Finite Group Databasebeta

← #14316045

Subgroups — #14316045

Order 1920.

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

normal subgroups only

This group has 532 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
1C22×C3×D40C211yesmaximal, characteristic, complemented
2#11751216C211yesmaximal, characteristic, complemented
3C2×#90938C212yesmaximal, complemented
4C5×#4549C211yesmaximal, characteristic, complemented
5#11745892C212yesmaximal, complemented
6#10599901—31nomaximal, Hall
7C22×C3×D20—21no—
8C22×C3×C5×C8C2211yescharacteristic
9#91819—21no—
10C2×D120C2211yescharacteristic, complemented
11C2×C3×D40—21no—
12C2×C3×D40—24no—
13C2×C3×D40C2212yes—
14#91105—21no—
15#91102C2211yescharacteristic, complemented
16C2×C5×C3⋊C16C2212yescomplemented
17#90938—24no—
18#72035—51nomaximal, Hall
19C22×D40D311yescharacteristic, complemented
20#65404—31no—
21C2×D80—32no—
22C5×C22⋊C16—31no—
23#64729—32no—
24C23×C3×D5—41no—
25C22×C3×C4×C5D411yescharacteristic
26C2×#1220—41no—
27C2×D60—21no—
28C2×C3×D20—24no—
29C2×C3×D20—22no—
30C2×C3×D20—42no—
31C2×C3×D20—41no—
32C2×C3×C5×C8—22no—
33C2×C3×C5×C8D411yescharacteristic
34C2×C3×C5×C8C2311yescharacteristic
35#6714—41no—
36C4⋊Dic15—21no—
37D120—22no—
38C3×D40—24no—
39C3×D40—22no—
40C3×D40D414yescomplemented
41C5×C3⋊C16—22no—
42C22×C3×D8—51no—
43C2×#826—52no—
44#5115—51no—
45#4562—52no—
46#4549D511yescharacteristic, complemented
47C22×D20—21no—
48C22×C5×C8C2×D311yescharacteristic
49#4076—61no—
50C2×D40—21no—
51C2×D40—24no—
52C2×D40—31no—
53C2×D40C2×D312yes—
54C2×C5×C16—32no—
55#3953—61no—
56#3950—31no—
57D80—64no—
58#2184—151noSylow
59C23×C3×C5D811yescharacteristic
60C22×D15—41no—
61C22×C3×D5—44no—
62C22×C3×D5—42no—
63C22×C3×D5—82no—
64C22×C3×D5—82no—
65C2×C3×C4×C5—21no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5D811yescharacteristic
68C2×C3×C4×C5C2×D411yescharacteristic
69#1220—82no—
70C2×Dic15—41no—
71D60—41no—
72D60—41no—
73C3×D20—24no—
74C3×D20—44no—
75C3×D20—42no—
76C3×C5×C8—21no—
77C3×C5×C8C2×D412yes—
78C22×C3×D4—101no—
79C2×C3×D8—52no—
80C2×C3×D8—104no—
81C2×C3×D8—101no—
82C22×C3×C8C2×D511yescharacteristic
83#930—101no—
84C2×D24—51no—
85#826—104no—
86#821—101no—
87#818—51no—
88C2×C3⋊C16C2×D512yescomplemented
89C23×D5—41no—
90C22×C4×C5#6711yescharacteristic
91C2×C22⋊D5—121no—
92C2×D20—24no—
93C2×D20—22no—
94C2×D20—42no—
95C2×D20—41no—
96C2×D20—61no—
97C2×C5×C8—22no—
98C2×C5×C8#6711yescharacteristic
99C2×C5×C8C22×D311yescharacteristic
100#685—121no—
101C4⋊Dic5—61no—
102D40—24no—
103D40—22no—
104D40—62no—
105D40#6714yescomplemented
106C5×C16—62no—
107C22×D8—51no—
108C2×D16—152no—
109#466—151no—
110#357—152no—
111C22⋊C16—31no—
112C22×C3×C5—21no—
113C22×C3×C5—21no—
114C22×C3×C5D1612yescomplemented
115C22×C3×C5C2×D811yescharacteristic
116C2×D15—81no—
117C2×D15—81no—
118C2×D15—81no—
119C2×C3×D5—44no—
120C2×C3×D5—88no—
121C2×C3×D5—82no—
122C2×C3×D5—82no—
123C3×C4×C5—21no—
124C3×C4×C5#12011yescharacteristic
125C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
126Dic15—81no—
127C24×C3—201no—
128C2×C3×D4—104no—
129C2×C3×D4—102no—
130C2×C3×D4—202no—
131C2×C3×D4—201no—
132C22×C3×C4D2011yescharacteristic
133C2×#67—201no—
134C2×D12—101no—
135C3×D8—54no—
136C3×D8—104no—
137C3×D8—102no—
138C2×C3×C8—22no—
139C2×C3×C8D2011yescharacteristic
140C2×C3×C8C22×D511yescharacteristic
141(C2×D3)⋊C4—201no—
142C4⋊Dic3—101no—
143D24—102no—
144C3⋊C16—22no—
145C23×C5#21311yescharacteristic
146C22×D5—44no—
147C22×D5—42no—
148C22×D5—82no—
149C22×D5—82no—
150C22×D5—121no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5#21311yescharacteristic
154C2×C4×C5C2×#6711yescharacteristic
155C22⋊D5—242no—
156C2×Dic5—121no—
157D20—24no—
158D20—44no—
159D20—42no—
160D20—121no—
161D20—121no—
162C5×C8—21no—
163C5×C8C2×#6712yes—
164C22×D4—101no—
165C2×D8—52no—
166C2×D8—104no—
167C2×D8—101no—
168C2×D8—151no—
169C22×C8D3×D511yescharacteristic
170#121—301no—
171D16—304no—
172C2×C16—32no—
173#107—151no—
174#102—301no—
175C2×C3×C5—22no—
176C2×C3×C5#44711yescharacteristic
177C2×C3×C5C2×D1611yescharacteristic
178C2×C3×C5#50911yescharacteristic
179D15—161no—
180C3×D5—84no—
181C23×C3—204no—
182C23×C3—202no—
183C23×C3—402no—
184C23×C3—402no—
185C23×C3D4011yescharacteristic
186C22×D3—201no—
187C3×D4—104no—
188C3×D4—204no—
189C3×D4—202no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4D4011yescharacteristic
193C2×C3×C4C2×D2011yescharacteristic
194#67—402no—
195C2×Dic3—201no—
196D12—201no—
197D12—201no—
198C3×C8—21no—
199C3×C8D4×D512yes—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5#82612yescomplemented
203C22×C5C2×#21311yescharacteristic
204C2×D5—44no—
205C2×D5—88no—
206C2×D5—82no—
207C2×D5—82no—
208C2×D5—241no—
209C2×D5—241no—
210C2×D5—241no—
211C4×C5—21no—
212C4×C5#93211yescharacteristic
213C4×C5#95311yescharacteristic
214Dic5—241no—
215C24—201no—
216C2×D4—104no—
217C2×D4—102no—
218C2×D4—202no—
219C2×D4—201no—
220C2×D4—301no—
221C2×D4—601no—
222C22×C4#120211yescharacteristic
223D8—54no—
224D8—104no—
225D8—102no—
226D8—302no—
227C2×C8—22no—
228C2×C8#120211yescharacteristic
229C2×C8C2×D3×D511yescharacteristic
230C4⋊C4—301no—
231C22⋊C4—601no—
232C16—62no—
233C3×C5#218411yescharacteristic, complemented, Hall
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—204no—
237C22×C3—408no—
238C22×C3—402no—
239C22×C3—402no—
240C22×C3D8012yescomplemented
241C22×C3C2×D4011yescharacteristic
242C2×D3—401no—
243C2×D3—401no—
244C2×D3—401no—
245C3×C4—21no—
246C3×C4#402811yescharacteristic
247C3×C4#405411yescharacteristic
248Dic3—401no—
249C2×C5—22no—
250C2×C5C2×#82611yescharacteristic
251C2×C5#514711yescharacteristic
252C2×C5#521711yescharacteristic
253D5—84no—
254D5—481no—
255C23—204no—
256C23—202no—
257C23—402no—
258C23—402no—
259C23—601no—
260C23#665311yescharacteristic
261D4—104no—
262D4—204no—
263D4—202no—
264D4—601no—
265D4—601no—
266D4—1202no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—601no—
270C2×C4#665311yescharacteristic
271C2×C4C2×#120211yescharacteristic
272C8—21no—
273C8D5×#6712yes—
274C2×C3—22no—
275C2×C3—404no—
276C2×C3#6502111yescharacteristic
277C2×C3C2×D8011yescharacteristic
278C2×C3#6519711yescharacteristic
279D3—801no—
280C5#7203511yescharacteristic, complemented, Sylow
281C22—21no—
282C22—21no—
283C22—204no—
284C22—408no—
285C22—402no—
286C22—402no—
287C22—1201no—
288C22—1201no—
289C22—1201no—
290C22#9093812yescomplemented
291C22C2×#665311yescharacteristic
292C4—21no—
293C4—1201no—
294C4#9131211yescharacteristic
295C4#9156411yescharacteristic
296C3#1059990111yescharacteristic, complemented, Sylow
297C2—22no—
298C2—404no—
299C2—2401no—
300C2C2×#9093811yescharacteristic
301C2#1174754311yescharacteristic
302C2#1174851211yescharacteristic
subgroupG/H
centerC22C2×#6653
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C2×D8
hypercenterC22×C8D3×D5
hypocenterC3×C5#2184
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D40C2semidirect
2. #11751216C2semidirect
3. C2×#90938C2semidirect
4. C5×#4549C2semidirect
5. #11745892C2semidirect
10. C2×D120C22semidirect
15. #91102C22semidirect
16. C2×C5×C3⋊C16C22semidirect
19. C22×D40D3semidirect
40. C3×D40D4semidirect
46. #4549D5semidirect
88. C2×C3⋊C16C2×D5semidirect
105. D40#67semidirect
114. C22×C3×C5D16semidirect
202. C22×C5#826semidirect
233. C3×C5#2184semidirect
240. C22×C3D80semidirect
280. C5#72035semidirect
290. C22#90938semidirect
296. C3#10599901semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D402
#117512162
C2×#909382
C5×#45492
#117458922
#105999013
#720355