Finite Group Databasebeta

← #14412669

Subgroups — #14412669

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92017C211yesmaximal, characteristic
2C5×#5523C211yesmaximal, characteristic, complemented
3C2×#91288C211yesmaximal, characteristic, complemented
4#11751103C211yesmaximal, characteristic, complemented
5C3×#65290C211yesmaximal, characteristic, complemented
6#11748394C211yesmaximal, characteristic, complemented
7C2×#90964C211yesmaximal, characteristic, complemented
8#11747503C212yesmaximal, complemented
9#11747502C212yesmaximal, complemented
10#11747477C212yesmaximal, complemented
11D3×#3941C212yesmaximal, complemented
12#10614294—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C2×D5×#67—22no—
17#92017—24no—
18#92017C418yescomplemented
19C2×#6777—21no—
20C2×D3×D20C2212yes—
21C2×#6766—21no—
22C2×#6765C2212yes—
23C3×C5×#117C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C5×#892C2212yescomplemented
27C5×D3×C4⋊C4C2212yescomplemented
28C5×#67⋊C4—22no—
29C4×C5×D12—21no—
30C4×C5×Dic6—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32C2×#6650C2212yescomplemented
33#91288—24no—
34C2×D3×#168C2212yescomplemented
35#91094C2211yescharacteristic, complemented
36#91094C2211yescharacteristic, complemented
37#91093C2211yescharacteristic, complemented
38#91093C2211yescharacteristic, complemented
39C3×#3941C2212yescomplemented
40C3×#3941C2212yescomplemented
41#90975C2212yescomplemented
42#90969C2212yescomplemented
43#90964C2212yescomplemented
44#90964C2212yescomplemented
45#78925—51nomaximal, Hall
46C2×#4149—31no—
47C5×#520—31no—
48C2×#4094—31no—
49#65291—32no—
50#65291—31no—
51#65290—32no—
52#65290D311yescharacteristic, complemented
53#65255—31no—
54#65255—32no—
55C2×#3941—32no—
56C2×#3941—31no—
57C23×C3×D5—21no—
58C22×D3×D5—22no—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—21no—
61#6817—22no—
62#6817C2×C414yescomplemented
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×Dic30C2311yescharacteristic
66C2×C5×#67D412yes—
67C22×C5×Dic3—21no—
68C5×#235C2×C414yes—
69C5×#235D414yes—
70C2×C5×D12D411yescharacteristic
71C2×C4×C5×D3—22no—
72C2×C4×C5×D3C2312yes—
73C2×C5×Dic6D411yescharacteristic
74C2×C3×D20—21no—
75C2×C3×D20—22no—
76C2×C3×D20C2×C414yescomplemented
77C2×C3×D20C2312yes—
78D5×#67—216no—
79C2×#1202—22no—
80C2×#1201—22no—
81C2×D5×Dic3—22no—
82#6777—28no—
83D3×D20—24no—
84D3×D20C2×C418yescomplemented
85#6766—28no—
86#6765—24no—
87#6765C2×C418yescomplemented
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5—21no—
92C2×C3⋊#168—22no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×(C2×D3)⋊C4—22no—
96C5×C4⋊Dic3—21no—
97C5×C4⋊Dic3C2312yes—
98C5×Dic3⋊C4—22no—
99C4×C5×Dic3—22no—
100C3×#681—22no—
101C2×C3×#168C2312yes—
102#6650—24no—
103D3×#168—24no—
104C2×#1004—51no—
105C2×#907—51no—
106#5523D511yescharacteristic, complemented
107C3×#418—51no—
108C2×#832—51no—
109#5133—51no—
110#5002—51no—
111#4772—52no—
112#4771—52no—
113#4770—52no—
114D3×#102—52no—
115C2×C5×#41—31no—
116#4149—38no—
117#4149—64no—
118C2×#713—61no—
119C2×D4×D5—61no—
120C2×D4×D5—62no—
121C2×#709—31no—
122C2×#709—32no—
123C22×D20—32no—
124C22×D20C2×D311yescharacteristic
125C4×C5×Q8—61no—
126C4×C5×D4—61no—
127C4×C5×D4—62no—
128C5×#117—32no—
129C5×#117C2×D311yescharacteristic, complemented
130C2×C5×C4⋊C4—31no—
131C2×C5×C4⋊C4—32no—
132#4094—64no—
133C2×#681—32no—
134C2×#681C2×D311yescharacteristic, complemented
135C22×#168—31no—
136C22×#168—32no—
137#3942—31no—
138#3942—31no—
139#3942—32no—
140#3941—32no—
141#3941—32no—
142#3941—31no—
143#3941—31no—
144#3941—32no—
145#3941C2×D312yescomplemented
146#3941C2×D312yescomplemented
147#2897—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C5×D3C2×D412yes—
151C22×C3×D5—22no—
152C22×C3×D5—24no—
153C22×C3×D5—81no—
154C22×C3×D5—81no—
155C2×D3×D5—28no—
156C2×D3×D5—82no—
157C2×D3×D5—82no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5C22×C412yes—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—24no—
165C2×Dic15—21no—
166D60—21no—
167D60C22×C412yes—
168C4×D15—24no—
169Dic30—21no—
170Dic30C22×C412yes—
171C5×#67C22⋊C418yes—
172C2×C5×Dic3—22no—
173C2×C5×Dic3—81no—
174C2×C5×Dic3C2×D412yes—
175C5×D12C22⋊C414yes—
176C4×C5×D3—82no—
177C4×C5×D3C22×C414yes—
178C4×C5×D3C2×D414yes—
179C5×Dic6C22⋊C414yes—
180C3×D20—24no—
181C3×D20—22no—
182C3×D20C22×C414yes—
183#1202—28no—
184#1201—28no—
185D5×Dic3—28no—
186C3⋊#168—21no—
187C3⋊#168—21no—
188C3×#168—22no—
189C22×C3×D4—51no—
190C22×#67—102no—
191#1004—58no—
192#1004—104no—
193C2×#237—52no—
194C2×#237—101no—
195C2×D3×D4—52no—
196C2×D3×D4—101no—
197C2×#235—51no—
198C2×#235C2×D511yescharacteristic
199C2×C3×M16—51no—
200C3×#117C2×D511yescharacteristic, complemented
201C2×C4⋊Dic3C2×D511yescharacteristic, complemented
202C22×C3⋊C8—51no—
203#907—104no—
204C2×ΓL(1,𝔽25)—52no—
205C2×D3×C8—52no—
206#892C2×D512yescomplemented
207D3×C4⋊C4C2×D512yescomplemented
208#67⋊C4—22no—
209C4×D12—21no—
210C4×Dic6—21no—
211C3×#102—52no—
212C3×#102—52no—
213#832—52no—
214#832—52no—
215#821—52no—
216#816—52no—
217#810—51no—
218#810—51no—
219#809—51no—
220#809—51no—
221C23×D5—21no—
222C23×D5—62no—
223C5×#41—34no—
224C5×#41—34no—
225C2×C5×Q8—31no—
226C2×C5×D4—32no—
227C2×C5×D4—31no—
228C22×C4×C5—32no—
229C22×C4×C5—62no—
230C22×C4×C5—61no—
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—62no—
233C2×C22⋊D5—61no—
234#713—68no—
235D4×D5—68no—
236D4×D5—616no—
237#709—34no—
238#709—38no—
239#709—64no—
240#709—62no—
241C2×D20—21no—
242C2×D20—22no—
243C2×D20—31no—
244C2×D20—38no—
245C2×D20—64no—
246C2×D20—62no—
247C2×D20C4×D314yescomplemented
248C2×D20C22×D312yes—
249C2×C4×D5—62no—
250C2×C4×D5—61no—
251C2×Dic10—31no—
252C5×C4⋊C4—32no—
253C5×C4⋊C4—62no—
254C5×C4⋊C4—61no—
255C5×C4⋊C4C22×D311yescharacteristic
256C5×C4⋊C4C22×D311yescharacteristic
257C5×C22⋊C4—21no—
258C5×C22⋊C4—62no—
259C42×C5—21no—
260C42×C5—62no—
261#681—22no—
262#681—64no—
263C2×#168—31no—
264C2×#168—31no—
265C2×#168—64no—
266C2×#168—62no—
267C2×#168C22×D312yes—
268C2×H(5,𝔽2)—151no—
269C2×#131—151no—
270#520—31no—
271#418—51no—
272#418—152no—
273#417—152no—
274#417—151no—
275#416—152no—
276#416—151no—
277C2×#102—152no—
278C2×#102—151no—
279C22×C3×C5—21no—
280C22×C3×C5—21no—
281C22×C3×C5C2×C22⋊C412yes—
282C22×C3×C5C22×D411yescharacteristic
283C2×D15—22no—
284C2×D15—41no—
285C2×D15—41no—
286C2×C5×D3—22no—
287C2×C5×D3—22no—
288C2×C5×D3C2×C22⋊C414yes—
289C2×C3×D5—24no—
290C2×C3×D5—42no—
291C2×C3×D5—42no—
292C2×C3×D5—84no—
293D3×D5—88no—
294C3×C4×C5—41no—
295C3×C4×C5—41no—
296C3×C4×C5C2×C22⋊C412yes—
297C3×C4×C5C23×C411yescharacteristic
298C3×C4×C5C22×D411yescharacteristic
299Dic15—22no—
300C5×Dic3—42no—
301C5×Dic3C2×C22⋊C414yes—
302C24×C3—101no—
303C23×D3—102no—
304C2×C3×D4—54no—
305C2×C3×D4—52no—
306C2×C3×D4—102no—
307C2×C3×D4—101no—
308C22×C3×C4C22×D511yescharacteristic
309C2×#67—101no—
310C2×#67—102no—
311C2×#67—1016no—
312C2×#67—102no—
313C2×#67C22⋊D512yes—
314C22×Dic3—21no—
315C22×Dic3—102no—
316#237—58no—
317#237—104no—
318#237—108no—
319D3×D4—58no—
320D3×D4—108no—
321D3×D4—104no—
322#235—54no—
323#235—102no—
324#235C4×D514yes—
325#235D2014yes—
326C2×D12—51no—
327C2×D12C22⋊D511yescharacteristic
328C2×C4×D3—22no—
329C2×C4×D3—101no—
330C2×C4×D3C22×D512yes—
331C2×Dic6—51no—
332C2×Dic6C22⋊D511yescharacteristic
333C3×M16—102no—
334C2×C3×C8—52no—
335C3×C4⋊C4C22×D511yescharacteristic
336C3×C4⋊C4C22×D511yescharacteristic
337C3×C22⋊C4—21no—
338C3×C42—21no—
339(C2×D3)⋊C4—22no—
340C4⋊Dic3—21no—
341C4⋊Dic3C22×D512yes—
342Dic3⋊C4—22no—
343C4×Dic3—22no—
344C2×C3⋊C8—51no—
345C2×C3⋊C8—51no—
346C2×C3⋊C8—102no—
347ΓL(1,𝔽25)—104no—
348D3×C8—104no—
349C23×C5—32no—
350C23×C5D3×D411yescharacteristic
351C22×D5—22no—
352C22×D5—24no—
353C22×D5—68no—
354C22×D5—61no—
355C22×D5—81no—
356C22×D5—81no—
357C22×D5—242no—
358C22×D5—242no—
359C5×Q8—34no—
360C5×D4—38no—
361C5×D4—34no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—32no—
365C2×C4×C5—34no—
366C2×C4×C5—34no—
367C2×C4×C5—62no—
368C2×C4×C5—242no—
369C2×C4×C5—241no—
370C2×C4×C5C2×C4×D312yes—
371C2×C4×C5D3×D412yes—
372C2×C4×C5D3×D411yescharacteristic
373C2×C4×C5C23×D311yescharacteristic
374C22⋊D5—68no—
375C22⋊D5—64no—
376C2×Dic5—61no—
377D20—24no—
378D20—22no—
379D20—32no—
380D20—68no—
381D20—61no—
382D20C2×C4×D314yes—
383C4×D5—68no—
384C4×D5—64no—
385Dic10—32no—
386Dic10—61no—
387#168—22no—
388#168—61no—
389#168—61no—
390H(5,𝔽2)—158no—
391H(5,𝔽2)—304no—
392C2×#41—31no—
393C2×#41—152no—
394C2×#41—151no—
395C2×#41—301no—
396C22×D4—51no—
397C22×D4—152no—
398C22×D4—301no—
399C22×D4—302no—
400#131—304no—
401C2×M16—51no—
402C2×M16—152no—
403C22×C8—152no—
404C22×C8—151no—
405C4×Q8—61no—
406C4×D4—61no—
407C4×D4—62no—
408#117—32no—
409#117D3×D511yescharacteristic, complemented
410C2×C4⋊C4—31no—
411C2×C4⋊C4—32no—
412#103—152no—
413#103—151no—
414#103—151no—
415#102—52no—
416#102—52no—
417#102—152no—
418#102—152no—
419#102—152no—
420#102—151no—
421#102—151no—
422C2×C3×C5—22no—
423C2×C3×C5C22×C22⋊C411yescharacteristic
424C2×C3×C5#57611yescharacteristic
425C2×C3×C5#57711yescharacteristic
426D15—42no—
427C3×D5—44no—
428C5×D3—24no—
429C23×C3—102no—
430C23×C3—104no—
431C23×C3—401no—
432C23×C3—401no—
433C23×C3C2×C22⋊D511yescharacteristic
434C22×D3—101no—
435C22×D3—108no—
436C22×D3—402no—
437C22×D3—402no—
438C22×D3C2×C22⋊D512yes—
439C3×D4—54no—
440C3×D4—102no—
441C3×D4—104no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4C2×C4×D512yes—
445C2×C3×C4C2×D2012yes—
446C2×C3×C4C2×C22⋊D511yescharacteristic
447C2×C3×C4C23×D511yescharacteristic
448#67—104no—
449#67—108no—
450#67—108no—
451#67#68518yes—
452C2×Dic3—22no—
453C2×Dic3—81no—
454C2×Dic3—101no—
455C2×Dic3—108no—
456C2×Dic3C2×C22⋊D512yes—
457D12—52no—
458D12—101no—
459D12#68514yes—
460C4×D3—82no—
461C4×D3—104no—
462C4×D3C2×C4×D514yes—
463C4×D3C2×D2014yes—
464Dic6—52no—
465Dic6—101no—
466Dic6#68514yes—
467C3×C8—102no—
468C3⋊C8—101no—
469C3⋊C8—101no—
470C22×C5—21no—
471C22×C5—21no—
472C22×C5—34no—
473C22×C5—62no—
474C22×C5—62no—
475C22×C5D3×C22⋊C412yes—
476C22×C5C2×D3×D411yescharacteristic
477C2×D5—24no—
478C2×D5—42no—
479C2×D5—42no—
480C2×D5—62no—
481C2×D5—84no—
482C2×D5—121no—
483C2×D5—121no—
484C2×D5—248no—
485C4×C5—34no—
486C4×C5—41no—
487C4×C5—41no—
488C4×C5—122no—
489C4×C5D3×C22⋊C412yes—
490C4×C5C22×C4×D311yescharacteristic
491C4×C5C2×D3×D411yescharacteristic
492Dic5—62no—
493C24—101no—
494C24—302no—
495#41—34no—
496#41—34no—
497#41—158no—
498#41—154no—
499#41—304no—
500#41—308no—
501#41—302no—
502C2×Q8—31no—
503C2×Q8—151no—
504C2×D4—32no—
505C2×D4—31no—
506C2×D4—54no—
507C2×D4—52no—
508C2×D4—102no—
509C2×D4—101no—
510C2×D4—158no—
511C2×D4—151no—
512C2×D4—304no—
513C2×D4—302no—
514C2×D4—308no—
515C2×D4—3016no—
516C2×D4—302no—
517C2×D4—301no—
518C22×C4—32no—
519C22×C4—62no—
520C22×C4—61no—
521C22×C4—302no—
522C22×C4—301no—
523C22×C4C2×D3×D511yescharacteristic
524M16—102no—
525M16—304no—
526C2×C8—52no—
527C2×C8—151no—
528C2×C8—151no—
529C2×C8—304no—
530C2×C8—302no—
531C4⋊C4—32no—
532C4⋊C4—62no—
533C4⋊C4—61no—
534C4⋊C4C2×D3×D511yescharacteristic
535C4⋊C4C2×D3×D511yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—62no—
538C42—21no—
539C42—62no—
540C3×C5#289711yescharacteristic, complemented, Hall
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—104no—
544C22×C3—202no—
545C22×C3—202no—
546C22×C3—404no—
547C22×C3C2×#68512yes—
548C22×C3C22×C22⋊D511yescharacteristic
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—102no—
552C2×D3—201no—
553C2×D3—201no—
554C2×D3—408no—
555C2×D3C2×#68514yes—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4C2×#68512yes—
559C3×C4C22×C4×D511yescharacteristic
560C3×C4C22×D2011yescharacteristic
561Dic3—42no—
562Dic3—102no—
563Dic3C2×#68514yes—
564C2×C5—22no—
565C2×C5—64no—
566C2×C5C2×D3×C22⋊C411yescharacteristic
567C2×C5#577411yescharacteristic
568C2×C5#577511yescharacteristic
569D5—44no—
570D5—122no—
571C23—32no—
572C23—102no—
573C23—104no—
574C23—308no—
575C23—301no—
576C23—401no—
577C23—401no—
578C23—1202no—
579C23—1202no—
580C23D3×C22⋊D511yescharacteristic
581Q8—34no—
582Q8—152no—
583Q8—301no—
584D4—38no—
585D4—34no—
586D4—54no—
587D4—104no—
588D4—102no—
589D4—152no—
590D4—308no—
591D4—308no—
592D4—304no—
593D4—301no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—32no—
597C2×C4—34no—
598C2×C4—34no—
599C2×C4—62no—
600C2×C4—242no—
601C2×C4—241no—
602C2×C4—308no—
603C2×C4—301no—
604C2×C4—304no—
605C2×C4C4×D3×D512yes—
606C2×C4D3×D2012yes—
607C2×C4D3×C22⋊D511yescharacteristic
608C2×C4C22×D3×D511yescharacteristic
609C8—102no—
610C8—301no—
611C8—301no—
612C2×C3—22no—
613C2×C3—204no—
614C2×C3C22×#68511yescharacteristic
615C2×C3#6616911yescharacteristic
616C2×C3#6617111yescharacteristic
617D3—24no—
618D3—202no—
619C5#7892511yescharacteristic, complemented, Sylow
620C22—21no—
621C22—21no—
622C22—34no—
623C22—62no—
624C22—62no—
625C22—104no—
626C22—202no—
627C22—202no—
628C22—302no—
629C22—404no—
630C22—601no—
631C22—601no—
632C22—1208no—
633C22D3×#68512yes—
634C22C2×D3×C22⋊D511yescharacteristic
635C4—34no—
636C4—41no—
637C4—41no—
638C4—122no—
639C4—302no—
640C4D3×#68512yes—
641C4C2×C4×D3×D511yescharacteristic
642C4C2×D3×D2011yescharacteristic
643C3#1061429411yescharacteristic, complemented, Sylow
644C2—22no—
645C2—64no—
646C2—204no—
647C2—602no—
648C2C2×D3×#68511yescharacteristic
649C2#1175532311yescharacteristic
650C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#92017C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C5×#5523C2semidirect
3. C2×#91288C2semidirect
4. #11751103C2semidirect
5. C3×#65290C2semidirect
6. #11748394C2semidirect
7. C2×#90964C2semidirect
8. #11747503C2semidirect
9. #11747502C2semidirect
10. #11747477C2semidirect
11. D3×#3941C2semidirect
18. #92017C4semidirect
23. C3×C5×#117C22semidirect
24. C22×C3⋊#168C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C5×#892C22semidirect
27. C5×D3×C4⋊C4C22semidirect
31. C2×C3×#681C22semidirect
32. C2×#6650C22semidirect
34. C2×D3×#168C22semidirect
35. #91094C22semidirect
36. #91094C22semidirect
37. #91093C22semidirect
38. #91093C22semidirect
39. C3×#3941C22semidirect
40. C3×#3941C22semidirect
41. #90975C22semidirect
42. #90969C22semidirect
43. #90964C22semidirect
44. #90964C22semidirect
52. #65290D3semidirect
62. #6817C2×C4semidirect
76. C2×C3×D20C2×C4semidirect
84. D3×D20C2×C4semidirect
87. #6765C2×C4semidirect
106. #5523D5semidirect
129. C5×#117C2×D3semidirect
134. C2×#681C2×D3semidirect
145. #3941C2×D3semidirect
146. #3941C2×D3semidirect
200. C3×#117C2×D5semidirect
201. C2×C4⋊Dic3C2×D5semidirect
206. #892C2×D5semidirect
207. D3×C4⋊C4C2×D5semidirect
247. C2×D20C4×D3semidirect
409. #117D3×D5semidirect
540. C3×C5#2897semidirect
619. C5#78925semidirect
643. C3#10614294semidirect

Maximal subgroups

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

subgroupindex
C2×#920172
C5×#55232
C2×#912882
#117511032
C3×#652902
#117483942
C2×#909642
#117475032
#117475022
#117474772
D3×#39412
#106142943
#789255