Finite Group Databasebeta

← #14471788

Subgroups — #14471788

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×#5559C211yesmaximal, characteristic, complemented
2#11752597C211yesmaximal, characteristic, complemented
3#11751110C211yesmaximal, characteristic, complemented
4C3×C4×#686C211yesmaximal, characteristic, complemented
5#11748982C211yesmaximal, characteristic, complemented
6#11748981C211yesmaximal, characteristic
7#11748942C211yesmaximal, characteristic, complemented
8#11748941C211yesmaximal, characteristic, complemented
9#11747418C211yesmaximal, characteristic, complemented
10#11747395C211yesmaximal, characteristic, complemented
11#11747221C211yesmaximal, characteristic, complemented
12#11747219C211yesmaximal, characteristic, complemented
13#11747027C211yesmaximal, characteristic, complemented
14#11746907C211yesmaximal, characteristic, complemented
15Dic6×#168C211yesmaximal, characteristic, complemented
16#10615444—31nomaximal, Hall
17C3×C4×C5×D4C2211yescharacteristic
18#91759C2211yescharacteristic
19C5×#940C2211yescharacteristic
20C5×#936C2211yescharacteristic
21C5×#929—21no—
22C4×C5×#67—21no—
23C5×#893C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C5×#885—21no—
26C5×#883—21no—
27C5×#875C2211yescharacteristic
28C4×C5×Dic6C2211yescharacteristic
29C2×C3×#686C2211yescharacteristic
30C3×C4×D20C2211yescharacteristic
31#91469C2211yescharacteristic
32#91430—21no—
33Dic3×D20C2211yescharacteristic
34Dic3×D20C2211yescharacteristic
35#91421—21no—
36D5×Dic3⋊C4—21no—
37#91381C2211yescharacteristic
38#91349—21no—
39C2×#6655C2211yescharacteristic
40C2×#6652C2211yescharacteristic
41#91116C2211yescharacteristic
42#91116C2211yescharacteristic
43#91092C2211yescharacteristic
44#91091C2211yescharacteristic
45C4⋊(C3⋊#168)C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3941C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4×#168C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90973C2211yescharacteristic
53#90973C2211yescharacteristic
54#90972C2211yescharacteristic
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90966C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#79569—51nomaximal, Hall
61C5×#559—31no—
62#65913—31no—
63#65361—31no—
64#65359—31no—
65#65346—31no—
66#65346—31no—
67#65345—31no—
68#65345—31no—
69C4×#688—31no—
70Q8×#168—31no—
71#65310—31no—
72C4×#686—31no—
73C4×#686D311yescharacteristic, complemented
74#65298—31no—
75#65298—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×C5×#67—21no—
79C2×C5×#67—21no—
80C2×C5×D12C2311yescharacteristic
81C2×C4×C5×D3—21no—
82C2×C5×Dic6D411yescharacteristic
83C2×C5×Dic6C2311yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×#1204—21no—
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95#6712—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×#217—21no—
100C5×(C2×D3)⋊C4—21no—
101C5×(C2×D3)⋊C4—21no—
102C5×(C2×D3)⋊C4—21no—
103C5×C4⋊Dic3D411yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4D411yescharacteristic
106C5×Dic3⋊C4D411yescharacteristic
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C3×#686—22no—
111C3×#685—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6668—21no—
118#6665—21no—
119#6665—21no—
120#6655—22no—
121#6652—22no—
122#5559D511yescharacteristic, complemented
123#5539—51no—
124C3×C4×D8—51no—
125#5153—51no—
126#5150—51no—
127#5016—51no—
128#5009—51no—
129#4891—51no—
130#4875—51no—
131#4768—51no—
132#4760—51no—
133#4758—51no—
134#4756—51no—
135#4697—51no—
136C8×Dic6—51no—
137C5×#127—31no—
138C5×#124—31no—
139C5×#124—31no—
140C5×#124—61no—
141C5×#123—61no—
142C5×#123—61no—
143C4×C5×Q8—31no—
144C4×C5×Q8—31no—
145C4×C5×D4—31no—
146C4×C5×D4—61no—
147C4×C5×D4C2×D311yescharacteristic
148#4092—61no—
149C2×#688—31no—
150C2×#686—31no—
151C2×#686C2×D311yescharacteristic
152#4042—61no—
153#4042—61no—
154D5×C4⋊C4—61no—
155C4×D20—31no—
156C4×D20—31no—
157C4×D20C2×D311yescharacteristic
158#4016—31no—
159#4016—31no—
160#4015—31no—
161#3967—31no—
162#3967—31no—
163#3967—31no—
164#3964—31no—
165#3964—31no—
166#3964—31no—
167#3964—31no—
168#3964—31no—
169#3964C2×D311yescharacteristic
170#3941C2×D311yescharacteristic
171#3940—31no—
172#3939—31no—
173#3939C2×D311yescharacteristic
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×C5×D3—21no—
183C22×C3×D5—21no—
184C3×C5×D4—21no—
185C3×C5×D4—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—81no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15—21no—
193C5×#67—42no—
194C5×#67—81no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C5×D12—21no—
201C5×D12—21no—
202C4×C5×D3—81no—
203C5×Dic6—22no—
204C5×Dic6—21no—
205C5×Dic6—21no—
206C2×C3×Dic5—21no—
207C3×D20—21no—
208C3×D20#4112yes—
209C3×C4×D5—81no—
210#1204—81no—
211D5×Dic3—42no—
212D5×Dic3—81no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C2×C3×D8—51no—
218C3×C4×D4—51no—
219C3×C4×D4C2×D511yescharacteristic
220#940C2×D511yescharacteristic
221#936C2×D511yescharacteristic
222D4×Dic3—51no—
223D4×Dic3—51no—
224C2×#214—51no—
225C2×#213—51no—
226#929—21no—
227C4×#67—21no—
228#924—101no—
229C2×Dic3⋊C4—101no—
230#893C2×D511yescharacteristic
231#890—51no—
232#888—51no—
233#887C2×D511yescharacteristic
234#885—21no—
235#883—21no—
236#878—101no—
237#878—101no—
238#875C2×D511yescharacteristic
239#870—51no—
240C4×Dic6C2×D511yescharacteristic
241C3×#107—51no—
242C3×#102—51no—
243C3×#102—51no—
244C3×C4×C8—51no—
245#832—51no—
246#832—51no—
247#821—51no—
248#821—51no—
249#816—51no—
250#816—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253C8×Dic3—51no—
254C8×Dic3—51no—
255#810—51no—
256#809—51no—
257#808—51no—
258#807—51no—
259C4⋊(C3⋊C8)—51no—
260C2×C5×Q8—31no—
261C2×C5×Q8—31no—
262C2×C5×D4—31no—
263C2×C5×D4—61no—
264C2×C5×D4—61no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—21no—
267C22×C4×C5—61no—
268C2×D20C22×D311yescharacteristic
269C2×C4×D5—21no—
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—61no—
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—21no—
279C5×C22⋊C4—61no—
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—22no—
290#686—62no—
291#685—21no—
292#685—61no—
293#685—61no—
294C4⋊Dic5—31no—
295C4⋊Dic5—31no—
296C4⋊Dic5—61no—
297C4⋊Dic5C22×D311yescharacteristic
298#683—61no—
299#683—61no—
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—151no—
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—51no—
320C4×D8—151no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C22×D411yescharacteristic
325C2×C5×D3—41no—
326C2×C5×D3—41no—
327C2×C5×D3—41no—
328C2×C3×D5—22no—
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C3×C4×C5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C52−1+411yescharacteristic
336Dic15—41no—
337Dic15—41no—
338C3×Dic5—41no—
339C5×Dic3—21no—
340C5×Dic3—21no—
341C5×Dic3—21no—
342C5×Dic3—41no—
343C5×Dic3#13512yes—
344C2×C3×D4—51no—
345C2×C3×D4C22×D511yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—101no—
348C2×#67—21no—
349C2×#67—21no—
350C22×Dic3—101no—
351C22×Dic3—101no—
352C2×D12C22×D511yescharacteristic
353C2×C4×D3—21no—
354C2×Dic6—101no—
355C2×Dic6C22⋊D511yescharacteristic
356C2×Dic6C22×D511yescharacteristic
357C3×D8—102no—
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4C22×D511yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—101no—
364C3×C42C22×D511yescharacteristic
365#217—21no—
366#217—21no—
367#217—101no—
368#217—101no—
369#214—102no—
370#213—102no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3C22⋊D511yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4C22⋊D511yescharacteristic
384Dic3⋊C4C22⋊D511yescharacteristic
385C4×Dic3—21no—
386C4×Dic3C22×D511yescharacteristic
387C4×Dic3C22×D511yescharacteristic
388C2×C3⋊C8—51no—
389C2×C3⋊C8—51no—
390C23×C5—21no—
391C23×C5—61no—
392C22×D5—21no—
393C5×Q8—62no—
394C5×Q8—61no—
395C5×Q8—61no—
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—81no—
409C2×C4×C5—241no—
410C2×C4×C5D3×D411yescharacteristic
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5C23×D311yescharacteristic
413C2×Dic5—21no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416D20—21no—
417D20#23512yes—
418C4×D5—81no—
419C4×D5—122no—
420C4×D5—241no—
421Dic10—241no—
422#168—21no—
423#168—21no—
424#168—61no—
425#168—61no—
426C2×SD16—151no—
427C2×D8—51no—
428C2×D8—151no—
429C4⋊Q8—151no—
430#127—31no—
431#125—151no—
432#125—151no—
433#124—31no—
434#124—31no—
435#124—61no—
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—51no—
445C4×D4—61no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4D3×D511yescharacteristic
449C2×C4⋊C4—301no—
450#107—51no—
451#107—151no—
452#106—151no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—151no—
457#103—151no—
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
473C3×D5—42no—
474C5×D3—81no—
475C23×C3—21no—
476C23×C3—101no—
477C22×D3—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—52no—
481C3×D4—101no—
482C2×C3×C4—21no—
483C2×C3×C4—81no—
484C2×C3×C4—101no—
485C2×C3×C4—401no—
486C2×C3×C4C2×C22⋊D511yescharacteristic
487C2×C3×C4C2×C22⋊D511yescharacteristic
488C2×C3×C4C23×D511yescharacteristic
489#67—42no—
490#67—81no—
491C2×Dic3—21no—
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3—202no—
495C2×Dic3—401no—
496C2×Dic3C2×C22⋊D511yescharacteristic
497C2×Dic3C2×C22⋊D511yescharacteristic
498C2×Dic3C2×C22⋊D511yescharacteristic
499C2×Dic3C2×C22⋊D511yescharacteristic
500D12—21no—
501D12—21no—
502C4×D3—81no—
503Dic6—22no—
504Dic6—21no—
505Dic6—21no—
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—22no—
519C2×D5—41no—
520C2×D5—41no—
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×C5C2×#23511yescharacteristic
530C4×C5#101011yescharacteristic
531Dic5—41no—
532Dic5—121no—
533Dic5—121no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×Q8—301no—
537C2×D4—31no—
538C2×D4—51no—
539C2×D4—61no—
540C2×D4—61no—
541C2×D4C2×D3×D511yescharacteristic
542C22×C4—21no—
543C22×C4—61no—
544C22×C4—101no—
545C22×C4—301no—
546C22×C4—301no—
547SD16—302no—
548D8—102no—
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—51no—
558C4⋊C4—61no—
559C4⋊C4—151no—
560C4⋊C4—151no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4C2×D3×D511yescharacteristic
567C22⋊C4—21no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—101no—
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×C3—102no—
585C22×C3—201no—
586C22×C3—201no—
587C22×C3C22×C22⋊D511yescharacteristic
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—201no—
595C3×C4D5×#4111yescharacteristic
596C3×C4#415011yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603Dic3#409612yes—
604C2×C5—81no—
605C2×C5—241no—
606C2×C5#555211yescharacteristic
607C2×C5#575711yescharacteristic
608C2×C5D3×#13511yescharacteristic
609D5—42no—
610C23—21no—
611C23—61no—
612C23—101no—
613Q8—62no—
614Q8—61no—
615Q8—61no—
616Q8—1201no—
617D4—21no—
618D4—21no—
619D4—52no—
620D4—61no—
621D4—61no—
622D4—101no—
623D4—122no—
624D4—241no—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—61no—
631C2×C4—81no—
632C2×C4—101no—
633C2×C4—241no—
634C2×C4—301no—
635C2×C4—301no—
636C2×C4—401no—
637C2×C4—602no—
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×C3—202no—
648C2×C3C2×#409611yescharacteristic
649C2×C3#6616511yescharacteristic
650C2×C3#6616911yescharacteristic
651D3—81no—
652C5#7956911yescharacteristic, complemented, Sylow
653C22—41no—
654C22—41no—
655C22—41no—
656C22—102no—
657C22—121no—
658C22—121no—
659C22—121no—
660C22—201no—
661C22—201no—
662C22C2×D3×C22⋊D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—32no—
666C4—41no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—121no—
671C4—201no—
672C4—601no—
673C4—601no—
674C4#9200111yescharacteristic
675C4D5×#23511yescharacteristic
676C3#1061544411yescharacteristic, complemented, Sylow
677C2—81no—
678C2—202no—
679C2—241no—
680C2#1175433811yescharacteristic
681C2#1175469711yescharacteristic
682C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11748981C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5559C2semidirect
2. #11752597C2semidirect
3. #11751110C2semidirect
4. C3×C4×#686C2semidirect
5. #11748982C2semidirect
7. #11748942C2semidirect
8. #11748941C2semidirect
9. #11747418C2semidirect
10. #11747395C2semidirect
11. #11747221C2semidirect
12. #11747219C2semidirect
13. #11747027C2semidirect
14. #11746907C2semidirect
15. Dic6×#168C2semidirect
73. C4×#686D3semidirect
122. #5559D5semidirect
580. C3×C5#3361semidirect
652. C5#79569semidirect
676. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
C5×#55592
#117525972
#117511102
C3×C4×#6862
#117489822
#117489812
#117489422
#117489412
#117474182
#117473952
#117472212
#117472192
#117470272
#117469072
Dic6×#1682
#106154443
#795695