Finite Group Databasebeta

← #14317134

Subgroups — #14317134

Order 1920.

332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×C3×#3932C211yesmaximal, characteristic
2#11748033C211yesmaximal, characteristic, complemented
3Dic3×D40C211yesmaximal, characteristic
4C2×#90942C211yesmaximal, characteristic
5#11746324C211yesmaximal, characteristic, complemented
6C5×Dic3⋊C16C211yesmaximal, characteristic, complemented
7#11745898C211yesmaximal, characteristic, complemented
8#10600080—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12Dic3×D20—21no—
13#91389—21no—
14C2×#6662—21no—
15C2×C3×C5×C16C2211yescharacteristic
16#91102C2211yescharacteristic
17C5×C8×Dic3C2211yescharacteristic
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×#3932—22no—
20#90965—21no—
21#90942—22no—
22#71476—51nomaximal, Hall
23C2×#3932—31no—
24C2×#3932D311yescharacteristic
25#64988—31no—
26C4×D40—31no—
27C5×C4⋊C16—31no—
28#64723—31no—
29#64723—31no—
30C2×Dic30—21no—
31C2×C3×D20—21no—
32C2×C3×Dic10—21no—
33C2×D5×Dic3—41no—
34C2×C3×C5×C8C2311yescharacteristic
35C4⋊Dic15—21no—
36Dic60—21no—
37Dic60—21no—
38C4×C5×Dic3D411yescharacteristic
39C2×C5×C3⋊C8D411yescharacteristic
40C3×Dic20—21no—
41C3×Dic20—21no—
42C3×D40—21no—
43C3×D40D412yes—
44Dic3⋊Dic5—41no—
45Dic3⋊Dic5—41no—
46#6665—41no—
47#6662—42no—
48C3×C5×C16—21no—
49C5×C3⋊C16—21no—
50C2×C3×SD32—51no—
51#5183—51no—
52Dic3×D8—51no—
53C2×#827—51no—
54#4564—51no—
55#4503—51no—
56Dic3⋊C16D511yescharacteristic, complemented
57C2×Dic20—31no—
58C2×Dic20—61no—
59C2×Dic20C2×D311yescharacteristic
60C2×D40C2×D311yescharacteristic
61C4×D20—61no—
62#4015—61no—
63C2×C5×C16—31no—
64C2×C5×C16C2×D311yescharacteristic
65C4×C5×C8—31no—
66#3953—61no—
67#3950—31no—
68#3932—22no—
69#3932—62no—
70#2208—151noSylow
71C22×C3×D5—41no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×Dic15—41no—
74C2×Dic15—41no—
75Dic30—41no—
76Dic30—41no—
77C2×C5×Dic3D811yescharacteristic
78C2×C5×Dic3D811yescharacteristic
79C2×C3×Dic5—41no—
80C3×D20—22no—
81C3×D20—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84D5×Dic3—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C5×C3⋊C8—21no—
88C2×C3×Q16—51no—
89C2×C3×D8—51no—
90#944—101no—
91C2×#216—101no—
92D4×Dic3—101no—
93C2×Dic12—51no—
94C3×SD32—102no—
95C2×C3×C16C2×D511yescharacteristic
96#832—101no—
97#827—102no—
98#818—51no—
99C8×Dic3C2×D511yescharacteristic
100C2×C3⋊C16C2×D511yescharacteristic
101C2×D20—21no—
102C2×C4×D5—121no—
103C2×Dic10—21no—
104C2×Dic10—61no—
105C2×C5×C8—31no—
106C2×C5×C8C22×D311yescharacteristic
107C42×C5—31no—
108#685—121no—
109C4⋊Dic5—61no—
110C4⋊Dic5—121no—
111C4⋊Dic5—121no—
112Dic20—21no—
113Dic20—21no—
114Dic20—61no—
115Dic20—61no—
116Dic20—122no—
117D40—21no—
118D40#6712yes—
119C5×C16—21no—
120C5×C16—61no—
121C2×SD32—51no—
122C2×SD32—151no—
123#494—151no—
124C4×D8—151no—
125C4⋊C16—31no—
126#358—151no—
127#358—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C3×D5—42no—
130C2×C3×D5—81no—
131C2×C3×D5—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—81no—
135Dic15—81no—
136C3×Dic5—81no—
137C5×Dic3—21no—
138C5×Dic3SD3212yescomplemented
139C2×C3×Q8—101no—
140C2×C3×D4—101no—
141C22×Dic3—201no—
142C2×Dic6—101no—
143C3×Q16—101no—
144C3×Q16—101no—
145C3×D8—52no—
146C3×D8—101no—
147C2×C3×C8C22×D511yescharacteristic
148#217—201no—
149#216—202no—
150C4⋊Dic3—101no—
151Dic3⋊C4—201no—
152Dic3⋊C4—201no—
153C4×Dic3D2011yescharacteristic
154C2×C3⋊C8D2011yescharacteristic
155Dic12—101no—
156Dic12—101no—
157C3×C16—21no—
158C3⋊C16—21no—
159C22×D5—41no—
160C2×C4×C5—31no—
161C2×C4×C5—31no—
162C2×C4×C5D3×D411yescharacteristic
163C2×Dic5—41no—
164C2×Dic5—121no—
165C2×Dic5—121no—
166D20—22no—
167D20—41no—
168C4×D5—242no—
169Dic10—41no—
170Dic10—41no—
171Dic10—121no—
172Dic10—121no—
173C5×C8—61no—
174C5×C8#23711yescharacteristic
175C5×C8C2×#6711yescharacteristic
176C2×Q16—51no—
177C2×Q16—151no—
178C2×Q16—301no—
179C2×D8—51no—
180C4⋊Q8—301no—
181C4×D4—301no—
182SD32—102no—
183SD32—302no—
184C2×C16—31no—
185C2×C16D3×D511yescharacteristic
186#107—151no—
187#102—301no—
188C4×C8—31no—
189C2×C3×C5#45911yescharacteristic
190C2×C3×C5C2×SD3211yescharacteristic
191C2×C3×C5#51011yescharacteristic
192C3×D5—82no—
193C23×C3—201no—
194C3×Q8—201no—
195C3×Q8—201no—
196C3×D4—102no—
197C3×D4—201no—
198C2×C3×C4—201no—
199C2×C3×C4C2×D2011yescharacteristic
200C2×Dic3—201no—
201C2×Dic3—201no—
202C2×Dic3—402no—
203C2×Dic3D4011yescharacteristic
204C2×Dic3D4011yescharacteristic
205Dic6—201no—
206Dic6—201no—
207C3×C8D4×D511yescharacteristic
208C3×C8#71311yescharacteristic
209C3⋊C8—21no—
210C22×C5D3×D811yescharacteristic
211C2×D5—42no—
212C2×D5—81no—
213C2×D5—81no—
214C4×C5—32no—
215C4×C5—61no—
216C4×C5#91111yescharacteristic
217C4×C5#93911yescharacteristic
218Dic5—81no—
219Dic5—241no—
220Dic5—241no—
221C2×Q8—101no—
222C2×Q8—301no—
223C2×D4—101no—
224C22×C4—601no—
225Q16—101no—
226Q16—101no—
227Q16—301no—
228Q16—301no—
229Q16—602no—
230D8—52no—
231D8—101no—
232C2×C8—31no—
233C2×C8C2×D3×D511yescharacteristic
234C4⋊C4—301no—
235C4⋊C4—601no—
236C4⋊C4—601no—
237C22⋊C4—601no—
238C42—31no—
239C16—21no—
240C16—61no—
241C3×C5#220811yescharacteristic, complemented, Hall
242C22×C3—202no—
243C22×C3—401no—
244C22×C3—401no—
245C22×C3C2×D4011yescharacteristic
246C3×C4—401no—
247C3×C4#404111yescharacteristic
248C3×C4#405411yescharacteristic
249Dic3—21no—
250Dic3—401no—
251Dic3—401no—
252Dic3#393212yescomplemented
253C2×C5D3×SD3211yescharacteristic
254C2×C5#491511yescharacteristic
255C2×C5#515011yescharacteristic
256D5—82no—
257C23—201no—
258Q8—201no—
259Q8—201no—
260Q8—601no—
261Q8—601no—
262D4—102no—
263D4—201no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—201no—
267C2×C4—601no—
268C2×C4—601no—
269C2×C4—1202no—
270C2×C4D3×D2011yescharacteristic
271C8—61no—
272C8#676611yescharacteristic
273C8D5×#6711yescharacteristic
274C2×C3—402no—
275C2×C3#6513211yescharacteristic
276C2×C3C2×#393211yescharacteristic
277C2×C3#6519811yescharacteristic
278C5#7147611yescharacteristic, complemented, Sylow
279C22—202no—
280C22—401no—
281C22—401no—
282C22D3×D4011yescharacteristic
283C4—32no—
284C4—61no—
285C4—401no—
286C4—1201no—
287C4—1201no—
288C4#9125411yescharacteristic
289C4#9140911yescharacteristic
290C3#1060008011yescharacteristic, complemented, Sylow
291C2—402no—
292C2D3×#393211yescharacteristic
293C2#1174683711yescharacteristic
294C2#1174775411yescharacteristic
subgroupG/H
centerC22D3×D40
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenterC2×C16D3×D5
hypocenterC3×C5#2208
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. #11748033C2semidirect
5. #11746324C2semidirect
6. C5×Dic3⋊C16C2semidirect
7. #11745898C2semidirect
56. Dic3⋊C16D5semidirect
138. C5×Dic3SD32semidirect
241. C3×C5#2208semidirect
252. Dic3#3932semidirect
278. C5#71476semidirect
290. C3#10600080semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#39322
#117480332
Dic3×D402
C2×#909422
#117463242
C5×Dic3⋊C162
#117458982
#106000803
#714765