Finite Group Databasebeta

← #14293610

Subgroups — #14293610

Order 1920.

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

normal subgroups only

This group has 356 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
1#11750782C211yesmaximal, characteristic, complemented
2C3×#64983C211yesmaximal, characteristic
3#11746921C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5#11746890C211yesmaximal, characteristic
6#11746890C211yesmaximal, characteristic
7C5×C8×C3⋊C8C211yesmaximal, characteristic, complemented
8#10598854—31nomaximal, Hall
9#91758C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4020C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C3×C4×C5×C8C2211yescharacteristic
14#91100—22no—
15C4×C5×C3⋊C8C2211yescharacteristic
16C4×C5×C3⋊C8C2211yescharacteristic
17C3×#3953—22no—
18#90974—22no—
19#90971—22no—
20#90965—22no—
21#90965—22no—
22#71183—51nomaximal, Hall
23#64983—31no—
24#64983—31no—
25#64983D311yescharacteristic
26#64970—31no—
27#64970—31no—
28#64970—31no—
29C5×C82—31no—
30C2×Dic30—21no—
31C2×Dic30—21no—
32C2×C3×D20—21no—
33C2×C3×D20—21no—
34C2×C3×D20—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8D412yes—
37C3×C42×C5C2311yescharacteristic
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15—21no—
42C2×C5×C3⋊C8D412yes—
43C2×C5×C3⋊C8D412yes—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46C3×#486—51no—
47#5093—51no—
48#5079—51no—
49#5070—51no—
50#5070—51no—
51#4681—51no—
52C8×C3⋊C8D511yescharacteristic, complemented
53#4020C2×D311yescharacteristic
54#4015—31no—
55#4015—31no—
56#4015C2×D311yescharacteristic
57C4×C5×C8—31no—
58C4×C5×C8—31no—
59C4×C5×C8C2×D311yescharacteristic
60#3953—22no—
61#3953—62no—
62#3953—62no—
63#3948—62no—
64#3948—62no—
65#3948—62no—
66#1711—151noSylow
67C22×C3×D5—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×Dic15—41no—
72C2×Dic15—41no—
73Dic30—42no—
74Dic30—42no—
75C2×C3×Dic5—41no—
76C3×D20—42no—
77C3×D20—42no—
78C3×D20—42no—
79C3×Dic10—42no—
80C3×C5×C8—22no—
81C5×C3⋊C8—22no—
82C5×C3⋊C8—22no—
83C3×C4⋊Q8—51no—
84C3×#127—51no—
85#869—51no—
86#869—51no—
87C3×#102—102no—
88C3×C4×C8C2×D511yescharacteristic
89#835—102no—
90#832—102no—
91#832—102no—
92#816—102no—
93#810—102no—
94C4×C3⋊C8C2×D511yescharacteristic
95C4×C3⋊C8C2×D511yescharacteristic
96C2×D20—21no—
97C2×D20—21no—
98C2×D20—21no—
99C2×Dic10—21no—
100C2×Dic10—61no—
101C2×Dic10—61no—
102C2×C5×C8—32no—
103C2×C5×C8—32no—
104C2×C5×C8#6712yes—
105C42×C5C22×D311yescharacteristic
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112#487—151no—
113#487—151no—
114#487—151no—
115#486—51no—
116#486—151no—
117#486—151no—
118C82—31no—
119C22×C3×C5#12711yescharacteristic
120C2×C3×D5—81no—
121C2×C3×D5—81no—
122C2×C3×D5—81no—
123C3×C4×C5#13512yes—
124C3×C4×C5#13512yes—
125C3×C4×C5#13512yes—
126Dic15—81no—
127Dic15—81no—
128C3×Dic5—81no—
129C2×C3×Q8—101no—
130C2×C3×D4—101no—
131C2×C3×D4—101no—
132C2×C3×D4—101no—
133C2×Dic6—101no—
134C2×Dic6—101no—
135C2×C3×C8D2012yes—
136C3×C4⋊C4—101no—
137C3×C4⋊C4—101no—
138C3×C42C22×D511yescharacteristic
139C4⋊Dic3—101no—
140C4⋊Dic3—101no—
141C4⋊Dic3—101no—
142C4⋊Dic3—101no—
143C2×C3⋊C8D2012yes—
144C2×C3⋊C8D2012yes—
145C22×D5—41no—
146C2×C4×C5D3×D411yescharacteristic
147C2×C4×C5D3×D411yescharacteristic
148C2×C4×C5C2×#6711yescharacteristic
149C2×Dic5—41no—
150C2×Dic5—121no—
151C2×Dic5—121no—
152D20—42no—
153D20—42no—
154D20—42no—
155Dic10—42no—
156Dic10—122no—
157Dic10—122no—
158C5×C8—22no—
159C5×C8—62no—
160C5×C8—62no—
161C4⋊Q8—51no—
162C4⋊Q8—151no—
163C4⋊Q8—151no—
164#127—51no—
165#103—302no—
166#103—302no—
167#103—302no—
168#102—102no—
169#102—302no—
170#102—302no—
171C4×C8—31no—
172C4×C8—31no—
173C4×C8D3×D511yescharacteristic
174C2×C3×C5#49511yescharacteristic
175C2×C3×C5#49511yescharacteristic
176C2×C3×C5#49511yescharacteristic
177C3×D5—161no—
178C23×C3—201no—
179C3×Q8—202no—
180C3×D4—202no—
181C3×D4—202no—
182C3×D4—202no—
183C2×C3×C4—201no—
184C2×C3×C4C2×D2011yescharacteristic
185C2×C3×C4C2×D2011yescharacteristic
186C2×C3×C4C2×D2011yescharacteristic
187C2×Dic3—201no—
188C2×Dic3—201no—
189Dic6—202no—
190Dic6—202no—
191C3×C8—22no—
192C3⋊C8—22no—
193C3⋊C8—22no—
194C22×C5#94011yescharacteristic
195C2×D5—81no—
196C2×D5—81no—
197C2×D5—81no—
198C4×C5#91212yes—
199C4×C5#91612yes—
200C4×C5#95012yes—
201Dic5—81no—
202Dic5—241no—
203Dic5—241no—
204C2×Q8—101no—
205C2×Q8—301no—
206C2×Q8—301no—
207C2×D4—101no—
208C2×D4—101no—
209C2×D4—101no—
210C2×C8—32no—
211C2×C8—32no—
212C2×C8#120212yes—
213C4⋊C4—101no—
214C4⋊C4—101no—
215C4⋊C4—301no—
216C4⋊C4—301no—
217C4⋊C4—301no—
218C4⋊C4—301no—
219C42C2×D3×D511yescharacteristic
220C3×C5#171111yescharacteristic, complemented, Hall
221C22×C3—401no—
222C22×C3—401no—
223C22×C3—401no—
224C22×C3#402011yescharacteristic
225C3×C4—401no—
226C3×C4#405012yes—
227C3×C4#405012yes—
228C3×C4#405012yes—
229Dic3—401no—
230Dic3—401no—
231C2×C5#505911yescharacteristic
232C2×C5#515511yescharacteristic
233C2×C5#516811yescharacteristic
234D5—161no—
235C23—201no—
236Q8—202no—
237Q8—602no—
238Q8—602no—
239D4—202no—
240D4—202no—
241D4—202no—
242C2×C4—201no—
243C2×C4—601no—
244C2×C4—601no—
245C2×C4D3×D2011yescharacteristic
246C2×C4D3×D2011yescharacteristic
247C2×C4C2×#120211yescharacteristic
248C8—22no—
249C8—62no—
250C8—62no—
251C2×C3—801no—
252C2×C3#6498511yescharacteristic
253C2×C3#6498511yescharacteristic
254C2×C3#6498511yescharacteristic
255C5#7118311yescharacteristic, complemented, Sylow
256C22—401no—
257C22—401no—
258C22—401no—
259C22#9145811yescharacteristic
260C4—401no—
261C4—1201no—
262C4—1201no—
263C4#9127212yes—
264C4#9127312yes—
265C4#9131112yes—
266C3#1059885411yescharacteristic, complemented, Sylow
267C2—801no—
268C2#1174707211yescharacteristic
269C2#1174796911yescharacteristic
270C2#1174797111yescharacteristic
subgroupG/H
centerC22#91458
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#127
prime radicalC3×#4020C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1711
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
1. #11750782C2semidirect
3. #11746921C2semidirect
4. #11746920C2semidirect
7. C5×C8×C3⋊C8C2semidirect
52. C8×C3⋊C8D5semidirect
220. C3×C5#1711semidirect
255. C5#71183semidirect
266. C3#10598854semidirect

Maximal subgroups

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

subgroupindex
#117507822
C3×#649832
#117469212
#117469202
#117468902
C5×C8×C3⋊C82
#105988543
#711835