Finite Group Databasebeta

← #14287971

Subgroups — #14287971

Order 1920.

616 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756252C211yesmaximal, characteristic
2#11751048C211yesmaximal, characteristic, complemented
3#11750839C212yesmaximal, complemented
4C3×C5×#323C211yesmaximal, characteristic, complemented
5#11746291C212yesmaximal, complemented
6#10598901—31nomaximal, Hall
7C22×#1220—21no—
8C22×Dic30C2211yescharacteristic, complemented
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×#6719—21no—
11#91819—21no—
12#91819C2212yes—
13C2×#6706—22no—
14#91775—22no—
15#91771—22no—
16C3×C5×C22⋊C8C2212yescomplemented
17#91115—21no—
18#91115C2211yescharacteristic, complemented
19#91100—22no—
20#68108—51nomaximal, Hall
21#65827—31no—
22#65236—31no—
23#65027—32no—
24C5×#323D311yescharacteristic, complemented
25#64690—32no—
26C24×C3×C5D411yescharacteristic
27C23×D15—21no—
28C22×C3×C4×C5D411yescharacteristic
29C22×C3×C4×C5C2311yescharacteristic
30C2×#1220—22no—
31C2×#1220—22no—
32C2×#1220—42no—
33C2×#1220—42no—
34C22×Dic15—21no—
35C22×Dic15—21no—
36C22×Dic15—21no—
37C2×D60—21no—
38C2×D60D412yes—
39C2×Dic30—22no—
40C2×Dic30—42no—
41C2×C3×C5×C8—22no—
42C3×C5×C22⋊C4—22no—
43#6719—42no—
44#6714—22no—
45#6714—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48#6706—44no—
49#5493—51no—
50#4947—51no—
51#4738—52no—
52C3×#323D511yescharacteristic, complemented
53#4470—52no—
54C22×C22⋊D5—61no—
55C22×Dic10—31no—
56C2×C5×C22⋊C4C2×D311yescharacteristic
57C2×C22⋊Dic5—61no—
58#4076—32no—
59#4076—61no—
60C2×#677—62no—
61#4032—62no—
62#4028—62no—
63C5×C22⋊C8C2×D312yescomplemented
64#3963—31no—
65#3963—61no—
66#3948—62no—
67#1601—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5—21no—
70C23×C3×C5—41no—
71C23×C3×C5—41no—
72C23×C3×C5SD1612yescomplemented
73C23×C3×C5C2×D411yescharacteristic
74C22×D15—22no—
75C22×D15—42no—
76C22×D15—81no—
77C22×D15—81no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D412yes—
82#1220—44no—
83#1220—42no—
84#1220—42no—
85C2×Dic15—22no—
86C2×Dic15—22no—
87C2×Dic15—41no—
88C2×Dic15—42no—
89C2×Dic15—41no—
90C2×Dic15—41no—
91C2×Dic15—41no—
92C2×Dic15—41no—
93D60—42no—
94D60—81no—
95Dic30—24no—
96Dic30—42no—
97C3×C5×C8—42no—
98C22×#67—101no—
99C22×Dic6—51no—
100C2×C3×C22⋊C4C2×D511yescharacteristic
101C2×#217—101no—
102#930—52no—
103#930—101no—
104C2×#204—102no—
105#886—102no—
106#882—102no—
107C3×C22⋊C8C2×D512yescomplemented
108C3⋊#95—51no—
109C3⋊#95—101no—
110#816—102no—
111C24×C5D1211yescharacteristic
112C23×D5—61no—
113C22×C4×C5D1211yescharacteristic
114C22×C4×C5C22×D311yescharacteristic
115C2×C22⋊D5—62no—
116C2×C22⋊D5—62no—
117C2×C22⋊D5—122no—
118C2×C22⋊D5—122no—
119C22×Dic5—61no—
120C22×Dic5—61no—
121C22×Dic5—61no—
122C2×D20—32no—
123C2×D20—61no—
124C2×Dic10—62no—
125C2×Dic10—122no—
126C2×C5×C8—22no—
127C5×C22⋊C4—22no—
128C22⋊Dic5—122no—
129#685—62no—
130#685—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—61no—
133#677—124no—
134#534—151no—
135#448—152no—
136#393—151no—
137#327—152no—
138#323D1511yescharacteristic, complemented
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—22no—
142C22×C3×C5—42no—
143C22×C3×C5—41no—
144C22×C3×C5—41no—
145C22×C3×C5—81no—
146C22×C3×C5#12011yescharacteristic
147C22×C3×C5C2×SD1611yescharacteristic
148C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
149C2×D15—42no—
150C2×D15—42no—
151C2×D15—42no—
152C2×D15—84no—
153C3×C4×C5—22no—
154C3×C4×C5—41no—
155Dic15—42no—
156Dic15—42no—
157Dic15—81no—
158C24×C3D2011yescharacteristic
159C23×D3—101no—
160C22×C3×C4D2011yescharacteristic
161C22×C3×C4C22×D511yescharacteristic
162C2×#67—102no—
163C2×#67—102no—
164C2×#67—202no—
165C2×#67—202no—
166C22×Dic3—101no—
167C22×Dic3—101no—
168C22×Dic3—101no—
169C2×D12—52no—
170C2×D12—101no—
171C2×Dic6—102no—
172C2×Dic6—202no—
173C2×C3×C8—22no—
174C3×C22⋊C4—22no—
175#217—202no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—102no—
178C4⋊Dic3—52no—
179C4⋊Dic3—101no—
180#204—204no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5#20412yescomplemented
186C23×C5C2×D1211yescharacteristic
187C22×D5—62no—
188C22×D5—122no—
189C22×D5—241no—
190C22×D5—241no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5D3×D412yes—
195C22⋊D5—124no—
196C22⋊D5—122no—
197C22⋊D5—122no—
198C2×Dic5—62no—
199C2×Dic5—62no—
200C2×Dic5—121no—
201C2×Dic5—122no—
202C2×Dic5—121no—
203C2×Dic5—121no—
204C2×Dic5—121no—
205C2×Dic5—121no—
206D20—122no—
207D20—241no—
208Dic10—64no—
209Dic10—122no—
210C5×C8—42no—
211C22×Q8—151no—
212C22×D4—301no—
213C2×SD16—302no—
214#123—302no—
215#121—152no—
216#121—301no—
217#120—302no—
218C2×C22⋊C4—301no—
219C2×C22⋊C4C2×D1511yescharacteristic
220#103—302no—
221C22⋊C8C2×D1512yescomplemented
222#95—151no—
223#95—301no—
224C2×C3×C5—21no—
225C2×C3×C5—21no—
226C2×C3×C5—42no—
227C2×C3×C5#45011yescharacteristic
228C2×C3×C5#45511yescharacteristic
229C2×C3×C5B(4,𝔽2)11yescharacteristic
230D15—82no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3#67712yescomplemented
236C23×C3C2×D2011yescharacteristic
237C22×D3—102no—
238C22×D3—202no—
239C22×D3—401no—
240C22×D3—401no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4D4×D512yes—
245#67—204no—
246#67—202no—
247#67—202no—
248C2×Dic3—102no—
249C2×Dic3—102no—
250C2×Dic3—201no—
251C2×Dic3—202no—
252C2×Dic3—201no—
253C2×Dic3—201no—
254C2×Dic3—201no—
255C2×Dic3—201no—
256D12—202no—
257D12—401no—
258Dic6—104no—
259Dic6—202no—
260C3×C8—42no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—22no—
264C22×C5—42no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5#88211yescharacteristic
269C22×C5C2×#20411yescharacteristic
270C22×C5#90811yescharacteristic
271C2×D5—122no—
272C2×D5—122no—
273C2×D5—122no—
274C2×D5—244no—
275C4×C5—22no—
276C4×C5—41no—
277Dic5—122no—
278Dic5—122no—
279Dic5—241no—
280C24—301no—
281C24D6011yescharacteristic
282C2×Q8—302no—
283C2×Q8—602no—
284C2×D4—152no—
285C2×D4—301no—
286C2×D4—302no—
287C2×D4—302no—
288C2×D4—602no—
289C2×D4—602no—
290C22×C4—301no—
291C22×C4—301no—
292C22×C4—301no—
293C22×C4D6011yescharacteristic
294C22×C4C22×D1511yescharacteristic
295SD16—604no—
296C2×C8—22no—
297C4⋊C4—152no—
298C4⋊C4—301no—
299C22⋊C4—22no—
300C22⋊C4—302no—
301C22⋊C4—302no—
302C22⋊C4—602no—
303C3×C5#160111yescharacteristic, complemented, Hall
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—22no—
307C22×C3—42no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—81no—
311C22×C3#402811yescharacteristic
312C22×C3C2×#67711yescharacteristic
313C22×C3#405411yescharacteristic
314C2×D3—202no—
315C2×D3—202no—
316C2×D3—202no—
317C2×D3—404no—
318C3×C4—22no—
319C3×C4—41no—
320Dic3—202no—
321Dic3—202no—
322Dic3—401no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—42no—
326C2×C5#473111yescharacteristic
327C2×C5#474111yescharacteristic
328C2×C5#474611yescharacteristic
329D5—242no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—302no—
335C23—602no—
336C23—1201no—
337C23—1201no—
338C23#670612yescomplemented
339C23C2×D6011yescharacteristic
340Q8—304no—
341Q8—602no—
342D4—602no—
343D4—604no—
344D4—602no—
345D4—602no—
346D4—1201no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—302no—
351C2×C4—302no—
352C2×C4—602no—
353C2×C4—601no—
354C2×C4—601no—
355C2×C4—601no—
356C2×C4—601no—
357C2×C4—601no—
358C2×C4D4×D1512yes—
359C8—42no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3#6502011yescharacteristic
364C2×C3#6503011yescharacteristic
365C2×C3#6503511yescharacteristic
366D3—402no—
367C5#6810811yescharacteristic, complemented, Sylow
368C22—21no—
369C22—21no—
370C22—22no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—602no—
376C22—602no—
377C22—602no—
378C22—1204no—
379C22#9177111yescharacteristic
380C22C2×#670611yescharacteristic
381C22#9179711yescharacteristic
382C4—22no—
383C4—41no—
384C4—602no—
385C4—602no—
386C4—1201no—
387C3#1059890111yescharacteristic, complemented, Sylow
388C2—21no—
389C2—21no—
390C2—42no—
391C2—1202no—
392C2#1175083211yescharacteristic
393C2#1175084211yescharacteristic
394C2#1175084711yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#323C2
socleC22×C3×C5#120
prime radical#11756252C2
hypercenter#323D15
hypocenterC3×C5#1601
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #11751048C2semidirect
3. #11750839C2semidirect
4. C3×C5×#323C2semidirect
5. #11746291C2semidirect
8. C22×Dic30C22semidirect
16. C3×C5×C22⋊C8C22semidirect
18. #91115C22semidirect
24. C5×#323D3semidirect
52. C3×#323D5semidirect
63. C5×C22⋊C8C2×D3semidirect
72. C23×C3×C5SD16semidirect
107. C3×C22⋊C8C2×D5semidirect
138. #323D15semidirect
185. C23×C5#204semidirect
221. C22⋊C8C2×D15semidirect
235. C23×C3#677semidirect
303. C3×C5#1601semidirect
338. C23#6706semidirect
367. C5#68108semidirect
387. C3#10598901semidirect

Maximal subgroups

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

subgroupindex
#117562522
#117510482
#117508392
C3×C5×#3232
#117462912
#105989013
#681085