Finite Group Databasebeta

← #14293606

Subgroups — #14293606

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#11751171C211yesmaximal, characteristic
2C5×#5070C211yesmaximal, characteristic
3C3×#65359C211yesmaximal, characteristic
4#11746929C211yesmaximal, characteristic, complemented
5#11746924C211yesmaximal, characteristic, complemented
6#11746921C211yesmaximal, characteristic, complemented
7C3⋊C8×#168C211yesmaximal, characteristic, complemented
8#10601976—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91116—22no—
14C4×C3⋊#168C2211yescharacteristic
15C5×#832—22no—
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3964—22no—
18C3×C4×#168C2211yescharacteristic
19#90974—22no—
20#90973—22no—
21#90970—22no—
22#71183—51nomaximal, Hall
23C5×#486—31no—
24#65382—31no—
25#65370—31no—
26#65359—31no—
27#65359D311yescharacteristic
28#64970—31no—
29C8×#168—31no—
30C2×C3×C5×D4—21no—
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4—21no—
33C2×Dic30—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
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×#486—51no—
47#5093—51no—
48#5079—51no—
49#5070—51no—
50#5070D511yescharacteristic
51#4681—51no—
52C8×C3⋊C8—51no—
53C5×C4⋊Q8—31no—
54C5×#127C2×D311yescharacteristic
55#4015—31no—
56#4015C2×D311yescharacteristic
57C5×#102—62no—
58C4×C5×C8—31no—
59#3967—62no—
60#3964—22no—
61#3964—62no—
62#3948—62no—
63#3942—62no—
64C4×#168—31no—
65C4×#168C2×D311yescharacteristic
66#1711—151noSylow
67C23×C3×C5—41no—
68C3×C5×D4—42no—
69C3×C5×D4—42no—
70C3×C5×D4—42no—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—41no—
75Dic30—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×#127C2×D511yescharacteristic
85#869—51no—
86#869C2×D511yescharacteristic
87C3×#102—102no—
88C3×C4×C8—51no—
89#835—102no—
90#832—22no—
91#832—102no—
92#816—102no—
93#810—102no—
94C4×C3⋊C8—51no—
95C4×C3⋊C8C2×D511yescharacteristic
96C2×C5×Q8—61no—
97C2×C5×D4—21no—
98C2×C5×D4—21no—
99C2×C5×D4—21no—
100C2×Dic10—21no—
101C2×Dic10—61no—
102C2×C5×C8—32no—
103C5×C4⋊C4—61no—
104C5×C4⋊C4—61no—
105C42×C5C22×D311yescharacteristic
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C2×#168—32no—
111C2×#168#6712yes—
112#487—151no—
113#487—151no—
114#487—151no—
115#486—31no—
116#486—51no—
117#486—151no—
118C82—151no—
119C22×C3×C5—81no—
120C22×C3×C5—81no—
121C22×C3×C5—81no—
122C22×C3×C5#12711yescharacteristic
123C3×C4×C5#13512yes—
124C3×C4×C5#13512yes—
125C3×C4×C5#13512yes—
126Dic15—81no—
127C3×Dic5—81no—
128C5×Dic3—81no—
129C2×C3×Q8—101no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×Dic6—21no—
134C2×Dic6—101no—
135C2×C3×C8—52no—
136C3×C4⋊C4—101no—
137C3×C4⋊C4—101no—
138C3×C42C22×D511yescharacteristic
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—101no—
142C4⋊Dic3—101no—
143C2×C3⋊C8—52no—
144C2×C3⋊C8C22⋊D512yes—
145C23×C5—41no—
146C5×Q8—122no—
147C5×D4—42no—
148C5×D4—42no—
149C5×D4—42no—
150C2×C4×C5—121no—
151C2×C4×C5D3×D411yescharacteristic
152C2×C4×C5D3×D411yescharacteristic
153C2×C4×C5C2×#6711yescharacteristic
154C2×Dic5—41no—
155C2×Dic5—121no—
156Dic10—42no—
157Dic10—122no—
158C5×C8—62no—
159#168—22no—
160#168—62no—
161C4⋊Q8—31no—
162C4⋊Q8—51no—
163C4⋊Q8—151no—
164#127D3×D511yescharacteristic
165#103—302no—
166#103—302no—
167#103—302no—
168#102—62no—
169#102—102no—
170#102—302no—
171C4×C8—31no—
172C4×C8—51no—
173C4×C8—151no—
174C2×C3×C5—161no—
175C2×C3×C5#49511yescharacteristic
176C2×C3×C5#49511yescharacteristic
177C2×C3×C5#49511yescharacteristic
178C23×C3—41no—
179C3×Q8—202no—
180C3×D4—42no—
181C3×D4—42no—
182C3×D4—42no—
183C2×C3×C4—201no—
184C2×C3×C4D4×D511yescharacteristic
185C2×C3×C4D4×D511yescharacteristic
186C2×C3×C4C2×C22⋊D511yescharacteristic
187C2×Dic3—41no—
188C2×Dic3—201no—
189Dic6—42no—
190Dic6—202no—
191C3×C8—102no—
192C3⋊C8—22no—
193C3⋊C8—102no—
194C22×C5—81no—
195C22×C5—81no—
196C22×C5—81no—
197C22×C5#94011yescharacteristic
198C4×C5—241no—
199C4×C5#91212yes—
200C4×C5#91612yes—
201C4×C5#95012yes—
202Dic5—81no—
203Dic5—241no—
204C2×Q8—61no—
205C2×Q8—101no—
206C2×Q8—301no—
207C2×D4—21no—
208C2×D4—21no—
209C2×D4—21no—
210C2×C8—32no—
211C2×C8—52no—
212C2×C8—152no—
213C4⋊C4—61no—
214C4⋊C4—61no—
215C4⋊C4—101no—
216C4⋊C4—101no—
217C4⋊C4—301no—
218C4⋊C4—301no—
219C42C2×D3×D511yescharacteristic
220C3×C5#171111yescharacteristic, complemented, Hall
221C22×C3—81no—
222C22×C3—81no—
223C22×C3—81no—
224C22×C3#408611yescharacteristic
225C3×C4—401no—
226C3×C4#405812yes—
227C3×C4#406212yes—
228C3×C4#409612yes—
229Dic3—81no—
230Dic3—401no—
231C2×C5—161no—
232C2×C5#505911yescharacteristic
233C2×C5#515511yescharacteristic
234C2×C5#516811yescharacteristic
235C23—41no—
236Q8—122no—
237Q8—202no—
238Q8—602no—
239D4—42no—
240D4—42no—
241D4—42no—
242C2×C4—121no—
243C2×C4—201no—
244C2×C4—601no—
245C2×C4D5×#6711yescharacteristic
246C2×C4D3×C22⋊D511yescharacteristic
247C2×C4#679011yescharacteristic
248C8—62no—
249C8—102no—
250C8—302no—
251C2×C3—161no—
252C2×C3#6534811yescharacteristic
253C2×C3#6544411yescharacteristic
254C2×C3#6545711yescharacteristic
255C5#7118311yescharacteristic, complemented, Sylow
256C22—81no—
257C22—81no—
258C22—81no—
259C22#9156711yescharacteristic
260C4—241no—
261C4—401no—
262C4—1201no—
263C4#9149012yes—
264C4#9149512yes—
265C4#9149712yes—
266C3#1060197611yescharacteristic, complemented, Sylow
267C2—161no—
268C2#1174906711yescharacteristic
269C2#1174907211yescharacteristic
270C2#1174907811yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#127
hypercenter#127D3×D5
hypocenterC3×C5#1711
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
4. #11746929C2semidirect
5. #11746924C2semidirect
6. #11746921C2semidirect
7. C3⋊C8×#168C2semidirect
220. C3×C5#1711semidirect
255. C5#71183semidirect
266. C3#10601976semidirect

Maximal subgroups

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

subgroupindex
#117511712
C5×#50702
C3×#653592
#117469292
#117469242
#117469212
C3⋊C8×#1682
#106019763
#711835