Finite Group Databasebeta

← #14471752

Subgroups — #14471752

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#11756344C211yesmaximal, characteristic, complemented
2#11756302C211yesmaximal, characteristic, complemented
3C3×C4×C5×SD16C211yesmaximal, characteristic, complemented
4#11751266C212yesmaximal, complemented
5#11751122C211yesmaximal, characteristic, complemented
6#11751116C211yesmaximal, characteristic
7#11750972C212yesmaximal, complemented
8#11750901C212yesmaximal, complemented
9#11750857C212yesmaximal, complemented
10#11750795C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13C2×C3×C5×SD16C2211yescharacteristic
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91836C2212yes—
17D4×Dic15C2212yes—
18C2×#6715C2212yes—
19C2×C4⋊Dic15—21no—
20#91813—21no—
21#91783—22no—
22#91782C2212yes—
23#91779C2212yes—
24#91767—22no—
25#91764—21no—
26#91763C2211yescharacteristic
27C4×D60—21no—
28#91758C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#106C2211yescharacteristic
31C3×C5×#103C2211yescharacteristic
32C3×C5×#102C2211yescharacteristic
33C3×C4×C5×C8C2211yescharacteristic
34#91119C2212yes—
35#91105C2212yes—
36#91105C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79621—51nomaximal, Hall
43#65919—31no—
44#65877—31no—
45C4×C5×SD16D311yescharacteristic, complemented
46#65454—32no—
47#65310—31no—
48#65304—31no—
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C22×Dic15—22no—
58C2×D60—21no—
59C2×D60—21no—
60C2×D60C2312yes—
61C2×C4×D15—22no—
62C2×Dic30—21no—
63C2×Dic30D411yescharacteristic
64C3×C5×SD16—22no—
65C2×C3×C5×C8C2311yescharacteristic
66C2×C3×C5×C8C2311yescharacteristic
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71C3×C42×C5—21no—
72C3×C42×C5C2311yescharacteristic
73#6719—22no—
74#6715—24no—
75#6714—22no—
76#6714—22no—
77#6714—22no—
78C4⋊Dic15—21no—
79C4⋊Dic15—22no—
80C4⋊Dic15D411yescharacteristic
81C4⋊Dic15C2312yes—
82#6712—22no—
83#6712D412yes—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2312yes—
86#5585—51no—
87#5543—51no—
88C3×C4×SD16D511yescharacteristic, complemented
89#5165—52no—
90#5021—51no—
91#5015—51no—
92#4871—52no—
93#4800—52no—
94#4756—52no—
95#4694—51no—
96C8×Dic6—51no—
97C2×C5×SD16C2×D311yescharacteristic
98C4×C5×Q8C2×D311yescharacteristic
99C4×C5×D4C2×D311yescharacteristic
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×Dic10—31no—
114C5×#106C2×D311yescharacteristic
115C5×#103C2×D311yescharacteristic
116C5×#102C2×D311yescharacteristic
117C4×C5×C8C2×D311yescharacteristic
118#3967—32no—
119#3953—32no—
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×D15—22no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C3×C5×D4—21no—
132C3×C5×D4#4112yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15—22no—
141C2×Dic15—82no—
142C2×Dic15C2×D412yes—
143C2×Dic15C2×D412yes—
144D60—22no—
145D60—22no—
146D60—42no—
147D60—81no—
148C4×D15—82no—
149Dic30—22no—
150Dic30—81no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C3⋊#168—22no—
154C2×C3×SD16C2×D511yescharacteristic
155C3×C4×Q8C2×D511yescharacteristic
156C3×C4×D4C2×D511yescharacteristic
157#947—52no—
158D4×Dic3—52no—
159C2×#213—52no—
160C2×C4⋊Dic3—101no—
161#924—101no—
162#894—102no—
163#893—52no—
164#890—52no—
165#878—102no—
166#875—101no—
167#874—51no—
168C4×D12—101no—
169#869—51no—
170C4×Dic6—51no—
171C3×#106C2×D511yescharacteristic
172C3×#103C2×D511yescharacteristic
173C3×#102C2×D511yescharacteristic
174C3×C4×C8C2×D511yescharacteristic
175#835—52no—
176#821—52no—
177#821—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#809—52no—
181#807—52no—
182C4⋊(C3⋊C8)—51no—
183C2×C5×Q8C22×D311yescharacteristic
184C2×C5×D4C22×D311yescharacteristic
185C22×C4×C5—21no—
186C22×Dic5—62no—
187C2×D20—32no—
188C2×D20—61no—
189C2×D20—61no—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10—61no—
193C5×SD16—22no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—21no—
197C5×C4⋊C4C22×D311yescharacteristic
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C22⋊C4—21no—
200C42×C5—21no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—62no—
203#686—64no—
204#685—62no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5—32no—
209C4⋊Dic5—62no—
210C4⋊Dic5—61no—
211#683—32no—
212#683—62no—
213C4×Dic5—32no—
214C2×#168—32no—
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—151no—
224C4×SD16D1511yescharacteristic, complemented
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5—41no—
236C3×C4×C5—41no—
237C3×C4×C5#13512yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C52−1+411yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—42no—
243C2×C3×Q8C22×D511yescharacteristic
244C2×C3×D4C22×D511yescharacteristic
245C22×C3×C4—21no—
246C22×Dic3—102no—
247C2×D12—52no—
248C2×D12—101no—
249C2×D12—101no—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6—101no—
253C3×SD16—22no—
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—21no—
257C3×C4⋊C4C22×D511yescharacteristic
258C3×C4⋊C4C22×D511yescharacteristic
259C3×C22⋊C4—21no—
260C3×C42—21no—
261C3×C42C22×D511yescharacteristic
262#217—102no—
263#213—104no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—51no—
268C4⋊Dic3—52no—
269C4⋊Dic3—102no—
270C4⋊Dic3—101no—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273C4×Dic3—52no—
274C2×C3⋊C8—52no—
275C23×C5—21no—
276C22×D5—62no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×D4—21no—
280C5×D4#23512yes—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—42no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—62no—
291C2×Dic5—242no—
292D20—62no—
293D20—62no—
294D20—122no—
295D20—241no—
296C4×D5—242no—
297Dic10—62no—
298Dic10—241no—
299C5×C8—21no—
300C5×C8—21no—
301#168—62no—
302C2×SD16C2×D1511yescharacteristic
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—151no—
313C4×Q8C2×D1511yescharacteristic
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—301no—
317C4×D4C2×D1511yescharacteristic
318C2×C4⋊C4—301no—
319#107—152no—
320#106C2×D1511yescharacteristic
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—152no—
324#103C2×D1511yescharacteristic
325#102—152no—
326#102—152no—
327#102—152no—
328#102C2×D1511yescharacteristic
329C4×C8—152no—
330C4×C8C2×D1511yescharacteristic
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335D15—82no—
336C23×C3—21no—
337C22×D3—102no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×D4—21no—
341C3×D4#70912yes—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—52no—
350C2×Dic3—52no—
351C2×Dic3—102no—
352C2×Dic3—402no—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—102no—
359Dic6—401no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—102no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—41no—
373C4×C5—41no—
374C4×C5#91612yes—
375C4×C5C2×#23511yescharacteristic
376C4×C5#101011yescharacteristic
377Dic5—62no—
378Dic5—62no—
379Dic5—122no—
380C2×Q8—151no—
381C2×Q8—301no—
382C2×Q8C22×D1511yescharacteristic
383C2×D4—152no—
384C2×D4—301no—
385C2×D4—301no—
386C2×D4C22×D1511yescharacteristic
387C22×C4—21no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—22no—
391D8—304no—
392C2×C8—152no—
393C2×C8C22×D1511yescharacteristic
394C2×C8C22×D1511yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—151no—
397C4⋊C4—152no—
398C4⋊C4—152no—
399C4⋊C4—302no—
400C4⋊C4—302no—
401C4⋊C4—301no—
402C4⋊C4C22×D1511yescharacteristic
403C4⋊C4C22×D1511yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—21no—
410C42—152no—
411C42C22×D1511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4#406212yes—
425C3×C4C2×#70911yescharacteristic
426C3×C4#415011yescharacteristic
427Dic3—102no—
428Dic3—102no—
429Dic3—202no—
430C2×C5—42no—
431C2×C5#555211yescharacteristic
432C2×C5C2×#91611yescharacteristic
433C2×C5#576911yescharacteristic
434D5—242no—
435C23—21no—
436C23—302no—
437Q8—21no—
438Q8—21no—
439Q8—302no—
440Q8—1201no—
441D4—21no—
442D4—302no—
443D4—302no—
444D4—602no—
445D4—1201no—
446D4#681712yes—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—42no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D4×D1511yescharacteristic
457C2×C4D4×D1511yescharacteristic
458C2×C4C23×D1511yescharacteristic
459C8—21no—
460C8—21no—
461C8—302no—
462C2×C3—42no—
463C2×C3#6588611yescharacteristic
464C2×C3C2×#406211yescharacteristic
465C2×C3#6610311yescharacteristic
466D3—402no—
467C5#7962111yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D4×D1511yescharacteristic
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—302no—
480C4—302no—
481C4—602no—
482C4#9180512yes—
483C4C2×#681711yescharacteristic
484C4#9210111yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—42no—
487C2—1202no—
488C2#1175631111yescharacteristic
489C2C2×#9180511yescharacteristic
490C2#1175652811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×SD16C2
socleC22×C3×C5C22×D4
prime radical#11751116C2
hypercenterC4×SD16D15
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #11756344C2semidirect
2. #11756302C2semidirect
3. C3×C4×C5×SD16C2semidirect
4. #11751266C2semidirect
5. #11751122C2semidirect
7. #11750972C2semidirect
8. #11750901C2semidirect
9. #11750857C2semidirect
10. #11750795C2semidirect
11. C8×Dic30C2semidirect
45. C4×C5×SD16D3semidirect
88. C3×C4×SD16D5semidirect
224. C4×SD16D15semidirect
412. C3×C5#3361semidirect
467. C5#79621semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
#117563442
#117563022
C3×C4×C5×SD162
#117512662
#117511222
#117511162
#117509722
#117509012
#117508572
#117507952
C8×Dic302
#106113523
#796215