Finite Group Databasebeta

← #14471777

Subgroups — #14471777

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5681C211yesmaximal, characteristic, complemented
2#11752616C211yesmaximal, characteristic, complemented
3#11751158C211yesmaximal, characteristic, complemented
4C3×#65345C211yesmaximal, characteristic, complemented
5#11749359C211yesmaximal, characteristic, complemented
6#11749236C211yesmaximal, characteristic, complemented
7#11749232C211yesmaximal, characteristic, complemented
8#11749188C211yesmaximal, characteristic, complemented
9#11749087C211yesmaximal, characteristic, complemented
10#11748987C211yesmaximal, characteristic
11#11748986C211yesmaximal, characteristic, complemented
12#11748941C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11746902C211yesmaximal, characteristic, complemented
15Dic6×#168C211yesmaximal, characteristic, complemented
16#10615444—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18C2×#6717C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×#947C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C5×#940C2211yescharacteristic
24C5×D4×Dic3C2211yescharacteristic
25C5×#886—21no—
26C5×#885—21no—
27C5×#883—21no—
28C5×#67⋊C4—21no—
29C4×C5×D12C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic
31C3×#4016C2211yescharacteristic
32#91469C2211yescharacteristic
33#91428C2211yescharacteristic
34#91428C2211yescharacteristic
35#91424—21no—
36#91419—21no—
37#91404—21no—
38#91381C2211yescharacteristic
39#91377—21no—
40C2×#6654C2211yescharacteristic
41#91119C2211yescharacteristic
42#91116C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×C4×#168C2211yescharacteristic
49#90989C2211yescharacteristic
50#90988C2211yescharacteristic
51#90986C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90969C2211yescharacteristic
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81633—51nomaximal, Hall
61C5×#559—31no—
62#65913—31no—
63#65361—31no—
64#65359—31no—
65#65346—31no—
66#65346—31no—
67#65345—31no—
68#65345D311yescharacteristic, complemented
69C4×#688—31no—
70Q8×#168—31no—
71#65310—31no—
72C4×#686—31no—
73C4×#686—31no—
74#65298—31no—
75#65298—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×C5×#67—21no—
81C2×C5×#67—21no—
82C22×C5×Dic3—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C5×Dic6D411yescharacteristic
86C2×#1204—21no—
87C2×#1200—21no—
88C2×#1200—21no—
89C3×C5×C22⋊C4—21no—
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92#6717—22no—
93#6715—22no—
94#6714—21no—
95C4⋊Dic15C2311yescharacteristic
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×(C2×D3)⋊C4—21no—
100C5×(C2×D3)⋊C4—21no—
101C5×(C2×D3)⋊C4—21no—
102C5×C4⋊Dic3—21no—
103C5×C4⋊Dic3D411yescharacteristic
104C5×C4⋊Dic3C2311yescharacteristic
105C5×Dic3⋊C4D411yescharacteristic
106C5×Dic3⋊C4D411yescharacteristic
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×#683—21no—
114C2×C3×#168C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119#6667—21no—
120#6667—21no—
121#6654—22no—
122#5690—51no—
123#5681D511yescharacteristic, complemented
124C3×#488—51no—
125#5066—51no—
126#5057—51no—
127#4819—51no—
128#4800—51no—
129#4793—51no—
130#4788—51no—
131#4786—51no—
132#4766—51no—
133#4760—51no—
134#4756—51no—
135C4×D24—51no—
136C8×Dic6—51no—
137C5×#127—31no—
138C5×#124—31no—
139C5×#124—61no—
140C5×#124C2×D311yescharacteristic
141C5×#123—61no—
142C5×#123—61no—
143C4×C5×Q8—31no—
144C4×C5×Q8—31no—
145C4×C5×D4—31no—
146C4×C5×D4—31no—
147C4×C5×D4—61no—
148#4092—61no—
149C2×#688—31no—
150C2×#686—31no—
151C2×#686—31no—
152#4042—61no—
153#4042—61no—
154D5×C4⋊C4—61no—
155C4×D20—31no—
156C4×D20—31no—
157C4×D20—31no—
158#4016—31no—
159#4016C2×D311yescharacteristic
160#4015—31no—
161#3967—31no—
162#3967C2×D311yescharacteristic
163#3967C2×D311yescharacteristic
164#3964—31no—
165#3964—31no—
166#3964—31no—
167#3964—31no—
168#3964C2×D311yescharacteristic
169#3964C2×D311yescharacteristic
170#3941—31no—
171#3940—31no—
172#3939—31no—
173#3939—31no—
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4×#168—31no—
178C4×#168—31no—
179C4×#168C2×D311yescharacteristic
180#3361—151noSylow
181C23×C3×C5—21no—
182C22×D15—21no—
183C22×C5×D3—21no—
184C3×C5×Q8—21no—
185C3×C5×Q8—21no—
186C3×C5×D4—21no—
187C3×C5×D4—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2411yescharacteristic
192C2×Dic15—21no—
193D60—21no—
194D60#4112yes—
195C4×D15—81no—
196C5×#67—42no—
197C5×#67—81no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—81no—
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C2×C5×Dic3C2×D411yescharacteristic
204C5×D12—21no—
205C5×D12—21no—
206C4×C5×D3—81no—
207C5×Dic6—22no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210#1204—81no—
211#1200—42no—
212#1200—81no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C3×#125—51no—
218C3×#124C2×D511yescharacteristic
219#947C2×D511yescharacteristic
220Q8×Dic3C2×D511yescharacteristic
221C2×#215—51no—
222#940C2×D511yescharacteristic
223D4×Dic3C2×D511yescharacteristic
224C2×#213—51no—
225C2×D24—51no—
226#897—101no—
227#896—101no—
228#896—101no—
229#893—51no—
230#893—51no—
231D3×C4⋊C4—101no—
232#890—51no—
233#888—51no—
234#886—21no—
235#885—21no—
236#883—21no—
237#67⋊C4—21no—
238C4×D12—51no—
239C4×D12C2×D511yescharacteristic
240C4×Dic6C2×D511yescharacteristic
241C3×#103—51no—
242C3×#103—51no—
243C3×#102—51no—
244C3×#102—51no—
245C3×C4×C8—51no—
246#835—51no—
247#832—51no—
248#821—51no—
249#821—51no—
250#818—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253C8×Dic3—51no—
254C8×Dic3—51no—
255#809—51no—
256#809—51no—
257#808—51no—
258#807—51no—
259C4⋊(C3⋊C8)—51no—
260C2×C5×Q8—31no—
261C2×C5×Q8C22×D311yescharacteristic
262C2×C5×D4—31no—
263C2×C5×D4—61no—
264C2×C5×D4—61no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—61no—
267C22×C4×C5—61no—
268C2×D20—31no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×Dic10—61no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—61no—
278C5×C22⋊C4—21no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—61no—
281C5×C22⋊C4—61no—
282C5×C22⋊C4—61no—
283C5×C22⋊C4—61no—
284C42×C5—31no—
285C42×C5—31no—
286C42×C5—61no—
287C42×C5C22×D311yescharacteristic
288#688—62no—
289#686—62no—
290#686—62no—
291#685—61no—
292#685—61no—
293#685—61no—
294C4⋊Dic5—31no—
295C4⋊Dic5—61no—
296C4⋊Dic5C22×D311yescharacteristic
297C4⋊Dic5C22×D311yescharacteristic
298#683—21no—
299#683—21no—
300#683—61no—
301#683—61no—
302C2×#168—31no—
303C2×#168—31no—
304C2×#168C22×D311yescharacteristic
305C2×#168C22×D311yescharacteristic
306#559—31no—
307#554—151no—
308#488—51no—
309#488—151no—
310#486—151no—
311#478—151no—
312#478—151no—
313#477—151no—
314#463—151no—
315#463—151no—
316#459—151no—
317C8×Q8—151no—
318C4×SD16—151no—
319C4×D8—151no—
320C4×D8—151no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C22×D411yescharacteristic
325C2×D15—22no—
326C2×D15—41no—
327C2×D15—41no—
328C2×C5×D3—41no—
329C2×C5×D3—41no—
330C2×C5×D3—41no—
331C3×C4×C5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C52−1+411yescharacteristic
336Dic15—41no—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C5×Dic3—21no—
340C5×Dic3—21no—
341C5×Dic3—21no—
342C5×Dic3—41no—
343C5×Dic3#13512yes—
344C2×C3×Q8C22×D511yescharacteristic
345C2×C3×D4C22×D511yescharacteristic
346C2×#67—21no—
347C2×#67—21no—
348C22×Dic3—21no—
349C2×D12—51no—
350C2×D12C22×D511yescharacteristic
351C2×C4×D3—21no—
352C2×C4×D3—101no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×Dic6—101no—
356C2×Dic6C22⋊D511yescharacteristic
357C2×C3×C8—51no—
358C2×C3×C8—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C42C22×D511yescharacteristic
366#217—21no—
367#215—102no—
368#213—102no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—101no—
373(C2×D3)⋊C4—101no—
374(C2×D3)⋊C4—101no—
375C4⋊Dic3—21no—
376C4⋊Dic3—51no—
377C4⋊Dic3—101no—
378C4⋊Dic3C22⋊D511yescharacteristic
379C4⋊Dic3C22×D511yescharacteristic
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4C22⋊D511yescharacteristic
383Dic3⋊C4C22⋊D511yescharacteristic
384C4×Dic3—21no—
385C4×Dic3C22×D511yescharacteristic
386C4×Dic3C22×D511yescharacteristic
387C2×C3⋊C8—51no—
388C2×C3⋊C8—51no—
389D24—102no—
390C23×C5—21no—
391C23×C5—61no—
392C22×D5—61no—
393C5×Q8—21no—
394C5×Q8—21no—
395C5×Q8—62no—
396C5×D4—21no—
397C5×D4—21no—
398C5×D4—61no—
399C5×D4—61no—
400C5×D4—122no—
401C5×D4—241no—
402C2×C4×C5—21no—
403C2×C4×C5—31no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—61no—
408C2×C4×C5—241no—
409C2×C4×C5—241no—
410C2×C4×C5D3×D411yescharacteristic
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—61no—
416D20—32no—
417D20—61no—
418C4×D5—122no—
419C4×D5—241no—
420C4×D5—241no—
421Dic10—241no—
422#168—21no—
423#168—21no—
424#168—61no—
425#168—61no—
426C2×SD16—151no—
427C2×D8—151no—
428C2×D8—151no—
429C4⋊Q8—151no—
430#127—31no—
431#125—51no—
432#125—151no—
433#124—31no—
434#124—61no—
435#124D3×D511yescharacteristic
436#123—61no—
437#123—61no—
438C22⋊Q8—301no—
439C22⋊Q8—301no—
440C22⋊Q8—301no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—61no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—151no—
449C2×C4⋊C4—301no—
450#107—151no—
451#107—151no—
452#106—151no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—51no—
457#103—51no—
458#103—151no—
459#102—51no—
460#102—51no—
461#102—151no—
462#102—151no—
463#102—151no—
464#102—151no—
465#102—151no—
466C4×C8—51no—
467C4×C8—151no—
468C4×C8—151no—
469C2×C3×C5—81no—
470C2×C3×C5#54811yescharacteristic
471C2×C3×C5C2×#13511yescharacteristic
472C2×C3×C5#57611yescharacteristic
473D15—42no—
474C5×D3—81no—
475C23×C3—21no—
476C22×D3—21no—
477C22×D3—101no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×D4—21no—
481C3×D4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—101no—
484C2×C3×C4—101no—
485C2×C3×C4C2×C22⋊D511yescharacteristic
486C2×C3×C4C2×C22⋊D511yescharacteristic
487C2×C3×C4C23×D511yescharacteristic
488#67—42no—
489#67—81no—
490C2×Dic3—21no—
491C2×Dic3—81no—
492C2×Dic3—101no—
493C2×Dic3C2×C22⋊D511yescharacteristic
494C2×Dic3C2×C22⋊D511yescharacteristic
495C2×Dic3C2×C22⋊D511yescharacteristic
496C2×Dic3C2×C22⋊D511yescharacteristic
497D12—21no—
498D12—21no—
499D12—52no—
500D12—101no—
501C4×D3—81no—
502C4×D3—202no—
503C4×D3—401no—
504C4×D3—401no—
505Dic6—22no—
506Dic6—401no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—121no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C2×D3×D411yescharacteristic
518C2×D5—62no—
519C2×D5—121no—
520C2×D5—121no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—32no—
524C4×C5—41no—
525C4×C5—61no—
526C4×C5—61no—
527C4×C5—61no—
528C4×C5—121no—
529C4×C5D3×#4111yescharacteristic
530C4×C5#101011yescharacteristic
531Dic5—41no—
532Dic5—41no—
533Dic5—121no—
534C2×Q8—31no—
535C2×Q8—301no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4—151no—
541C2×D4C2×D3×D511yescharacteristic
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—301no—
545C22×C4—301no—
546C22×C4—301no—
547SD16—302no—
548D8—302no—
549D8—302no—
550C2×C8—51no—
551C2×C8—51no—
552C2×C8—151no—
553C2×C8—151no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—51no—
559C4⋊C4—51no—
560C4⋊C4—61no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C42—31no—
577C42—31no—
578C42—61no—
579C42C2×D3×D511yescharacteristic
580C3×C5#336111yescharacteristic, complemented, Hall
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3C22×C22⋊D511yescharacteristic
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—102no—
589C2×D3—201no—
590C2×D3—201no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—201no—
595C3×C4—201no—
596C3×C4D5×#4111yescharacteristic
597C3×C4#415011yescharacteristic
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—41no—
602Dic3—201no—
603Dic3#409612yes—
604C2×C5—81no—
605C2×C5—241no—
606C2×C5#567711yescharacteristic
607C2×C5D3×#13511yescharacteristic
608C2×C5#576911yescharacteristic
609D5—122no—
610C23—21no—
611C23—61no—
612C23—301no—
613Q8—21no—
614Q8—21no—
615Q8—62no—
616Q8—1201no—
617D4—21no—
618D4—21no—
619D4—61no—
620D4—61no—
621D4—122no—
622D4—152no—
623D4—241no—
624D4—301no—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—61no—
631C2×C4—101no—
632C2×C4—101no—
633C2×C4—241no—
634C2×C4—241no—
635C2×C4—301no—
636C2×C4—602no—
637C2×C4—1201no—
638C2×C4—1201no—
639C2×C4D3×C22⋊D511yescharacteristic
640C2×C4D3×C22⋊D511yescharacteristic
641C2×C4C22×D3×D511yescharacteristic
642C8—101no—
643C8—101no—
644C8—301no—
645C8—301no—
646C2×C3—81no—
647C2×C3C2×#409611yescharacteristic
648C2×C3#6616511yescharacteristic
649C2×C3#6616911yescharacteristic
650D3—81no—
651D3—202no—
652C5#8163311yescharacteristic, complemented, Sylow
653C22—41no—
654C22—41no—
655C22—41no—
656C22—121no—
657C22—121no—
658C22—121no—
659C22—302no—
660C22—601no—
661C22—601no—
662C22C2×D3×C22⋊D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—32no—
666C4—41no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—121no—
671C4—201no—
672C4—201no—
673C4—601no—
674C4#9202011yescharacteristic
675C4#9202411yescharacteristic
676C3#1061544411yescharacteristic, complemented, Sylow
677C2—81no—
678C2—241no—
679C2—602no—
680C2#1175495111yescharacteristic
681C2D3×#409611yescharacteristic
682C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radical#11748987C2
hypercenter#124D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5681C2semidirect
2. #11752616C2semidirect
3. #11751158C2semidirect
4. C3×#65345C2semidirect
5. #11749359C2semidirect
6. #11749236C2semidirect
7. #11749232C2semidirect
8. #11749188C2semidirect
9. #11749087C2semidirect
11. #11748986C2semidirect
12. #11748941C2semidirect
13. C4×#6654C2semidirect
14. #11746902C2semidirect
15. Dic6×#168C2semidirect
68. #65345D3semidirect
123. #5681D5semidirect
580. C3×C5#3361semidirect
652. C5#81633semidirect
676. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
C5×#56812
#117526162
#117511582
C3×#653452
#117493592
#117492362
#117492322
#117491882
#117490872
#117489872
#117489862
#117489412
C4×#66542
#117469022
Dic6×#1682
#106154443
#816335