Finite Group Databasebeta

← #14471620

Subgroups — #14471620

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
1C3×#66005C211yesmaximal, characteristic, complemented
2#11752591C211yesmaximal, characteristic, complemented
3#11751158C211yesmaximal, characteristic
4C5×#5056C211yesmaximal, characteristic, complemented
5#11749349C211yesmaximal, characteristic, complemented
6#11749332C211yesmaximal, characteristic, complemented
7#11749222C211yesmaximal, characteristic, complemented
8#11749221C211yesmaximal, characteristic, complemented
9#11749104C211yesmaximal, characteristic, complemented
10#11749085C211yesmaximal, characteristic, complemented
11#11748980C211yesmaximal, characteristic
12#11748975C211yesmaximal, characteristic
13C4×#6658C211yesmaximal, characteristic, complemented
14#11746919C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
16#10613363—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18C2×#6717C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C5×#870C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×#4090C2211yescharacteristic
24C3×#4082C2211yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×#4025—21no—
27C3×#4025—21no—
28C3×#4024—21no—
29C3×#4023—21no—
30C3×C4×Dic10C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91468C2211yescharacteristic
33#91429—21no—
34#91418C2211yescharacteristic
35#91418C2211yescharacteristic
36#91411—21no—
37#91404—21no—
38#91388C2211yescharacteristic
39#91377—21no—
40C2×#6658C2211yescharacteristic
41#91119C2211yescharacteristic
42#91116C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C5×#835C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#832C2211yescharacteristic
47C5×#832C2211yescharacteristic
48C4×C5×C3⋊C8C2211yescharacteristic
49#90989C2211yescharacteristic
50#90987C2211yescharacteristic
51#90986C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90971C2211yescharacteristic
55#90970C2211yescharacteristic
56#90970C2211yescharacteristic
57#90968C2211yescharacteristic
58Dic5×C3⋊C8C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83667—51nomaximal, Hall
61#66024—31no—
62#66005D311yescharacteristic, complemented
63C5×#488—31no—
64#65352—31no—
65#65346—31no—
66#65107—31no—
67#65088—31no—
68#65081—31no—
69#65077—31no—
70#65076—31no—
71#65057—31no—
72#65050—31no—
73#65045—31no—
74C4×#677—31no—
75C8×Dic10—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C22×C3×Dic5—21no—
81C2×C3×Dic10D411yescharacteristic
82C2×C3×Dic10C2311yescharacteristic
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×C4⋊Dic3C2311yescharacteristic
96C5×C4⋊Dic3C2311yescharacteristic
97C5×Dic3⋊C4—21no—
98C5×Dic3⋊C4—21no—
99C2×C5×C3⋊C8C2311yescharacteristic
100C2×C5×C3⋊C8C2311yescharacteristic
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5D411yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×#683—21no—
109C3×#683—21no—
110C3×#683D411yescharacteristic
111C3×#683D411yescharacteristic
112C3×C4×Dic5—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119#6667—21no—
120#6667—21no—
121#6658—22no—
122C3×#556—51no—
123#5579—51no—
124#5083—51no—
125#5079—51no—
126#5057—51no—
127#5057—51no—
128#5056—51no—
129#5056D511yescharacteristic, complemented
130C4×#215—51no—
131C4×#215—51no—
132Q8×C3⋊C8—51no—
133#5022—51no—
134#5022—51no—
135C4×#213—51no—
136#5008—51no—
137C5×#125—31no—
138C5×#124C2×D311yescharacteristic
139Q8×Dic5C2×D311yescharacteristic
140#4090C2×D311yescharacteristic
141C2×#688—31no—
142#4082C2×D311yescharacteristic
143D4×Dic5C2×D311yescharacteristic
144C2×#686—31no—
145C2×#677—31no—
146#4043—61no—
147#4042—61no—
148#4042—61no—
149#4039—31no—
150#4039—31no—
151D5×C4⋊C4—61no—
152#4036—31no—
153#4034—31no—
154#4025—21no—
155#4025—21no—
156#4024—21no—
157#4023—21no—
158C4×D20—31no—
159C4×Dic10C2×D311yescharacteristic
160C4×Dic10C2×D311yescharacteristic
161C5×#103—31no—
162C5×#103—31no—
163C5×#102—31no—
164C5×#102—31no—
165C4×C5×C8—31no—
166#3967—31no—
167#3964—31no—
168#3953—31no—
169#3949—31no—
170#3948—31no—
171#3946—31no—
172#3946—31no—
173C8×Dic5—31no—
174C8×Dic5—31no—
175#3942—31no—
176#3942—31no—
177#3940—31no—
178#3939—31no—
179C4⋊#168—31no—
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×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—42no—
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C3×Dic10—22no—
205C3×Dic10—21no—
206C3×Dic10—21no—
207#1204—81no—
208#1200—42no—
209#1200—81no—
210C3⋊#168—21no—
211C3⋊#168—21no—
212C5×C3⋊C8—21no—
213C5×C3⋊C8—21no—
214C3×C4⋊Q8—51no—
215C3×#126—101no—
216C3×#126—101no—
217C3×#124—51no—
218C3×#124C2×D511yescharacteristic
219C3×C22⋊Q8—101no—
220C3×C4×Q8—51no—
221C3×C4×Q8—51no—
222C3×C4×Q8—51no—
223C3×C4×D4—51no—
224C3×#117—101no—
225#946—101no—
226C2×#215—51no—
227C2×#215—51no—
228C2×#213—51no—
229#896—101no—
230#896—101no—
231D3×C4⋊C4—101no—
232C4×D12—51no—
233C4×D12—51no—
234C4×D12—51no—
235#870—51no—
236#870C2×D511yescharacteristic
237#869—51no—
238#835—51no—
239#835—51no—
240#835—51no—
241#835—51no—
242#835C2×D511yescharacteristic
243#835C2×D511yescharacteristic
244#832—51no—
245#832C2×D511yescharacteristic
246#832C2×D511yescharacteristic
247#809—51no—
248#808—51no—
249#808—51no—
250#807—51no—
251C4⋊(C3⋊C8)—51no—
252C4⋊(C3⋊C8)—51no—
253C4⋊(C3⋊C8)—51no—
254C4×C3⋊C8—51no—
255C4×C3⋊C8—51no—
256C4×C3⋊C8C2×D511yescharacteristic
257C2×C5×Q8C22×D311yescharacteristic
258C2×C5×D4C22×D311yescharacteristic
259C22×Dic5—21no—
260C2×D20—31no—
261C2×C4×D5—61no—
262C2×C4×D5—61no—
263C2×C4×D5—61no—
264C2×Dic10—61no—
265C2×Dic10#6711yescharacteristic
266C2×Dic10C22×D311yescharacteristic
267C2×C5×C8—31no—
268C2×C5×C8—31no—
269C5×C4⋊C4—31no—
270C5×C4⋊C4—31no—
271C5×C4⋊C4—61no—
272C5×C4⋊C4—61no—
273C5×C22⋊C4—21no—
274C5×C22⋊C4—21no—
275C42×C5C22×D311yescharacteristic
276C22⋊Dic5—21no—
277C22⋊Dic5—21no—
278C22⋊Dic5—21no—
279#688—62no—
280#686—62no—
281#685—61no—
282#685—61no—
283#685—61no—
284C4⋊Dic5—21no—
285C4⋊Dic5—31no—
286C4⋊Dic5—61no—
287C4⋊Dic5#6711yescharacteristic
288C4⋊Dic5C22×D311yescharacteristic
289#683—21no—
290#683—21no—
291#683—21no—
292#683—61no—
293#683—61no—
294#683#6711yescharacteristic
295#683#6711yescharacteristic
296C4×Dic5—21no—
297C4×Dic5—21no—
298C4×Dic5C22×D311yescharacteristic
299C4×Dic5C22×D311yescharacteristic
300C2×#168—31no—
301C2×#168—31no—
302#677—62no—
303#556—51no—
304#554—151no—
305#488—31no—
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—21no—
332C3×Dic5—21no—
333C3×Dic5—21no—
334C3×Dic5—41no—
335C3×Dic5—41no—
336C3×Dic5#13512yes—
337C5×Dic3—41no—
338C5×Dic3—41no—
339C2×C3×Q8—51no—
340C2×C3×Q8—51no—
341C2×C3×Q8C22×D511yescharacteristic
342C2×C3×D4C22×D511yescharacteristic
343C22×C3×C4—101no—
344C2×D12—51no—
345C2×C4×D3—101no—
346C2×C4×D3—101no—
347C2×C4×D3—101no—
348C2×Dic6—101no—
349C3×C4⋊C4—51no—
350C3×C4⋊C4—51no—
351C3×C4⋊C4—51no—
352C3×C4⋊C4—51no—
353C3×C4⋊C4—101no—
354C3×C4⋊C4—101no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4—101no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—101no—
360C3×C22⋊C4—101no—
361C3×C22⋊C4—101no—
362C3×C42—51no—
363C3×C42—51no—
364C3×C42—101no—
365C3×C42—101no—
366C3×C42C22×D511yescharacteristic
367#215—102no—
368#215—102no—
369#213—102no—
370(C2×D3)⋊C4—101no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4—101no—
373C4⋊Dic3—51no—
374C4⋊Dic3—101no—
375C4⋊Dic3C22×D511yescharacteristic
376C4⋊Dic3C22×D511yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381C2×C3⋊C8—51no—
382C2×C3⋊C8—51no—
383C2×C3⋊C8C22×D511yescharacteristic
384C2×C3⋊C8C22×D511yescharacteristic
385C23×C5—21no—
386C22×D5—61no—
387C5×Q8—21no—
388C5×Q8—21no—
389C5×D4—21no—
390C5×D4—21no—
391C2×C4×C5—21no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5C2×#6711yescharacteristic
395C2×C4×C5C2×#6711yescharacteristic
396C2×C4×C5C23×D311yescharacteristic
397C2×Dic5—21no—
398C2×Dic5—21no—
399C2×Dic5—42no—
400C2×Dic5—61no—
401C2×Dic5C2×#6711yescharacteristic
402C2×Dic5C2×#6711yescharacteristic
403C2×Dic5C2×#6711yescharacteristic
404C2×Dic5C2×#6711yescharacteristic
405D20—32no—
406D20—61no—
407C4×D5—122no—
408C4×D5—241no—
409C4×D5—241no—
410Dic10—22no—
411Dic10—21no—
412Dic10—21no—
413Dic10—241no—
414C5×C8—61no—
415C5×C8—61no—
416#168—61no—
417#168—61no—
418C2×SD16—151no—
419C2×SD16—151no—
420C2×D8—151no—
421C4⋊Q8—51no—
422C4⋊Q8—151no—
423#126—101no—
424#126—101no—
425#125—31no—
426#125—151no—
427#124—51no—
428#124D3×D511yescharacteristic
429C22⋊Q8—101no—
430C22⋊Q8—301no—
431C22⋊Q8—301no—
432C22⋊Q8—301no—
433C4×Q8—51no—
434C4×Q8—51no—
435C4×Q8—51no—
436C4×D4—51no—
437C4×D4—151no—
438C4×D4—151no—
439C4×D4—151no—
440#117—101no—
441C2×C4⋊C4—301no—
442#107—151no—
443#106—151no—
444#106—151no—
445C4⋊C8—151no—
446C4⋊C8—151no—
447C4⋊C8—151no—
448#103—31no—
449#103—31no—
450#103—151no—
451#103—151no—
452#103—151no—
453#103—151no—
454#102—31no—
455#102—31no—
456#102—151no—
457#102—151no—
458C4×C8—31no—
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×Q8—102no—
471C3×Q8—101no—
472C3×Q8—101no—
473C3×D4—21no—
474C3×D4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—51no—
477C2×C3×C4—51no—
478C2×C3×C4—51no—
479C2×C3×C4—51no—
480C2×C3×C4—101no—
481C2×C3×C4—101no—
482C2×C3×C4—202no—
483C2×C3×C4D4×D511yescharacteristic
484C2×C3×C4D4×D511yescharacteristic
485C2×C3×C4C23×D511yescharacteristic
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—101no—
489D12—52no—
490D12—101no—
491C4×D3—202no—
492C4×D3—401no—
493C4×D3—401no—
494Dic6—401no—
495C3⋊C8—21no—
496C3⋊C8—21no—
497C3⋊C8—101no—
498C3⋊C8—101no—
499C22×C5—41no—
500C22×C5—41no—
501C22×C5—41no—
502C22×C5C22×#6711yescharacteristic
503C2×D5—62no—
504C2×D5—121no—
505C2×D5—121no—
506C4×C5—21no—
507C4×C5—21no—
508C4×C5—41no—
509C4×C5—121no—
510C4×C5—121no—
511C4×C5D3×#4111yescharacteristic
512C4×C5#101011yescharacteristic
513Dic5—21no—
514Dic5—21no—
515Dic5—21no—
516Dic5—41no—
517Dic5—41no—
518Dic5—121no—
519Dic5#95012yes—
520C2×Q8—51no—
521C2×Q8—51no—
522C2×Q8—301no—
523C2×Q8C2×D3×D511yescharacteristic
524C2×D4—151no—
525C2×D4C2×D3×D511yescharacteristic
526C22×C4—101no—
527C22×C4—301no—
528C22×C4—301no—
529C22×C4—301no—
530SD16—302no—
531SD16—302no—
532D8—302no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—151no—
536C2×C8—151no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—51no—
540C4⋊C4—51no—
541C4⋊C4—51no—
542C4⋊C4—51no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—101no—
546C4⋊C4—101no—
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—101no—
556C22⋊C4—101no—
557C22⋊C4—101no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—51no—
562C42—51no—
563C42—101no—
564C42—101no—
565C42C2×D3×D511yescharacteristic
566C3×C5#336011yescharacteristic, complemented, Hall
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3C2×D4×D511yescharacteristic
571C2×D3—102no—
572C2×D3—201no—
573C2×D3—201no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—41no—
577C3×C4—52no—
578C3×C4—101no—
579C3×C4—101no—
580C3×C4—101no—
581C3×C4—201no—
582C3×C4—201no—
583C3×C4D5×#4111yescharacteristic
584C3×C4#415011yescharacteristic
585Dic3—41no—
586Dic3—41no—
587Dic3—201no—
588C2×C5—81no—
589C2×C5C2×#95011yescharacteristic
590C2×C5#583111yescharacteristic
591C2×C5#583711yescharacteristic
592D5—122no—
593C23—21no—
594C23—301no—
595Q8—21no—
596Q8—21no—
597Q8—102no—
598Q8—101no—
599Q8—101no—
600Q8—1201no—
601D4—21no—
602D4—21no—
603D4—152no—
604D4—301no—
605C2×C4—21no—
606C2×C4—51no—
607C2×C4—51no—
608C2×C4—51no—
609C2×C4—51no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—202no—
615C2×C4—301no—
616C2×C4—602no—
617C2×C4—1201no—
618C2×C4—1201no—
619C2×C4D5×#6711yescharacteristic
620C2×C4D5×#6711yescharacteristic
621C2×C4C22×D3×D511yescharacteristic
622C8—61no—
623C8—61no—
624C8—301no—
625C8—301no—
626C2×C3—81no—
627C2×C3#6601111yescharacteristic
628C2×C3D5×#13511yescharacteristic
629C2×C3#6610411yescharacteristic
630D3—202no—
631C5#8366711yescharacteristic, complemented, Sylow
632C22—41no—
633C22—41no—
634C22—41no—
635C22—302no—
636C22—601no—
637C22—601no—
638C22C2×D5×#6711yescharacteristic
639C4—21no—
640C4—21no—
641C4—41no—
642C4—52no—
643C4—101no—
644C4—101no—
645C4—101no—
646C4—121no—
647C4—121no—
648C4—201no—
649C4—201no—
650C4—601no—
651C4#9202011yescharacteristic
652C4#9202411yescharacteristic
653C3#1061336311yescharacteristic, complemented, Sylow
654C2—81no—
655C2—602no—
656C2#1175493911yescharacteristic
657C2D5×#95011yescharacteristic
658C2#1175531911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. C3×#66005C2semidirect
2. #11752591C2semidirect
4. C5×#5056C2semidirect
5. #11749349C2semidirect
6. #11749332C2semidirect
7. #11749222C2semidirect
8. #11749221C2semidirect
9. #11749104C2semidirect
10. #11749085C2semidirect
13. C4×#6658C2semidirect
14. #11746919C2semidirect
15. C3⋊C8×Dic10C2semidirect
62. #66005D3semidirect
129. #5056D5semidirect
566. C3×C5#3360semidirect
631. C5#83667semidirect
653. C3#10613363semidirect

Maximal subgroups

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

subgroupindex
C3×#660052
#117525912
#117511582
C5×#50562
#117493492
#117493322
#117492222
#117492212
#117491042
#117490852
#117489802
#117489752
C4×#66582
#117469192
C3⋊C8×Dic102
#106133633
#836675