Finite Group Databasebeta

← #14471842

Subgroups — #14471842

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752662C211yesmaximal, characteristic, complemented
2#11752660C211yesmaximal, characteristic, complemented
3#11750795C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic, complemented
5C3×C8×Dic10C211yesmaximal, characteristic, complemented
6#11747985C212yesmaximal, complemented
7#11747773C212yesmaximal, complemented
8#11747770C212yesmaximal, complemented
9#11747745C212yesmaximal, complemented
10#11747037C211yesmaximal, characteristic
11#11746961C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13#91763C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×#204C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91433—22no—
20#91432—22no—
21#91428—21no—
22D3×C4⋊Dic5—21no—
23#91418C2212yes—
24Dic5×D12C2212yes—
25#91388C2212yes—
26#91375C2212yes—
27#91374—21no—
28#91369—21no—
29C2×#6654C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91105C2212yes—
33C5×#821C2211yescharacteristic
34C5×#817C2211yescharacteristic
35C5×#816C2211yescharacteristic
36C3×#3946C2212yes—
37C3×C8×Dic5C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90973C2212yes—
41#90969C2212yes—
42#79927—51nomaximal, Hall
43#65919—31no—
44#65877—31no—
45C4×C5×SD16—31no—
46#65454—32no—
47#65310—31no—
48#65304—31no—
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10D311yescharacteristic, complemented
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30—21no—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×Dic10D411yescharacteristic
62C2×#1200—22no—
63C2×D3×Dic5—22no—
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15—21no—
68C4⋊Dic15C2312yes—
69C5×(C2×D3)⋊C4—21no—
70C5×C4⋊Dic3C2311yescharacteristic
71C5×C4⋊Dic3C2311yescharacteristic
72C5×Dic3⋊C4—21no—
73C4×C5×Dic3—21no—
74C5×#204—22no—
75C3×C4⋊Dic5D411yescharacteristic
76C3×#683D412yes—
77C3×C4×Dic5C2312yes—
78C2×C3×#168C2312yes—
79Dic3⋊Dic5—22no—
80#6669—22no—
81#6667—22no—
82#6667—22no—
83#6667—22no—
84(C2×D3)⋊Dic5—22no—
85#6654—24no—
86#5585—51no—
87#5579—51no—
88C3×C8×Q8—51no—
89#4850—51no—
90#4847—52no—
91#4844—52no—
92#4843—51no—
93#4697—52no—
94#4694—51no—
95C4×D24—52no—
96C4×#204D511yescharacteristic, complemented
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4—31no—
100#4093—32no—
101D4×Dic5—32no—
102C2×#686—32no—
103C2×C4⋊Dic5—61no—
104#4070—61no—
105#4040—62no—
106#4039—32no—
107#4036—32no—
108#4024—62no—
109#4021—61no—
110#4020—31no—
111C4×D20—61no—
112#4015—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953—32no—
120#3953—32no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3941—32no—
124#3939—32no—
125C4⋊#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—22no—
128C22×C5×D3—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133D60—22no—
134D60—22no—
135D60—42no—
136D60—81no—
137Dic30—81no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C5×D12—21no—
142C5×D12#4112yes—
143C4×C5×D3—42no—
144C5×Dic6—21no—
145C5×Dic6—21no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×Dic10—22no—
149#1200—82no—
150D3×Dic5—82no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C3×#168—22no—
154C3×C4×Q8—51no—
155#947—101no—
156#946—101no—
157C2×D24—52no—
158C2×#204C2×D511yescharacteristic
159#896—102no—
160#894—102no—
161#893—101no—
162D3×C4⋊C4—101no—
163#875—52no—
164#874—51no—
165C4×D12—52no—
166C4×D12—52no—
167C4×D12C2×D511yescharacteristic
168#870—52no—
169#869—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×C4⋊C8—52no—
172C3×C4⋊C8—51no—
173C3×C4×C8—52no—
174C3×C4×C8C2×D511yescharacteristic
175#821—52no—
176#821—52no—
177#821—52no—
178#821C2×D511yescharacteristic
179#818—52no—
180#817C2×D511yescharacteristic
181#816—52no—
182#816C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×C5×D4—31no—
185C22×C4×C5—61no—
186C22×Dic5—62no—
187C2×D20—32no—
188C2×D20—61no—
189C2×D20—61no—
190C2×C4×D5—62no—
191C2×Dic10—61no—
192C2×Dic10D1211yescharacteristic
193C5×SD16—62no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—31no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—61no—
199C5×C22⋊C4—61no—
200C42×C5—61no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—62no—
203#686—64no—
204#685—62no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—32no—
208C4⋊Dic5—61no—
209C4⋊Dic5—62no—
210C4⋊Dic5D1211yescharacteristic
211#683—62no—
212#683D1212yes—
213C4×Dic5C22×D312yes—
214C2×#168C22×D312yes—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—51no—
224C4×SD16—31no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—42no—
228C2×D15—42no—
229C2×D15—42no—
230C2×C5×D3—22no—
231C2×C5×D3—41no—
232C2×C5×D3—41no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—42no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C5×Dic3—41no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8—51no—
244C2×D12—52no—
245C2×D12—101no—
246C2×D12—101no—
247C2×D12C22×D511yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×Dic6—101no—
252C2×Dic6C22×D511yescharacteristic
253C2×C3×C8—52no—
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C4⋊C4—51no—
258C3×C42—52no—
259C3×C42C22×D511yescharacteristic
260(C2×D3)⋊C4—21no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—52no—
266C4⋊Dic3—101no—
267C4⋊Dic3C22×D511yescharacteristic
268C4⋊Dic3C22×D511yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C4×Dic3—21no—
273D24—104no—
274#204—22no—
275C23×C5—61no—
276C22×D5—62no—
277C5×Q8—61no—
278C5×Q8—61no—
279C5×D4—32no—
280C5×D4—61no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5C2×D1211yescharacteristic
286C2×C4×C5C2×D1211yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—62no—
289C2×Dic5—242no—
290C2×Dic5C2×D1212yes—
291C2×Dic5C2×D1212yes—
292D20—62no—
293D20—62no—
294D20—122no—
295D20—241no—
296C4×D5—242no—
297Dic10—22no—
298Dic10—241no—
299C5×C8—21no—
300C5×C8—21no—
301#168—22no—
302C2×SD16—31no—
303C2×D8—152no—
304C4⋊Q8—151no—
305#127—151no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—51no—
314C4×D4—31no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—31no—
321C4⋊C8—52no—
322C4⋊C8—51no—
323#103—31no—
324#103—152no—
325#102—31no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—52no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—82no—
335C5×D3—42no—
336C22×D3—21no—
337C22×D3—102no—
338C3×Q8—102no—
339C2×C3×C4—52no—
340C2×C3×C4—52no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—102no—
348D12—21no—
349D12—102no—
350D12—102no—
351D12—202no—
352D12—401no—
353D12#70912yes—
354C4×D3—42no—
355C4×D3—402no—
356C4×D3—402no—
357Dic6—21no—
358Dic6—21no—
359Dic6—401no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—102no—
363C22×C5—62no—
364C22×C5—121no—
365C22×C5—121no—
366C22×C5C22×D1211yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—121no—
372C4×C5—121no—
373C4×C5—121no—
374C4×C5#90412yes—
375C4×C5#100711yescharacteristic
376C4×C5D3×#4111yescharacteristic
377Dic5—22no—
378Dic5—22no—
379Dic5—122no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×Q8—301no—
383C2×D4—31no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—61no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—62no—
391D8—304no—
392C2×C8—52no—
393C2×C8C2×D3×D511yescharacteristic
394C2×C8C2×D3×D511yescharacteristic
395C4⋊C4—31no—
396C4⋊C4—31no—
397C4⋊C4—51no—
398C4⋊C4—52no—
399C4⋊C4—61no—
400C4⋊C4—152no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—61no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—52no—
410C42—61no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C2×D4×D511yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—102no—
422C3×C4—102no—
423C3×C4#406212yes—
424C3×C4C2×#70911yescharacteristic
425C3×C4#415011yescharacteristic
426Dic3—41no—
427Dic3—41no—
428Dic3—41no—
429Dic3—202no—
430C2×C5—122no—
431C2×C5#557611yescharacteristic
432C2×C5C2×#90411yescharacteristic
433C2×C5#575211yescharacteristic
434D5—242no—
435C23—61no—
436C23—302no—
437Q8—61no—
438Q8—61no—
439Q8—102no—
440Q8—1201no—
441D4—32no—
442D4—61no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—52no—
448C2×C4—52no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—122no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D5×D1211yescharacteristic
457C2×C4D5×D1211yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—21no—
460C8—21no—
461C8—102no—
462C2×C3#6588611yescharacteristic
463C2×C3C2×#406211yescharacteristic
464C2×C3#6610311yescharacteristic
465D3—42no—
466D3—402no—
467C5#7992711yescharacteristic, complemented, Sylow
468C22—62no—
469C22—121no—
470C22—121no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D5×D1211yescharacteristic
475C4—21no—
476C4—102no—
477C4—102no—
478C4—121no—
479C4—121no—
480C4—121no—
481C4—602no—
482C4#9126912yes—
483C4#9200411yescharacteristic
484C4D3×#70911yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—122no—
487C2—1202no—
488C2#1175253511yescharacteristic
489C2#1175396311yescharacteristic
490C2C2×#9126911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11747037C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752662C2semidirect
2. #11752660C2semidirect
3. #11750795C2semidirect
4. C4×C5×#204C2semidirect
5. C3×C8×Dic10C2semidirect
6. #11747985C2semidirect
7. #11747773C2semidirect
8. #11747770C2semidirect
9. #11747745C2semidirect
11. #11746961C2semidirect
53. C8×Dic10D3semidirect
96. C4×#204D5semidirect
412. C3×C5#3361semidirect
467. C5#79927semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
#117526622
#117526602
#117507952
C4×C5×#2042
C3×C8×Dic102
#117479852
#117477732
#117477702
#117477452
#117470372
#117469612
#106113523
#799275