Finite Group Databasebeta

← #14471618

Subgroups — #14471618

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5671C211yesmaximal, characteristic, complemented
2#11752616C211yesmaximal, characteristic, complemented
3#11751158C211yesmaximal, characteristic
4C3×#65345C211yesmaximal, characteristic, complemented
5#11749333C211yesmaximal, characteristic, complemented
6#11749233C211yesmaximal, characteristic, complemented
7#11749232C211yesmaximal, characteristic, complemented
8#11749187C211yesmaximal, characteristic, complemented
9#11749113C211yesmaximal, characteristic, complemented
10#11748990C211yesmaximal, characteristic
11#11748986C211yesmaximal, characteristic
12#11748942C211yesmaximal, characteristic, complemented
13C4×#6660C211yesmaximal, characteristic, complemented
14#11746926C211yesmaximal, characteristic, complemented
15Dic6×#168C211yesmaximal, characteristic, complemented
16#10615398—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18C2×#6717C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C5×#944C2211yescharacteristic
23C5×#936C2211yescharacteristic
24C5×D4×Dic3C2211yescharacteristic
25C5×#879—21no—
26C5×#879—21no—
27C5×#878—21no—
28C5×#877—21no—
29C4×C5×Dic6C2211yescharacteristic
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×#6660C2211yescharacteristic
41#91119C2211yescharacteristic
42#91116C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C3×#3967C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×C4×#168C2211yescharacteristic
49#90989C2211yescharacteristic
50#90986C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90973C2211yescharacteristic
55#90972C2211yescharacteristic
56#90972C2211yescharacteristic
57#90969C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#81632—51nomaximal, Hall
61C5×#556—31no—
62#65913—31no—
63#65372—31no—
64#65370—31no—
65#65346—31no—
66#65346—31no—
67#65345—31no—
68#65345D311yescharacteristic, complemented
69C4×#688—31no—
70C4×#688—31no—
71Q8×#168—31no—
72#65311—31no—
73#65311—31no—
74C4×#686—31no—
75#65297—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C22×C5×Dic3—21no—
81C2×C5×Dic6D411yescharacteristic
82C2×C5×Dic6C2311yescharacteristic
83C2×#1204—21no—
84C2×#1200—21no—
85C2×#1200—21no—
86C3×C5×C22⋊C4—21no—
87C3×C5×C22⋊C4—21no—
88C3×C42×C5C2311yescharacteristic
89#6717—22no—
90#6715—22no—
91#6714—21no—
92C4⋊Dic15C2311yescharacteristic
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#217—21no—
96C5×#217—21no—
97C5×#217—21no—
98C5×C4⋊Dic3—21no—
99C5×C4⋊Dic3D411yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4D411yescharacteristic
105C5×Dic3⋊C4D411yescharacteristic
106C4×C5×Dic3—21no—
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#6660—22no—
122#5690—51no—
123#5671D511yescharacteristic, complemented
124C3×#488—51no—
125#5063—51no—
126#5057—51no—
127#4818—51no—
128#4799—51no—
129#4792—51no—
130#4788—51no—
131#4787—51no—
132#4768—51no—
133#4761—51no—
134#4756—51no—
135C4×#204—51no—
136C8×Dic6—51no—
137C5×C4⋊Q8—31no—
138C5×#126—61no—
139C5×#126—61no—
140C5×#124—31no—
141C5×#124C2×D311yescharacteristic
142C5×C22⋊Q8—61no—
143C4×C5×Q8—31no—
144C4×C5×Q8—31no—
145C4×C5×Q8—31no—
146C4×C5×D4—31no—
147C5×#117—61no—
148#4092—61no—
149C2×#688—31no—
150C2×#688—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#3967—31no—
163#3967—31no—
164#3967—31no—
165#3967C2×D311yescharacteristic
166#3967C2×D311yescharacteristic
167#3964—31no—
168#3964C2×D311yescharacteristic
169#3964C2×D311yescharacteristic
170#3941—31no—
171#3940—31no—
172#3940—31no—
173#3939—31no—
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4×#168—31no—
178C4×#168—31no—
179C4×#168C2×D311yescharacteristic
180#3360—151noSylow
181C23×C3×C5—21no—
182C22×D15—21no—
183C3×C5×Q8—21no—
184C3×C5×Q8—21no—
185C3×C5×D4—21no—
186C3×C5×D4—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192D60—21no—
193D60#4112yes—
194C4×D15—81no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—42no—
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C5×Dic6—22no—
203C5×Dic6—21no—
204C5×Dic6—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207#1204—81no—
208#1200—42no—
209#1200—81no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C3×#168—21no—
213C3×#168—21no—
214C3×#125—51no—
215C3×#124C2×D511yescharacteristic
216Q8×Dic3C2×D511yescharacteristic
217#944C2×D511yescharacteristic
218C2×#215—51no—
219#936C2×D511yescharacteristic
220D4×Dic3C2×D511yescharacteristic
221C2×#213—51no—
222C2×#204—51no—
223#897—101no—
224#896—101no—
225#896—101no—
226#893—51no—
227#893—51no—
228D3×C4⋊C4—101no—
229#890—51no—
230#888—51no—
231#879—21no—
232#879—21no—
233#878—21no—
234#877—21no—
235C4×D12—51no—
236C4×Dic6C2×D511yescharacteristic
237C4×Dic6C2×D511yescharacteristic
238C3×#103—51no—
239C3×#103—51no—
240C3×#102—51no—
241C3×#102—51no—
242C3×C4×C8—51no—
243#835—51no—
244#832—51no—
245#821—51no—
246#817—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250C8×Dic3—51no—
251C8×Dic3—51no—
252#810—51no—
253#810—51no—
254#808—51no—
255#807—51no—
256C4⋊(C3⋊C8)—51no—
257C2×C5×Q8—31no—
258C2×C5×Q8—31no—
259C2×C5×Q8C22×D311yescharacteristic
260C2×C5×D4C22×D311yescharacteristic
261C22×C4×C5—61no—
262C2×D20—31no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C2×C4×D5—61no—
266C2×Dic10—61no—
267C5×C4⋊C4—31no—
268C5×C4⋊C4—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—31no—
271C5×C4⋊C4—61no—
272C5×C4⋊C4—61no—
273C5×C4⋊C4—61no—
274C5×C4⋊C4—61no—
275C5×C22⋊C4—21no—
276C5×C22⋊C4—21no—
277C5×C22⋊C4—61no—
278C5×C22⋊C4—61no—
279C5×C22⋊C4—61no—
280C42×C5—31no—
281C42×C5—31no—
282C42×C5—61no—
283C42×C5—61no—
284C42×C5C22×D311yescharacteristic
285#688—62no—
286#688—62no—
287#686—62no—
288#685—61no—
289#685—61no—
290#685—61no—
291C4⋊Dic5—31no—
292C4⋊Dic5—61no—
293C4⋊Dic5C22×D311yescharacteristic
294C4⋊Dic5C22×D311yescharacteristic
295#683—21no—
296#683—21no—
297#683—61no—
298#683—61no—
299C2×#168—31no—
300C2×#168—31no—
301C2×#168C22×D311yescharacteristic
302C2×#168C22×D311yescharacteristic
303#556—31no—
304#554—151no—
305#488—51no—
306#488—151no—
307#487—151no—
308#479—151no—
309#479—151no—
310#476—151no—
311#463—151no—
312#463—151no—
313#461—151no—
314C8×Q8—151no—
315C4×SD16—151no—
316C4×SD16—151no—
317C4×D8—151no—
318C22×C3×C5—41no—
319C22×C3×C5—41no—
320C22×C3×C5—41no—
321C22×C3×C5C22×D411yescharacteristic
322C2×D15—22no—
323C2×D15—41no—
324C2×D15—41no—
325C3×C4×C5—21no—
326C3×C4×C5—21no—
327C3×C4×C5—41no—
328C3×C4×C5C2×#4111yescharacteristic
329C3×C4×C52−1+411yescharacteristic
330Dic15—41no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C5×Dic3—21no—
334C5×Dic3—21no—
335C5×Dic3—21no—
336C5×Dic3—41no—
337C5×Dic3—41no—
338C5×Dic3#13512yes—
339C2×C3×Q8C22×D511yescharacteristic
340C2×C3×D4C22×D511yescharacteristic
341C22×Dic3—21no—
342C2×D12—51no—
343C2×C4×D3—101no—
344C2×C4×D3—101no—
345C2×C4×D3—101no—
346C2×Dic6—101no—
347C2×Dic6C22⋊D511yescharacteristic
348C2×Dic6C22×D511yescharacteristic
349C2×C3×C8—51no—
350C2×C3×C8—51no—
351C3×C4⋊C4—51no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4—101no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C42C22×D511yescharacteristic
358#217—21no—
359#217—21no—
360#217—21no—
361#215—102no—
362#213—102no—
363(C2×D3)⋊C4—101no—
364(C2×D3)⋊C4—101no—
365(C2×D3)⋊C4—101no—
366C4⋊Dic3—21no—
367C4⋊Dic3—51no—
368C4⋊Dic3—101no—
369C4⋊Dic3C22⋊D511yescharacteristic
370C4⋊Dic3C22×D511yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376Dic3⋊C4C22⋊D511yescharacteristic
377Dic3⋊C4C22⋊D511yescharacteristic
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3C22×D511yescharacteristic
381C4×Dic3C22×D511yescharacteristic
382C2×C3⋊C8—51no—
383C2×C3⋊C8—51no—
384#204—102no—
385C23×C5—21no—
386C22×D5—61no—
387C5×Q8—21no—
388C5×Q8—21no—
389C5×Q8—62no—
390C5×Q8—61no—
391C5×Q8—61no—
392C5×D4—21no—
393C5×D4—21no—
394C2×C4×C5—21no—
395C2×C4×C5—31no—
396C2×C4×C5—31no—
397C2×C4×C5—31no—
398C2×C4×C5—31no—
399C2×C4×C5—61no—
400C2×C4×C5—61no—
401C2×C4×C5—122no—
402C2×C4×C5D3×D411yescharacteristic
403C2×C4×C5D3×D411yescharacteristic
404C2×C4×C5C23×D311yescharacteristic
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—61no—
408D20—32no—
409D20—61no—
410C4×D5—122no—
411C4×D5—241no—
412C4×D5—241no—
413Dic10—241no—
414#168—21no—
415#168—21no—
416#168—61no—
417#168—61no—
418C2×SD16—151no—
419C2×SD16—151no—
420C2×D8—151no—
421C4⋊Q8—31no—
422C4⋊Q8—151no—
423#126—61no—
424#126—61no—
425#125—51no—
426#125—151no—
427#124—31no—
428#124D3×D511yescharacteristic
429C22⋊Q8—61no—
430C22⋊Q8—301no—
431C22⋊Q8—301no—
432C22⋊Q8—301no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×Q8—31no—
436C4×D4—31no—
437C4×D4—151no—
438C4×D4—151no—
439C4×D4—151no—
440#117—61no—
441C2×C4⋊C4—301no—
442#107—151no—
443#106—151no—
444#106—151no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—51no—
449#103—51no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#102—51no—
455#102—51no—
456#102—151no—
457#102—151no—
458C4×C8—51no—
459C4×C8—151no—
460C4×C8—151no—
461C2×C3×C5—81no—
462C2×C3×C5#54811yescharacteristic
463C2×C3×C5C2×#13511yescharacteristic
464C2×C3×C5#57711yescharacteristic
465D15—42no—
466C23×C3—21no—
467C22×D3—101no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×D4—21no—
471C3×D4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—101no—
474C2×C3×C4—101no—
475C2×C3×C4C2×C22⋊D511yescharacteristic
476C2×C3×C4C2×C22⋊D511yescharacteristic
477C2×C3×C4C23×D511yescharacteristic
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—42no—
481C2×Dic3—101no—
482C2×Dic3C2×C22⋊D511yescharacteristic
483C2×Dic3C2×C22⋊D511yescharacteristic
484C2×Dic3C2×C22⋊D511yescharacteristic
485C2×Dic3C2×C22⋊D511yescharacteristic
486D12—52no—
487D12—101no—
488C4×D3—202no—
489C4×D3—401no—
490C4×D3—401no—
491Dic6—22no—
492Dic6—21no—
493Dic6—21no—
494Dic6—401no—
495C3×C8—101no—
496C3×C8—101no—
497C3⋊C8—101no—
498C3⋊C8—101no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5C2×D3×D411yescharacteristic
503C2×D5—62no—
504C2×D5—121no—
505C2×D5—121no—
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—32no—
509C4×C5—41no—
510C4×C5—61no—
511C4×C5—61no—
512C4×C5—61no—
513C4×C5—121no—
514C4×C5—121no—
515C4×C5D3×#4111yescharacteristic
516C4×C5#101011yescharacteristic
517Dic5—41no—
518Dic5—41no—
519Dic5—121no—
520C2×Q8—31no—
521C2×Q8—31no—
522C2×Q8—301no—
523C2×Q8C2×D3×D511yescharacteristic
524C2×D4—151no—
525C2×D4C2×D3×D511yescharacteristic
526C22×C4—61no—
527C22×C4—301no—
528C22×C4—301no—
529C22×C4—301no—
530SD16—302no—
531SD16—302no—
532D8—302no—
533C2×C8—51no—
534C2×C8—51no—
535C2×C8—151no—
536C2×C8—151no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—51no—
542C4⋊C4—51no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—101no—
548C4⋊C4—101no—
549C4⋊C4—151no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4—301no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—61no—
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—31no—
562C42—31no—
563C42—61no—
564C42—61no—
565C42C2×D3×D511yescharacteristic
566C3×C5#336011yescharacteristic, complemented, Hall
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3C22×C22⋊D511yescharacteristic
571C2×D3—102no—
572C2×D3—201no—
573C2×D3—201no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—201no—
578C3×C4—201no—
579C3×C4D5×#4111yescharacteristic
580C3×C4#415011yescharacteristic
581Dic3—21no—
582Dic3—21no—
583Dic3—21no—
584Dic3—41no—
585Dic3—41no—
586Dic3—201no—
587Dic3#409612yes—
588C2×C5—81no—
589C2×C5#567711yescharacteristic
590C2×C5D3×#13511yescharacteristic
591C2×C5#577011yescharacteristic
592D5—122no—
593C23—21no—
594C23—301no—
595Q8—21no—
596Q8—21no—
597Q8—62no—
598Q8—61no—
599Q8—61no—
600Q8—1201no—
601D4—21no—
602D4—21no—
603D4—152no—
604D4—301no—
605C2×C4—21no—
606C2×C4—31no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—31no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—122no—
615C2×C4—301no—
616C2×C4—602no—
617C2×C4—1201no—
618C2×C4—1201no—
619C2×C4D3×C22⋊D511yescharacteristic
620C2×C4D3×C22⋊D511yescharacteristic
621C2×C4C22×D3×D511yescharacteristic
622C8—101no—
623C8—101no—
624C8—301no—
625C8—301no—
626C2×C3—81no—
627C2×C3C2×#409611yescharacteristic
628C2×C3#6616511yescharacteristic
629C2×C3#6617111yescharacteristic
630D3—202no—
631C5#8163211yescharacteristic, complemented, Sylow
632C22—41no—
633C22—41no—
634C22—41no—
635C22—302no—
636C22—601no—
637C22—601no—
638C22C2×D3×C22⋊D511yescharacteristic
639C4—21no—
640C4—21no—
641C4—32no—
642C4—41no—
643C4—61no—
644C4—61no—
645C4—61no—
646C4—121no—
647C4—121no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4#9202011yescharacteristic
652C4#9202411yescharacteristic
653C3#1061539811yescharacteristic, complemented, Sylow
654C2—81no—
655C2—602no—
656C2#1175495111yescharacteristic
657C2D3×#409611yescharacteristic
658C2#1175532611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenter#124D3×D5
hypocenterC3×C5#3360
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×#5671C2semidirect
2. #11752616C2semidirect
4. C3×#65345C2semidirect
5. #11749333C2semidirect
6. #11749233C2semidirect
7. #11749232C2semidirect
8. #11749187C2semidirect
9. #11749113C2semidirect
12. #11748942C2semidirect
13. C4×#6660C2semidirect
14. #11746926C2semidirect
15. Dic6×#168C2semidirect
68. #65345D3semidirect
123. #5671D5semidirect
566. C3×C5#3360semidirect
631. C5#81632semidirect
653. C3#10615398semidirect

Maximal subgroups

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

subgroupindex
C5×#56712
#117526162
#117511582
C3×#653452
#117493332
#117492332
#117492322
#117491872
#117491132
#117489902
#117489862
#117489422
C4×#66602
#117469262
Dic6×#1682
#106153983
#816325