Finite Group Databasebeta

← #14439383

Subgroups — #14439383

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#535C211yesmaximal, characteristic, complemented
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91839C211yesmaximal, characteristic, complemented
4C22×#6716C211yesmaximal, characteristic, complemented
5C2×#91821C211yesmaximal, characteristic, complemented
6#11756285C211yesmaximal, characteristic, complemented
7#11751177C212yesmaximal, complemented
8#11751175C212yesmaximal, complemented
9#11751161C212yesmaximal, complemented
10#11751160C212yesmaximal, complemented
11#11751098C211yesmaximal, characteristic, complemented
12#10615112—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C22×Dic30C2211yescharacteristic
17C3×C5×#127C2212yes—
18C3×C5×#124C2212yes—
19C3×C5×#121—22no—
20C3×C5×#120—22no—
21C3×C5×#117C2211yescharacteristic
22#91840—24no—
23#91839—24no—
24C2×#6718C2211yescharacteristic, complemented
25C2×#6718C2212yescomplemented
26C2×#6717C2211yescharacteristic, complemented
27C2×#6716—24no—
28C2×#6716C2212yes—
29C2×#6716C2212yes—
30C2×#6716C2212yes—
31C2×#6716C2212yescomplemented
32C2×#6716C2211yescharacteristic, complemented
33#91821—24no—
34C2×#6715C2212yes—
35C2×#6715C2211yescharacteristic, complemented
36C2×#6710C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic
38#91786—22no—
39#91775—22no—
40#91764C2212yescomplemented
41#91758C2212yescomplemented
42#91087C2212yescomplemented
43C4×C3⋊#168C2212yescomplemented
44#83381—51nomaximal, Hall
45C5×#535D311yescharacteristic, complemented
46C2×#4097—31no—
47C2×#4096—31no—
48C22×#687—31no—
49C2×#4078—31no—
50#65860—31no—
51#65365—32no—
52#65363—32no—
53#65349—32no—
54#65348—32no—
55#65286—31no—
56C24×C3×C5—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4—22no—
62C2×C3×C5×D4—22no—
63C2×C3×C5×D4—21no—
64C2×C3×C5×D4—24no—
65C2×C3×C5×D4C2312yes—
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220—21no—
70C22×Dic15—21no—
71#6817—22no—
72#6817—22no—
73C2×D60C2311yescharacteristic
74C2×C4×D15—21no—
75C2×Dic30—22no—
76C2×Dic30—22no—
77C2×Dic30—21no—
78C2×Dic30C2311yescharacteristic
79C2×Dic30C2312yes—
80C3×C5×C4⋊C4D412yes—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4D412yes—
83C3×C42×C5C2312yes—
84#6718—22no—
85#6718—24no—
86#6717—22no—
87#6716—24no—
88#6716—24no—
89#6716—24no—
90#6716—22no—
91#6716—24no—
92#6715—24no—
93#6715—22no—
94#6714—24no—
95C4⋊Dic15—24no—
96#6710D414yescomplemented
97C2×C3⋊#168D414yescomplemented
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C2×C3⋊#168C2312yes—
101C3×#535D511yescharacteristic, complemented
102C2×#951—51no—
103C2×#950—51no—
104C22×#214—51no—
105C2×#932—51no—
106#5526—51no—
107#5076—52no—
108#5074—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10—31no—
116C5×#127C2×D312yes—
117C5×#124C2×D312yes—
118C5×#121—22no—
119C5×#120—22no—
120C5×#117C2×D311yescharacteristic
121#4097—64no—
122#4096—64no—
123C2×#689—32no—
124C2×#689—31no—
125C2×#688—31no—
126C2×#687—32no—
127C2×#687—32no—
128C2×#687—32no—
129C2×#687—32no—
130C2×#687—31no—
131C2×#687—64no—
132#4078—64no—
133C2×#686—32no—
134C2×#686—31no—
135C2×#681—31no—
136C22×#168—31no—
137#4043—62no—
138#4032—62no—
139#4021—32no—
140#4015—32no—
141#3935—32no—
142C4×#168—32no—
143#3154—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—21no—
146C23×C3×C5—42no—
147C23×C3×C5—82no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—22no—
153C3×C5×D4—21no—
154C3×C5×D4—22no—
155C3×C5×D4—21no—
156C3×C5×D4—42no—
157C3×C5×D4—42no—
158C3×C5×D4—84no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5C2×D414yes—
162C2×C3×C4×C5C2×D411yescharacteristic
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2411yescharacteristic
166#1220—42no—
167C2×Dic15—21no—
168C2×Dic15—22no—
169C2×Dic15—42no—
170D60—21no—
171D60—21no—
172C4×D15—42no—
173Dic30—22no—
174Dic30—21no—
175Dic30—22no—
176Dic30—21no—
177Dic30—42no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C3⋊#168C2×D414yes—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×D4C2×D511yescharacteristic
183C2×#235—51no—
184C22×Dic6—51no—
185C3×#127C2×D512yes—
186C3×#124C2×D512yes—
187C3×#121—22no—
188C3×#120—22no—
189C3×#117C2×D511yescharacteristic
190#951—104no—
191#950—104no—
192C2×#216—51no—
193C2×#216—52no—
194C2×#215—51no—
195C2×#214—52no—
196C2×#214—52no—
197C2×#214—52no—
198C2×#214—51no—
199C2×#214—52no—
200C2×#214—104no—
201#932—104no—
202C2×#213—52no—
203C2×#213—51no—
204C2×#208—51no—
205C22×C3⋊C8—51no—
206#897—102no—
207#886—102no—
208#875—52no—
209#869—52no—
210#803—52no—
211C4×C3⋊C8—52no—
212C24×C5—21no—
213C5×#41—22no—
214C5×#41—22no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—21no—
220C2×C5×D4—24no—
221C2×C5×D4C22×D312yes—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
226C22×Dic5—61no—
227#709—62no—
228#709—62no—
229C2×D20—31no—
230C2×C4×D5—61no—
231C2×Dic10—32no—
232C2×Dic10—31no—
233C2×Dic10—62no—
234C2×Dic10—62no—
235C2×Dic10—61no—
236C5×C4⋊C4#6712yes—
237C5×C22⋊C4—24no—
238C5×C22⋊C4#6712yes—
239C42×C5C22×D312yes—
240#689—62no—
241#689—64no—
242#688—62no—
243#687—62no—
244#687—64no—
245#687—64no—
246#687—64no—
247#687—64no—
248#686—62no—
249#686—64no—
250#685—64no—
251C4⋊Dic5—64no—
252#681—34no—
253C2×#168—34no—
254C2×#168—31no—
255C2×#168—32no—
256C2×#168—31no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535D1511yescharacteristic, complemented
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—41no—
270C22×C3×C5—42no—
271C22×C3×C5—42no—
272C22×C3×C5—44no—
273C22×C3×C5—84no—
274C22×C3×C5#12712yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—41no—
277C2×D15—42no—
278C3×C4×C5—24no—
279C3×C4×C5—41no—
280C3×C4×C5#12712yes—
281C3×C4×C5C22×D411yescharacteristic
282C3×C4×C5C22×D411yescharacteristic
283Dic15—42no—
284Dic15—41no—
285C24×C3—21no—
286C3×#41—22no—
287C3×#41—22no—
288C2×C3×Q8C22×D511yescharacteristic
289C2×C3×D4—21no—
290C2×C3×D4—22no—
291C2×C3×D4—22no—
292C2×C3×D4—21no—
293C2×C3×D4—24no—
294C2×C3×D4C22×D512yes—
295C2×C3×D4C22×D511yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—101no—
299C22×Dic3—101no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—51no—
305C2×Dic6—52no—
306C2×Dic6—102no—
307C2×Dic6—102no—
308C2×Dic6—101no—
309C3×C4⋊C4C22⋊D512yes—
310C3×C22⋊C4—24no—
311C3×C22⋊C4C22⋊D512yes—
312C3×C42C22×D512yes—
313#216—102no—
314#216—104no—
315#215—102no—
316#214—104no—
317#214—104no—
318#214—104no—
319#214—102no—
320#214—104no—
321#213—104no—
322#213—102no—
323(C2×D3)⋊C4—104no—
324C4⋊Dic3—104no—
325#208—54no—
326C2×C3⋊C8—54no—
327C2×C3⋊C8—51no—
328C2×C3⋊C8—52no—
329C2×C3⋊C8—51no—
330C23×C5—22no—
331C23×C5—21no—
332C23×C5—42no—
333C23×C5—82no—
334C23×C5C2×#6711yescharacteristic
335C22×D5—61no—
336C5×Q8—21no—
337C5×Q8—21no—
338C5×D4—22no—
339C5×D4—21no—
340C5×D4—22no—
341C5×D4—21no—
342C5×D4—42no—
343C5×D4—42no—
344C5×D4—84no—
345C2×C4×C5—21no—
346C2×C4×C5—42no—
347C2×C4×C5D3×D412yes—
348C2×C4×C5D3×D412yes—
349C2×C4×C5C2×#6714yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—122no—
353C2×Dic5—61no—
354C2×Dic5—62no—
355C2×Dic5—122no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—62no—
360Dic10—61no—
361Dic10—62no—
362Dic10—61no—
363Dic10—122no—
364#168—32no—
365#168—32no—
366#168—34no—
367C2×#41—151no—
368C2×#41C2×D1511yescharacteristic
369C22×Q8—151no—
370C22×D4C2×D1511yescharacteristic
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—151no—
375C2×Q16—152no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16—151no—
386C22×C8—151no—
387C4⋊Q8—152no—
388#127C2×D1512yes—
389#124—152no—
390#124C2×D1512yes—
391#123—302no—
392C22⋊Q8—302no—
393#121—22no—
394#120—22no—
395#117C2×D1511yescharacteristic
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—81no—
400C2×C3×C5—82no—
401C2×C3×C5C2×#12711yescharacteristic
402C2×C3×C5#57712yes—
403D15—81no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—42no—
407C23×C3—82no—
408C23×C3C2×C22⋊D511yescharacteristic
409C22×D3—101no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×D4—22no—
413C3×D4—21no—
414C3×D4—22no—
415C3×D4—21no—
416C3×D4—42no—
417C3×D4—42no—
418C3×D4—84no—
419C2×C3×C4—21no—
420C2×C3×C4—42no—
421C2×C3×C4D4×D512yes—
422C2×C3×C4D4×D512yes—
423C2×C3×C4C2×C22⋊D514yes—
424C2×C3×C4C2×C22⋊D511yescharacteristic
425C2×C3×C4C23×D511yescharacteristic
426#67—202no—
427C2×Dic3—101no—
428C2×Dic3—102no—
429C2×Dic3—202no—
430D12—101no—
431D12—101no—
432C4×D3—202no—
433Dic6—102no—
434Dic6—101no—
435Dic6—102no—
436Dic6—101no—
437Dic6—202no—
438C3⋊C8—52no—
439C3⋊C8—52no—
440C3⋊C8—54no—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—44no—
446C22×C5—84no—
447C22×C5#94012yes—
448C22×C5C22×#6711yescharacteristic
449C2×D5—121no—
450C2×D5—122no—
451C4×C5—24no—
452C4×C5—41no—
453C4×C5#94012yes—
454C4×C5C2×D3×D411yescharacteristic
455C4×C5C2×D3×D411yescharacteristic
456Dic5—122no—
457Dic5—121no—
458C24—21no—
459#41—22no—
460#41—22no—
461#41—302no—
462#41—302no—
463C2×Q8—152no—
464C2×Q8—151no—
465C2×Q8—301no—
466C2×Q8—302no—
467C2×Q8—302no—
468C2×Q8C22×D1511yescharacteristic
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—24no—
474C2×D4—151no—
475C2×D4—301no—
476C2×D4C22×D1512yes—
477C2×D4C22×D1511yescharacteristic
478C22×C4—21no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4C22×D1511yescharacteristic
482Q16—302no—
483Q16—304no—
484SD16—304no—
485SD16—304no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—302no—
491D8—304no—
492M16—154no—
493C2×C8—154no—
494C2×C8—151no—
495C2×C8—152no—
496C2×C8—151no—
497C4⋊C4—304no—
498C4⋊C4#122012yes—
499C22⋊C4—24no—
500C22⋊C4—304no—
501C22⋊C4#122012yes—
502C42C22×D1512yes—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—44no—
509C22×C3—84no—
510C22×C3#408612yes—
511C22×C3C22×C22⋊D511yescharacteristic
512C2×D3—201no—
513C2×D3—202no—
514C3×C4—24no—
515C3×C4—41no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C2×D4×D511yescharacteristic
519Dic3—202no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5—82no—
523C2×C5—81no—
524C2×C5C2×#94011yescharacteristic
525C2×C5#583612yes—
526D5—241no—
527C23—22no—
528C23—21no—
529C23—42no—
530C23—82no—
531C23—301no—
532C23C2×#122011yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—302no—
536Q8—301no—
537Q8—302no—
538Q8—301no—
539Q8—602no—
540D4—22no—
541D4—21no—
542D4—22no—
543D4—21no—
544D4—42no—
545D4—42no—
546D4—84no—
547D4—301no—
548D4—301no—
549D4—602no—
550C2×C4—21no—
551C2×C4—42no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4—602no—
556C2×C4D4×D1512yes—
557C2×C4D4×D1512yes—
558C2×C4C2×#122014yes—
559C2×C4C2×#122011yescharacteristic
560C2×C4C23×D1511yescharacteristic
561C8—152no—
562C8—152no—
563C8—154no—
564C2×C3—22no—
565C2×C3—82no—
566C2×C3—81no—
567C2×C3C2×#408611yescharacteristic
568C2×C3#6617012yes—
569D3—401no—
570C5#8338111yescharacteristic, complemented, Sylow
571C22—22no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—44no—
576C22—84no—
577C22—601no—
578C22—602no—
579C22#9182912yes—
580C22C22×#122011yescharacteristic
581C4—24no—
582C4—41no—
583C4—601no—
584C4—602no—
585C4#9182912yes—
586C4C2×D4×D1511yescharacteristic
587C4C2×D4×D1511yescharacteristic
588C3#1061511211yescharacteristic, complemented, Sylow
589C2—22no—
590C2—82no—
591C2—81no—
592C2—1201no—
593C2C2×#9182911yescharacteristic
594C2#1175659512yes—
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#535C2
socleC22×C3×C5C22×D4
hypercenter#535D15
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C3×C5×#535C2semidirect
2. C2×#91840C2semidirect
3. C2×#91839C2semidirect
4. C22×#6716C2semidirect
5. C2×#91821C2semidirect
6. #11756285C2semidirect
7. #11751177C2semidirect
8. #11751175C2semidirect
9. #11751161C2semidirect
10. #11751160C2semidirect
11. #11751098C2semidirect
24. C2×#6718C22semidirect
25. C2×#6718C22semidirect
26. C2×#6717C22semidirect
31. C2×#6716C22semidirect
32. C2×#6716C22semidirect
35. C2×#6715C22semidirect
40. #91764C22semidirect
41. #91758C22semidirect
42. #91087C22semidirect
43. C4×C3⋊#168C22semidirect
45. C5×#535D3semidirect
96. #6710D4semidirect
97. C2×C3⋊#168D4semidirect
101. C3×#535D5semidirect
262. #535D15semidirect
503. C3×C5#3154semidirect
570. C5#83381semidirect
588. C3#10615112semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5352
C2×#918402
C2×#918392
C22×#67162
C2×#918212
#117562852
#117511772
#117511752
#117511612
#117511602
#117510982
#106151123
#833815