Finite Group Databasebeta

← #14471755

Subgroups — #14471755

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#11756489C211yesmaximal, characteristic, complemented
2#11756344C211yesmaximal, characteristic, complemented
3C3×C5×#477C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5C4×#6717C211yesmaximal, characteristic, complemented
6#11750992C212yesmaximal, complemented
7#11750973C212yesmaximal, complemented
8#11750944C211yesmaximal, characteristic
9#11750931C211yesmaximal, characteristic, complemented
10#11750920C212yesmaximal, complemented
11#11750901C212yesmaximal, complemented
12#10612865—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C4×C5×Q8C2211yescharacteristic
15#91836C2212yes—
16#91835—22no—
17C2×#6717C2211yescharacteristic
18C2×D120C2212yes—
19#91786—21no—
20#91783—22no—
21#91782C2212yes—
22#91782C2212yes—
23C4⋊C4×D15—21no—
24#91779C2212yes—
25#91764—21no—
26#91763C2211yescharacteristic
27C4×D60—21no—
28C4×D60C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#107C2212yes—
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×#103C2212yes—
33#91119C2211yescharacteristic
34#91105C2212yes—
35#91098C2212yes—
36C8×Dic15C2212yes—
37#91093C2212yes—
38#91093C2212yes—
39#91093C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#81134—51nomaximal, Hall
43#66064—31no—
44#65919—31no—
45C5×#477D311yescharacteristic, complemented
46#65377—31no—
47C4×#688—31no—
48#65180—32no—
49#65161—32no—
50#65132—31no—
51#65119—31no—
52#65108—32no—
53#65089—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×D60—21no—
57C2×D60—21no—
58C2×D60C2312yes—
59C2×D60C2311yescharacteristic
60C2×C4×D15—21no—
61C2×C4×D15—22no—
62C2×C4×D15—22no—
63C2×Dic30D411yescharacteristic
64C2×C3×C5×C8C2312yes—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C42×C5—21no—
70C3×C42×C5C2311yescharacteristic
71#6717—22no—
72#6714—21no—
73#6714—22no—
74#6714—22no—
75#6714—22no—
76#6714—22no—
77C4⋊Dic15—22no—
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80#6712—22no—
81#6712D412yes—
82C4×Dic15C2312yes—
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85D120—24no—
86#5730—51no—
87#5585—51no—
88C3×#477D511yescharacteristic, complemented
89#5088—51no—
90C4×#215—51no—
91#4891—52no—
92#4872—52no—
93#4843—51no—
94#4830—51no—
95#4819—52no—
96#4800—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C4×C5×Q8C2×D311yescharacteristic
99#4093—32no—
100#4092—62no—
101C2×#688—31no—
102C2×D40—32no—
103#4043—61no—
104#4040—62no—
105#4039—32no—
106#4039—32no—
107D5×C4⋊C4—61no—
108#4036—32no—
109#4021—61no—
110#4020—31no—
111C4×D20—31no—
112C4×D20—61no—
113C4×Dic10—31no—
114C5×#107C2×D312yes—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#103C2×D312yes—
117#3967—31no—
118#3953—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3941—31no—
122#3941—32no—
123#3941—32no—
124#3940—31no—
125C4×#168—31no—
126#3361—151noSylow
127C22×D15—21no—
128C22×D15—22no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C3×C5×Q8—81no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—21no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141D60—22no—
142D60—21no—
143D60—22no—
144D60—42no—
145D60—81no—
146D60#4112yes—
147C4×D15—42no—
148C4×D15—82no—
149C4×D15—82no—
150Dic30—22no—
151C3×C5×C8—22no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×C4×Q8C2×D511yescharacteristic
156#947—52no—
157#946—102no—
158C2×#215—51no—
159C2×D24—52no—
160#897—101no—
161#894—102no—
162#893—52no—
163#893—52no—
164D3×C4⋊C4—101no—
165#890—52no—
166#875—101no—
167#874—51no—
168C4×D12—51no—
169C4×D12—101no—
170C4×Dic6—51no—
171C3×#107C2×D512yes—
172C3×C4⋊C8C2×D511yescharacteristic
173C3×#103C2×D512yes—
174#835—51no—
175#821—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#809—52no—
180#809—52no—
181#808—51no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—21no—
184C2×C5×Q8C22×D311yescharacteristic
185C2×D20—31no—
186C2×D20—32no—
187C2×D20—61no—
188C2×D20—61no—
189C2×C4×D5—61no—
190C2×C4×D5—62no—
191C2×C4×D5—62no—
192C2×Dic10—31no—
193C2×C5×C8C22×D312yes—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4C22×D311yescharacteristic
197C5×C4⋊C4C22×D312yes—
198C42×C5—21no—
199C42×C5C22×D311yescharacteristic
200#688—62no—
201#685—62no—
202#685—62no—
203#685—62no—
204#685—62no—
205#685—61no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209#683—32no—
210#683—62no—
211C4×Dic5—32no—
212C2×#168—31no—
213C2×#168—31no—
214D40—64no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477D1511yescharacteristic, complemented
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5—41no—
236C3×C4×C5—42no—
237C3×C4×C5#13512yes—
238C3×C4×C5C2×#4111yescharacteristic
239C3×C4×C52−1+411yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—41no—
243C2×C3×Q8—21no—
244C2×C3×Q8C22×D511yescharacteristic
245C2×D12—51no—
246C2×D12—52no—
247C2×D12—101no—
248C2×D12—101no—
249C2×C4×D3—101no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C2×C3×C8C22×D512yes—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4C22×D511yescharacteristic
257C3×C4⋊C4C22×D512yes—
258C3×C42—21no—
259C3×C42C22×D511yescharacteristic
260#215—102no—
261(C2×D3)⋊C4—102no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—101no—
266C4⋊Dic3—51no—
267C4⋊Dic3—51no—
268C4⋊Dic3—102no—
269Dic3⋊C4—52no—
270Dic3⋊C4—102no—
271C4×Dic3—52no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274D24—104no—
275C22×D5—61no—
276C22×D5—62no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×Q8—81no—
280C2×C4×C5—22no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—32no—
287C2×Dic5—32no—
288C2×Dic5—61no—
289D20—32no—
290D20—61no—
291D20—62no—
292D20—62no—
293D20—122no—
294D20—241no—
295C4×D5—122no—
296C4×D5—242no—
297C4×D5—242no—
298Dic10—62no—
299C5×C8—22no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8C2×D1511yescharacteristic
305#127—151no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—301no—
311C22⋊Q8—302no—
312C4×Q8—151no—
313C4×Q8C2×D1511yescharacteristic
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—151no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107C2×D1512yes—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8C2×D1511yescharacteristic
323#103—151no—
324#103C2×D1512yes—
325#102—152no—
326#102—151no—
327#102—152no—
328#102—152no—
329C4×C8—152no—
330C4×C8—151no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—42no—
335D15—82no—
336C22×D3—101no—
337C22×D3—102no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—81no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—52no—
348C2×Dic3—52no—
349C2×Dic3—101no—
350D12—52no—
351D12—101no—
352D12—102no—
353D12—102no—
354D12—202no—
355D12—401no—
356C4×D3—202no—
357C4×D3—402no—
358C4×D3—402no—
359Dic6—102no—
360C3×C8—22no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5C2×D3×D411yescharacteristic
364C2×D5—62no—
365C2×D5—121no—
366C2×D5—121no—
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—41no—
373C4×C5—42no—
374C4×C5#91912yes—
375C4×C5#100711yescharacteristic
376C4×C5D3×#4111yescharacteristic
377Dic5—62no—
378Dic5—62no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—151no—
382C2×Q8C22×D1511yescharacteristic
383C2×D4—151no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—302no—
388C22×C4—302no—
389C22×C4—301no—
390SD16—302no—
391D8—304no—
392C2×C8—151no—
393C2×C8—151no—
394C2×C8C22×D1512yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—151no—
398C4⋊C4—152no—
399C4⋊C4—151no—
400C4⋊C4—302no—
401C4⋊C4—302no—
402C4⋊C4C22×D1512yes—
403C4⋊C4C22×D1511yescharacteristic
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—301no—
409C42—21no—
410C42—152no—
411C42C22×D1511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C2×D4×D511yescharacteristic
414C2×D3—102no—
415C2×D3—201no—
416C2×D3—201no—
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—42no—
423C3×C4—41no—
424C3×C4#406512yes—
425C3×C4#414711yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—102no—
428Dic3—102no—
429Dic3—201no—
430C2×C5#563311yescharacteristic
431C2×C5C2×#91911yescharacteristic
432C2×C5#577411yescharacteristic
433D5—122no—
434D5—242no—
435C23—301no—
436C23—302no—
437Q8—21no—
438Q8—21no—
439Q8—81no—
440Q8—302no—
441D4—152no—
442D4—301no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—301no—
453C2×C4—602no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D4×D1511yescharacteristic
457C2×C4D4×D1511yescharacteristic
458C2×C4C23×D1511yescharacteristic
459C8—22no—
460C8—301no—
461C8—301no—
462C2×C3#6596711yescharacteristic
463C2×C3C2×#406511yescharacteristic
464C2×C3#6610811yescharacteristic
465D3—202no—
466D3—402no—
467C5#8113411yescharacteristic, complemented, Sylow
468C22—302no—
469C22—601no—
470C22—601no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D4×D1511yescharacteristic
475C4—21no—
476C4—41no—
477C4—41no—
478C4—42no—
479C4—302no—
480C4—302no—
481C4—601no—
482C4#9180812yes—
483C4#9209811yescharacteristic
484C4#41×D1511yescharacteristic
485C3#1061286511yescharacteristic, complemented, Sylow
486C2—602no—
487C2—1202no—
488C2#1175639211yescharacteristic
489C2C2×#9180811yescharacteristic
490C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#477C2
socleC22×C3×C5C22×D4
prime radical#11750944C2
hypercenter#477D15
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
2. #11756344C2semidirect
3. C3×C5×#477C2semidirect
4. #11751189C2semidirect
5. C4×#6717C2semidirect
6. #11750992C2semidirect
7. #11750973C2semidirect
9. #11750931C2semidirect
10. #11750920C2semidirect
11. #11750901C2semidirect
45. C5×#477D3semidirect
88. C3×#477D5semidirect
220. #477D15semidirect
412. C3×C5#3361semidirect
467. C5#81134semidirect
485. C3#10612865semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117563442
C3×C5×#4772
#117511892
C4×#67172
#117509922
#117509732
#117509442
#117509312
#117509202
#117509012
#106128653
#811345