Finite Group Databasebeta

← #14287962

Subgroups — #14287962

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
2C3×C5×#393C211yesmaximal, characteristic, complemented
3#11751328C212yesmaximal, complemented
4#11746346C211yesmaximal, characteristic, complemented
5#11746272C212yesmaximal, complemented
6#10600492—31nomaximal, Hall
7C22×C3×C5×Q8C2211yescharacteristic, complemented
8C22×#1220—21no—
9C2×C3×C5×C22⋊C4—21no—
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6717—22no—
12#91819—21no—
13#91819C2212yes—
14#91775—22no—
15#91771—22no—
16C3×C5×#95—21no—
17C3×C5×#95C2211yescharacteristic, complemented
18#91119—22no—
19#91114C2212yescomplemented
20#69699—51nomaximal, Hall
21#65827—31no—
22C5×#393D311yescharacteristic, complemented
23#65516—32no—
24#64745—31no—
25#64671—32no—
26C24×C3×C5D411yescharacteristic
27C23×D15—21no—
28C2×C3×C5×Q8—22no—
29C2×C3×C5×Q8—42no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5—21no—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220—22no—
35C2×#1220—22no—
36C2×#1220—42no—
37C2×#1220—42no—
38C22×Dic15—21no—
39C2×D60—21no—
40C2×D60D412yes—
41C3×C5×C22⋊C4—22no—
42C3×C5×C22⋊C4—42no—
43#6717—44no—
44#6714—22no—
45#6714—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C2×C3⋊#168—22no—
49#5493—51no—
50C3×#393D511yescharacteristic, complemented
51#5227—52no—
52#4525—51no—
53#4451—52no—
54C22×C5×Q8C2×D311yescharacteristic, complemented
55C22×C22⋊D5—61no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4C2×D311yescharacteristic
58C2×#688—62no—
59#4076—32no—
60#4076—61no—
61#4032—62no—
62#4028—62no—
63C5×#95—21no—
64C5×#95C2×D311yescharacteristic, complemented
65#3967—62no—
66C22⋊#168—32no—
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—
78C3×C5×Q8—24no—
79C3×C5×Q8—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D412yes—
90#1220—44no—
91#1220—42no—
92#1220—42no—
93C2×Dic15—22no—
94C2×Dic15—42no—
95D60—42no—
96D60—81no—
97C3⋊#168—42no—
98C22×C3×Q8C2×D511yescharacteristic, complemented
99C22×#67—101no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4C2×D511yescharacteristic
102C2×#215—102no—
103#930—52no—
104#930—101no—
105#886—102no—
106#882—102no—
107C3×#95—21no—
108C3×#95C2×D511yescharacteristic, complemented
109#835—102no—
110#830—52no—
111C24×C5#6711yescharacteristic
112C23×D5—61no—
113C2×C5×Q8—22no—
114C2×C5×Q8—42no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5#6711yescharacteristic
118C22×C4×C5C22×D311yescharacteristic
119C2×C22⋊D5—62no—
120C2×C22⋊D5—62no—
121C2×C22⋊D5—122no—
122C2×C22⋊D5—122no—
123C22×Dic5—61no—
124C2×D20—32no—
125C2×D20—61no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—42no—
128#688—124no—
129#685—62no—
130#685—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—61no—
133C2×#168—62no—
134#534—151no—
135#448—152no—
136#393D1511yescharacteristic, complemented
137#327—152no—
138#323—151no—
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—
155C3×C4×C5—42no—
156C3×C4×C5—81no—
157Dic15—42no—
158C24×C3C22⋊D511yescharacteristic
159C23×D3—101no—
160C2×C3×Q8—22no—
161C2×C3×Q8—42no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4C22⋊D511yescharacteristic
165C22×C3×C4C22×D511yescharacteristic
166C2×#67—102no—
167C2×#67—102no—
168C2×#67—202no—
169C2×#67—202no—
170C22×Dic3—101no—
171C2×D12—52no—
172C2×D12—101no—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—42no—
175#215—204no—
176(C2×D3)⋊C4—102no—
177(C2×D3)⋊C4—102no—
178C4⋊Dic3—52no—
179C4⋊Dic3—101no—
180C2×C3⋊C8—102no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—41no—
184C23×C5—41no—
185C23×C5#21512yescomplemented
186C23×C5C2×#6711yescharacteristic
187C22×D5—62no—
188C22×D5—122no—
189C22×D5—241no—
190C22×D5—241no—
191C5×Q8—24no—
192C5×Q8—42no—
193C2×C4×C5—22no—
194C2×C4×C5—21no—
195C2×C4×C5—41no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5D3×D412yes—
203C22⋊D5—124no—
204C22⋊D5—122no—
205C22⋊D5—122no—
206C2×Dic5—62no—
207C2×Dic5—122no—
208D20—122no—
209D20—241no—
210#168—122no—
211C22×Q8C2×D1511yescharacteristic, complemented
212C22×D4—301no—
213C2×SD16—302no—
214#123—302no—
215#121—152no—
216#121—301no—
217#120—302no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×D1511yescharacteristic
220#103—302no—
221C22⋊C8—152no—
222#95—21no—
223#95C2×D1511yescharacteristic, complemented
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#68812yescomplemented
236C23×C3C2×C22⋊D511yescharacteristic
237C22×D3—102no—
238C22×D3—202no—
239C22×D3—401no—
240C22×D3—401no—
241C3×Q8—24no—
242C3×Q8—42no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4D4×D512yes—
253#67—204no—
254#67—202no—
255#67—202no—
256C2×Dic3—102no—
257C2×Dic3—202no—
258D12—202no—
259D12—401no—
260C3⋊C8—202no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—22no—
264C22×C5—42no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5#93711yescharacteristic
269C22×C5C2×#21511yescharacteristic
270C22×C5#94911yescharacteristic
271C2×D5—122no—
272C2×D5—122no—
273C2×D5—122no—
274C2×D5—244no—
275C4×C5—22no—
276C4×C5—42no—
277C4×C5—41no—
278C4×C5—81no—
279Dic5—122no—
280C24—301no—
281C24#122011yescharacteristic
282C2×Q8—22no—
283C2×Q8—42no—
284C2×D4—152no—
285C2×D4—301no—
286C2×D4—302no—
287C2×D4—302no—
288C2×D4—602no—
289C2×D4—602no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—301no—
293C22×C4#122011yescharacteristic
294C22×C4C22×D1511yescharacteristic
295SD16—604no—
296C2×C8—302no—
297C4⋊C4—152no—
298C4⋊C4—301no—
299C22⋊C4—22no—
300C22⋊C4—42no—
301C22⋊C4—302no—
302C22⋊C4—302no—
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#408311yescharacteristic
312C22×C3C2×#68811yescharacteristic
313C22×C3#409511yescharacteristic
314C2×D3—202no—
315C2×D3—202no—
316C2×D3—202no—
317C2×D3—404no—
318C3×C4—22no—
319C3×C4—42no—
320C3×C4—41no—
321C3×C4—81no—
322Dic3—202no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—42no—
326C2×C5#503211yescharacteristic
327C2×C5#504611yescharacteristic
328C2×C5#506111yescharacteristic
329D5—242no—
330C23—21no—
331C23—21no—
332C23—41no—
333C23—41no—
334C23—302no—
335C23—602no—
336C23—1201no—
337C23—1201no—
338C23#671712yescomplemented
339C23C2×#122011yescharacteristic
340Q8—24no—
341Q8—42no—
342D4—602no—
343D4—604no—
344D4—602no—
345D4—602no—
346D4—1201no—
347C2×C4—22no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—302no—
357C2×C4—602no—
358C2×C4D4×D1512yes—
359C8—602no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3#6532111yescharacteristic
364C2×C3#6533511yescharacteristic
365C2×C3#6535011yescharacteristic
366D3—402no—
367C5#6969911yescharacteristic, 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#9182611yescharacteristic
380C22C2×#671711yescharacteristic
381C22#9183811yescharacteristic
382C4—22no—
383C4—42no—
384C4—41no—
385C4—81no—
386C4—602no—
387C3#1060049211yescharacteristic, complemented, Sylow
388C2—21no—
389C2—21no—
390C2—42no—
391C2—1202no—
392C2#1175113311yescharacteristic
393C2#1175114711yescharacteristic
394C2#1175116211yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#393C2
socleC22×C3×C5#120
prime radical#11756252C2
hypercenter#393D15
hypocenterC3×C5#1601
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C3×C5×#393C2semidirect
3. #11751328C2semidirect
4. #11746346C2semidirect
5. #11746272C2semidirect
7. C22×C3×C5×Q8C22semidirect
17. C3×C5×#95C22semidirect
19. #91114C22semidirect
22. C5×#393D3semidirect
50. C3×#393D5semidirect
54. C22×C5×Q8C2×D3semidirect
64. C5×#95C2×D3semidirect
72. C23×C3×C5SD16semidirect
98. C22×C3×Q8C2×D5semidirect
108. C3×#95C2×D5semidirect
136. #393D15semidirect
185. C23×C5#215semidirect
211. C22×Q8C2×D15semidirect
223. #95C2×D15semidirect
235. C23×C3#688semidirect
303. C3×C5#1601semidirect
338. C23#6717semidirect
367. C5#69699semidirect
387. C3#10600492semidirect

Maximal subgroups

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

subgroupindex
#117562522
C3×C5×#3932
#117513282
#117463462
#117462722
#106004923
#696995