Finite Group Databasebeta

← #14471844

Subgroups — #14471844

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#11752654C211yesmaximal, characteristic, complemented
2#11752651C211yesmaximal, characteristic, complemented
3C4×#6706C211yesmaximal, characteristic, complemented
4C5×#4694C211yesmaximal, characteristic, complemented
5C3×C8×Dic10C211yesmaximal, characteristic, complemented
6#11747963C212yesmaximal, complemented
7#11747779C212yesmaximal, complemented
8#11747776C212yesmaximal, complemented
9#11747745C212yesmaximal, complemented
10#11747045C211yesmaximal, characteristic
11#11746963C211yesmaximal, characteristic, complemented
12#10613316—31nomaximal, Hall
13C2×#6706C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#874C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91437—21no—
20#91435—21no—
21#91424—22no—
22#91423—22no—
23#91418C2212yes—
24Dic5×D12C2212yes—
25#91390—21no—
26#91388C2212yes—
27#91373C2212yes—
28#91370—21no—
29C2×#6654C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2211yescharacteristic
32#91101C2211yescharacteristic
33#91100C2211yescharacteristic
34C5×#821C2212yes—
35C5×#821C2212yes—
36C3×#3946C2212yes—
37C3×C8×Dic5C2212yes—
38C3×C4⋊#168C2211yescharacteristic
39#90988C2212yes—
40#90975C2212yes—
41#90967C2212yes—
42#79927—51nomaximal, Hall
43#66064—31no—
44#66047—31no—
45C5×#486—31no—
46#65380—31no—
47#65361—31no—
48#65076—32no—
49#65057—32no—
50#65052—32no—
51#65045—32no—
52C4×#677—31no—
53C8×Dic10D311yescharacteristic, complemented
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C5×Dic6—21no—
61C2×C3×Dic10D411yescharacteristic
62C2×#1200—22no—
63C2×D3×Dic5—22no—
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67#6714—21no—
68C4⋊Dic15C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71C4×Dic15—21no—
72#6706—22no—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3C2312yes—
75C3×C4⋊Dic5D411yescharacteristic
76C3×#683D412yes—
77C3×C4×Dic5C2312yes—
78C2×C3×#168C2312yes—
79Dic3⋊Dic5—22no—
80#6669—22no—
81#6667—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—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#4694D511yescharacteristic, complemented
95C4×D24—52no—
96C4×#204—51no—
97C5×C4⋊Q8—31no—
98C5×#127—31no—
99#4092—62no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—61no—
105C2×#686—32no—
106C2×#677—31no—
107#4043—61no—
108#4039—32no—
109D5×C4⋊C4—61no—
110#4036—32no—
111C4×D20—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#102—32no—
115C5×#102—32no—
116C4×C5×C8C2×D311yescharacteristic
117#3964—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946C2×D312yes—
122C8×Dic5C2×D312yes—
123#3942—32no—
124#3939—32no—
125C4⋊#168C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—21no—
128C22×C5×D3—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135D60—21no—
136D60#4112yes—
137C4×D15—42no—
138Dic30—21no—
139Dic30—21no—
140C2×C5×Dic3—22no—
141C5×D12—22no—
142C5×D12—22no—
143C5×D12—42no—
144C5×D12—81no—
145C5×Dic6—81no—
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×#204—51no—
159#896—102no—
160#894—102no—
161#893—101no—
162D3×C4⋊C4—101no—
163#875—52no—
164#874C2×D511yescharacteristic
165C4×D12—52no—
166C4×D12—51no—
167C4×D12—52no—
168#870—52no—
169#869C2×D511yescharacteristic
170C4×Dic6—51no—
171C3×C4⋊C8—52no—
172C3×C4⋊C8—51no—
173C3×C4×C8—52no—
174C3×C4×C8C2×D511yescharacteristic
175#821—52no—
176#821—51no—
177#821C2×D512yes—
178#821C2×D512yes—
179#818—52no—
180#817—51no—
181#816—51no—
182#816—52no—
183C2×C5×Q8—61no—
184C2×C5×D4—32no—
185C2×C5×D4—61no—
186C2×C5×D4—61no—
187C22×Dic5—62no—
188C2×D20—31no—
189C2×C4×D5—61no—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10D1211yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C2×C5×C8C22×D311yescharacteristic
195C5×C4⋊C4—32no—
196C5×C4⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201#686—64no—
202#685—61no—
203#685—62no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5—62no—
207C4⋊Dic5D1211yescharacteristic
208#683—61no—
209#683—62no—
210#683D1212yes—
211C4×Dic5—61no—
212C4×Dic5C22×D312yes—
213C2×#168C22×D312yes—
214#677—62no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—31no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—51no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—41no—
238Dic15—41no—
239Dic15—41no—
240C3×Dic5—22no—
241C3×Dic5—22no—
242C5×Dic3—42no—
243C2×C3×Q8—51no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—51no—
247C2×D12C22×D512yes—
248C2×C4×D3—101no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×Dic6—21no—
252C2×Dic6—51no—
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—102no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—101no—
265C4⋊Dic3—21no—
266C4⋊Dic3—51no—
267C4⋊Dic3—51no—
268C4⋊Dic3C22×D512yes—
269Dic3⋊C4—102no—
270Dic3⋊C4—102no—
271Dic3⋊C4—101no—
272C4×Dic3—101no—
273D24—104no—
274#204—102no—
275C23×C5—62no—
276C22×D5—61no—
277C5×Q8—241no—
278C5×D4—62no—
279C5×D4—62no—
280C5×D4—122no—
281C5×D4—241no—
282C2×C4×C5—62no—
283C2×C4×C5C2×D1211yescharacteristic
284C2×C4×C5C2×D1211yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—61no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—242no—
290C2×Dic5C2×D1212yes—
291C2×Dic5C2×D1212yes—
292D20—32no—
293D20—61no—
294C4×D5—122no—
295C4×D5—242no—
296Dic10—22no—
297Dic10—61no—
298Dic10—61no—
299C5×C8—21no—
300C5×C8—21no—
301#168—22no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—31no—
305#127—31no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—51no—
313C4×Q8—151no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—52no—
322C4⋊C8—51no—
323#103—152no—
324#103—151no—
325#102—32no—
326#102—32no—
327#102—152no—
328#102—151no—
329C4×C8—52no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335C5×D3—82no—
336C22×D3—22no—
337C22×D3—101no—
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—22no—
345C2×Dic3—101no—
346C2×Dic3—101no—
347C2×Dic3—101no—
348D12—22no—
349D12—22no—
350D12—42no—
351D12—52no—
352D12—81no—
353D12—101no—
354C4×D3—202no—
355C4×D3—402no—
356C4×D3—402no—
357Dic6—81no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—21no—
361C3×C8—21no—
362C3×C8—102no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C22×D1211yescharacteristic
367C2×D5—62no—
368C2×D5—121no—
369C2×D5—121no—
370C4×C5—21no—
371C4×C5—122no—
372C4×C5#90412yes—
373C4×C5#100711yescharacteristic
374C4×C5D3×#4111yescharacteristic
375Dic5—22no—
376Dic5—22no—
377Dic5—121no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—51no—
381C2×Q8—61no—
382C2×Q8—151no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—151no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—52no—
393C2×C8C2×D3×D511yescharacteristic
394C2×C8C2×D3×D511yescharacteristic
395C4⋊C4—32no—
396C4⋊C4—51no—
397C4⋊C4—52no—
398C4⋊C4—61no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—52no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C2×D4×D511yescharacteristic
414C2×D3—42no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—102no—
418C2×D3—201no—
419C2×D3—201no—
420C3×C4—21no—
421C3×C4—102no—
422C3×C4—102no—
423C3×C4#406212yes—
424C3×C4D5×#4111yescharacteristic
425C3×C4#415011yescharacteristic
426Dic3—42no—
427Dic3—201no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—242no—
431C2×C5#557611yescharacteristic
432C2×C5C2×#90411yescharacteristic
433C2×C5#575211yescharacteristic
434D5—122no—
435C23—62no—
436C23—301no—
437Q8—102no—
438Q8—241no—
439Q8—301no—
440Q8—301no—
441D4—62no—
442D4—62no—
443D4—122no—
444D4—152no—
445D4—241no—
446D4—301no—
447C2×C4—52no—
448C2×C4—52no—
449C2×C4—62no—
450C2×C4—301no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D5×D1211yescharacteristic
457C2×C4D5×D1211yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—21no—
460C8—21no—
461C8—102no—
462C2×C3#6601111yescharacteristic
463C2×C3#6609111yescharacteristic
464C2×C3C2×#406211yescharacteristic
465D3—82no—
466D3—202no—
467C5#7992711yescharacteristic, complemented, Sylow
468C22—122no—
469C22—122no—
470C22—122no—
471C22—302no—
472C22—601no—
473C22—601no—
474C22C2×D5×D1211yescharacteristic
475C4—21no—
476C4—102no—
477C4—102no—
478C4—122no—
479C4—601no—
480C4—601no—
481C4—601no—
482C4#9126912yes—
483C4#9200411yescharacteristic
484C4#9201611yescharacteristic
485C3#1061331611yescharacteristic, complemented, Sylow
486C2—242no—
487C2—602no—
488C2#1175253711yescharacteristic
489C2#1175396111yescharacteristic
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#11747045C2
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. #11752654C2semidirect
2. #11752651C2semidirect
3. C4×#6706C2semidirect
4. C5×#4694C2semidirect
5. C3×C8×Dic10C2semidirect
6. #11747963C2semidirect
7. #11747779C2semidirect
8. #11747776C2semidirect
9. #11747745C2semidirect
11. #11746963C2semidirect
53. C8×Dic10D3semidirect
94. #4694D5semidirect
412. C3×C5#3361semidirect
467. C5#79927semidirect
485. C3#10613316semidirect

Maximal subgroups

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

subgroupindex
#117526542
#117526512
C4×#67062
C5×#46942
C3×C8×Dic102
#117479632
#117477792
#117477762
#117477452
#117470452
#117469632
#106133163
#799275