C2×D5—241no—
196C2×D5—241no—
197C2×D5—241no—
198C4×C5—81no—
199C4×C5—241no—
200C4×C5#91612yes—
201C4×C5#91912yes—
202C4×C5#95012yes—
203Dic5—81no—
204C2×Q8—21no—
205C2×Q8—61no—
206C2×Q8—101no—
207C2×D4—301no—
208C2×D4—301no—
209C2×D4—301no—
210C2×C8—32no—
211C2×C8—52no—
212C2×C8—152no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—101no—
218C4⋊C4—101no—
219C42C2×D3×D511yescharacteristic
220C3×C5#171111yescharacteristic, complemented, Hall
221C22×C3#408611yescharacteristic
222C2×D3—401no—
223C2×D3—401no—
224C2×D3—401no—
225C3×C4—81no—
226C3×C4—401no—
227C3×C4#406212yes—
228C3×C4#406512yes—
229C3×C4#409612yes—
230Dic3—81no—
231C2×C5#505911yescharacteristic
232C2×C5#516811yescharacteristic
233C2×C5#519111yescharacteristic
234D5—481no—
235C23—601no—
236Q8—42no—
237Q8—122no—
238Q8—202no—
239D4—602no—
240D4—602no—
241D4—602no—
242C2×C4—41no—
243C2×C4—121no—
244C2×C4—201no—
245C2×C4D5×#6711yescharacteristic
246C2×C4D3×C22⋊D511yescharacteristic
247C2×C4#679011yescharacteristic
248C8—62no—
249C8—102no—
250C8—302no—
251C2×C3#6534811yescharacteristic
252C2×C3#6545711yescharacteristic
253C2×C3#6548011yescharacteristic
254D3—801no—
255C5#7121511yescharacteristic, complemented, Sylow
256C22—1201no—
257C22—1201no—
258C22—1201no—
259C22#9156711yescharacteristic
260C4—81no—
261C4—241no—
262C4—401no—
263C4#9149512yes—
264C4#9151612yes—
265C4#9152312yes—
266C3#1060200811yescharacteristic, complemented, Sylow
267C2—2401no—
268C2#1174907811yescharacteristic
269C2#1174931611yescharacteristic
270C2#1174932111yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#127
prime radical#91763C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1711
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
2. C5×#5079C2semidirect
3. C3×#65382C2semidirect
4. #11746923C2semidirect
7. C3⋊C8×#168C2semidirect
24. #65382D3semidirect
50. #5079D5semidirect
220. C3×C5#1711semidirect
255. C5#71215semidirect
266. C3#10602008semidirect

Maximal subgroups

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

subgroupindex
#117511892
C5×#50792
C3×#653822
#117469232
#117469122
#117469102
C3⋊C8×#1682
#106020083
#712155