Finite Group Databasebeta

← #14300557

Subgroups — #14300557

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×M16C211yesmaximal, characteristic, complemented
2#11754564C211yesmaximal, characteristic
3C2×#91109C211yesmaximal, characteristic, complemented
4C4×#6665C211yesmaximal, characteristic, complemented
5C2×#90980C211yesmaximal, characteristic, complemented
6C5×#4555C211yesmaximal, characteristic, complemented
7#11745975C211yesmaximal, characteristic, complemented
8#10599548—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C3×D5×M16—22no—
17C3×D5×M16—22no—
18C2×C3×#676—21no—
19C2×C3×C8×D5—21no—
20#91564—21no—
21#91546—21no—
22C2×#6665—21no—
23#91450C411yescharacteristic, complemented
24#91450C411yescharacteristic, complemented
25C4×#1202—21no—
26C4×#1202—21no—
27#91360C411yescharacteristic, complemented
28#91360C411yescharacteristic, complemented
29#91109—22no—
30#90994—21no—
31#90980—22no—
32#71984—51nomaximal, Hall
33C2×D5×M16D311yescharacteristic, complemented
34#65858—31no—
35C2×#3957—31no—
36C4×#685—31no—
37C2×#3937—31no—
38C5×#339—31no—
39#64752—31no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C2×#1220—21no—
43C22×Dic15—21no—
44#6817—21no—
45#6817—21no—
46#6817—21no—
47#6817—21no—
48C2×D60C2×C411yescharacteristic
49C2×C4×D15—21no—
50C2×Dic30C2×C411yescharacteristic
51C22×C5×Dic3—21no—
52C22×C3×Dic5D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5—21no—
57C2×C3×C4×D5C2×C411yescharacteristic
58C2×C3×C4×D5C2×C411yescharacteristic
59C2×C3×C4×D5D411yescharacteristic
60C2×C3×C4×D5D411yescharacteristic
61C2×#1202—21no—
62C2×#1202—21no—
63C3×C5×M16—21no—
64C3×C5×M16D412yescomplemented
65C2×C3×C5×C8—21no—
66C4×Dic15—21no—
67C4×Dic15—21no—
68C5×#217—21no—
69C5×C4⋊Dic3C2×C411yescharacteristic
70C5×C4⋊Dic3C2×C411yescharacteristic
71C4×C5×Dic3—21no—
72C4×C5×Dic3—21no—
73C4×C5×Dic3—21no—
74C3×#681—21no—
75C3×#681D412yescomplemented
76C2×C3×#168—21no—
77C3×#676—24no—
78C3×C8×D5—24no—
79Dic3⋊Dic5—21no—
80Dic3⋊Dic5—21no—
81#6667—21no—
82#6667—21no—
83#6665—24no—
84#6665—21no—
85#6665—21no—
86C22×C3×M16—51no—
87#5791—51no—
88C4×#217—51no—
89C2×#825—51no—
90C2×#825—51no—
91#4555—51no—
92#4555D511yescharacteristic, complemented
93C2×#709—31no—
94C22×C4×D5C2×D311yescharacteristic
95C2×C5×M16C2×D311yescharacteristic
96C5×#117—31no—
97C2×C42×C5—31no—
98C2×#685—61no—
99C2×C4×Dic5—31no—
100C2×#681C2×D311yescharacteristic
101D5×M16—22no—
102D5×M16—22no—
103C2×#676—21no—
104C2×C8×D5—21no—
105#4043—31no—
106#4043—31no—
107#4041—31no—
108#4041—31no—
109#4032—61no—
110#4028—61no—
111C4×D20—61no—
112C4×D20—61no—
113#3963—61no—
114#3957—62no—
115#3937—62no—
116#1871—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—22no—
122C22×C3×D5—41no—
123C22×C3×D5C22⋊C411yescharacteristic
124C22×C3×D5C22⋊C411yescharacteristic
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5#4111yescharacteristic
131#1220—41no—
132#1220—41no—
133C2×Dic15—22no—
134C2×Dic15—21no—
135C2×Dic15—41no—
136C2×Dic15—41no—
137D60—21no—
138D60—21no—
139C4×D15—41no—
140C4×D15—41no—
141Dic30—21no—
142Dic30—21no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—41no—
147C2×C5×Dic3—41no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5C22⋊C411yescharacteristic
151C2×C3×Dic5C22⋊C411yescharacteristic
152C3×C4×D5—21no—
153C3×C4×D5—21no—
154C3×C4×D5—21no—
155C3×C4×D5—21no—
156C3×C4×D5—21no—
157C3×C4×D5—21no—
158C3×C4×D5—21no—
159C3×C4×D5—21no—
160#1202—42no—
161#1202—42no—
162C3×C5×C8—22no—
163C3×#168—22no—
164C23×C3×C4—51no—
165C2×#235—51no—
166C2×C3×M16—51no—
167C2×C3×M16—101no—
168C2×C3×M16—102no—
169C2×C3×M16—102no—
170C2×C3×M16C2×D511yescharacteristic
171C22×C3×C8—101no—
172#953—101no—
173C2×#217—101no—
174#930—51no—
175#930—51no—
176#929—101no—
177C4×#67—101no—
178C4×#67—101no—
179#926C2×D511yescharacteristic
180#924—51no—
181#924—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3C2×D511yescharacteristic
184C3⋊#95—101no—
185#825—102no—
186#825—102no—
187C23×D5D1211yescharacteristic
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—61no—
191C22×Dic5—61no—
192C22×Dic5D1211yescharacteristic
193#709—61no—
194#709—61no—
195#709—61no—
196#709—61no—
197C2×D20—31no—
198C2×D20—61no—
199C2×D20—61no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—61no—
205C2×C4×D5C4×D311yescharacteristic
206C2×C4×D5C4×D311yescharacteristic
207C2×C4×D5#6711yescharacteristic
208C2×C4×D5#6711yescharacteristic
209C2×Dic10—31no—
210C5×M16—21no—
211C5×M16#6712yescomplemented
212C2×C5×C8—21no—
213C5×C4⋊C4—31no—
214C5×C4⋊C4—31no—
215C5×C22⋊C4—61no—
216C42×C5—61no—
217C42×C5—61no—
218C42×C5—61no—
219#685—64no—
220#685—61no—
221#685—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—61no—
225C4⋊Dic5—61no—
226C4×Dic5—61no—
227C4×Dic5—61no—
228#681—21no—
229#681#6712yescomplemented
230C2×#168—21no—
231#676—24no—
232C8×D5—24no—
233C22×M16—51no—
234#525—151no—
235C2×#104—151no—
236C2×#104—151no—
237C4×C22⋊C4—151no—
238#339—31no—
239#339—151no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5C2×C22⋊C411yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5#12111yescharacteristic
245C2×D15—41no—
246C2×D15—41no—
247C2×D15—41no—
248C2×C3×D5—21no—
249C2×C3×D5—21no—
250C2×C3×D5—21no—
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5#10412yescomplemented
256C3×C4×C5C4×D411yescharacteristic
257C3×C4×C5C4×D411yescharacteristic
258C3×C4×C5#12011yescharacteristic
259C3×C4×C5#12311yescharacteristic
260Dic15—42no—
261Dic15—41no—
262C3×Dic5—21no—
263C3×Dic5—21no—
264C5×Dic3—42no—
265C5×Dic3—41no—
266C5×Dic3—41no—
267C24×C3—51no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—101no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C2×#67—101no—
280C2×#67—101no—
281C22×Dic3—21no—
282C22×Dic3—101no—
283#235—101no—
284#235—101no—
285#235—101no—
286#235—101no—
287C2×D12—51no—
288C2×C4×D3—101no—
289C2×Dic6—51no—
290C3×M16—21no—
291C3×M16—52no—
292C3×M16—104no—
293C3×M16—101no—
294C3×M16D2012yescomplemented
295C2×C3×C8—21no—
296C2×C3×C8—104no—
297C2×C3×C8—101no—
298#217—21no—
299#217—101no—
300#217—101no—
301#217—104no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—101no—
304C4⋊Dic3C4×D511yescharacteristic
305C4⋊Dic3C4×D511yescharacteristic
306Dic3⋊C4—101no—
307Dic3⋊C4—101no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—101no—
312C4×Dic3—101no—
313C23×C5C2×D1211yescharacteristic
314C22×D5—21no—
315C22×D5—21no—
316C22×D5—22no—
317C22×D5—41no—
318C22×D5—61no—
319C22×D5(C2×D3)⋊C411yescharacteristic
320C22×D5(C2×D3)⋊C411yescharacteristic
321C2×C4×C5—62no—
322C2×C4×C5—61no—
323C2×C4×C5—61no—
324C2×C4×C5—121no—
325C2×C4×C5—121no—
326C2×C4×C5C2×C4×D311yescharacteristic
327C2×C4×C5#23511yescharacteristic
328C2×C4×C5#23511yescharacteristic
329C2×C4×C5C2×#6711yescharacteristic
330C2×C4×C5C2×#6711yescharacteristic
331C2×C4×C5C2×#6711yescharacteristic
332C22⋊D5—121no—
333C22⋊D5—121no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—62no—
337C2×Dic5—61no—
338C2×Dic5—121no—
339C2×Dic5—121no—
340C2×Dic5(C2×D3)⋊C411yescharacteristic
341C2×Dic5(C2×D3)⋊C411yescharacteristic
342D20—61no—
343D20—61no—
344D20—122no—
345D20—122no—
346C4×D5—21no—
347C4×D5—21no—
348C4×D5—21no—
349C4×D5—21no—
350C4×D5—21no—
351C4×D5—21no—
352C4×D5—21no—
353C4×D5—21no—
354C4×D5—121no—
355C4×D5—121no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—22no—
359#168—22no—
360C2×#41—151no—
361C23×C4—51no—
362C2×M16—51no—
363C2×M16—101no—
364C2×M16—102no—
365C2×M16—102no—
366C2×M16D3×D511yescharacteristic
367C22×C8—101no—
368#123—301no—
369C22⋊Q8—151no—
370C22⋊Q8—151no—
371#121—151no—
372#121—151no—
373#120—301no—
374C4×D4—301no—
375C4×D4—301no—
376#117—31no—
377C2×C22⋊C4—301no—
378C2×C42—31no—
379C2×C42—151no—
380#104—302no—
381#104—302no—
382#95—301no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5#38611yescharacteristic
386C2×C3×C5C2×#10411yescharacteristic
387C2×C3×C5#42111yescharacteristic
388D15—81no—
389C3×D5—22no—
390C3×D5—41no—
391C23×C3—51no—
392C23×C3—51no—
393C23×C3—102no—
394C23×C3—101no—
395C23×C3—101no—
396C23×C3—201no—
397C23×C3D4×D511yescharacteristic
398C22×D3—101no—
399C2×C3×C4—51no—
400C2×C3×C4—51no—
401C2×C3×C4—101no—
402C2×C3×C4—101no—
403C2×C3×C4—101no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—101no—
407C2×C3×C4—101no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—101no—
411C2×C3×C4C2×C4×D511yescharacteristic
412C2×C3×C4C2×D2011yescharacteristic
413C2×C3×C4#70911yescharacteristic
414C2×C3×C4D4×D511yescharacteristic
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4#71311yescharacteristic
417#67—202no—
418#67—202no—
419#67—201no—
420#67—201no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—21no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—102no—
427C2×Dic3—101no—
428C2×Dic3—201no—
429C2×Dic3—201no—
430D12—101no—
431D12—101no—
432C4×D3—201no—
433C4×D3—201no—
434Dic6—101no—
435Dic6—101no—
436C3×C8—22no—
437C3×C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5C2×(C2×D3)⋊C411yescharacteristic
441C22×C5#93011yescharacteristic
442C22×C5#93011yescharacteristic
443C2×D5—21no—
444C2×D5—21no—
445C2×D5—21no—
446C2×D5—21no—
447C2×D5—21no—
448C2×D5—42no—
449C2×D5—42no—
450C2×D5—121no—
451C2×D5—121no—
452C2×D5—121no—
453C2×D5#82512yescomplemented
454C4×C5—122no—
455C4×C5—121no—
456C4×C5—121no—
457C4×C5C4×#6711yescharacteristic
458C4×C5C4×#6711yescharacteristic
459C4×C5#92911yescharacteristic
460C4×C5#95311yescharacteristic
461Dic5—21no—
462Dic5—21no—
463Dic5—122no—
464Dic5—121no—
465C24—51no—
466#41—301no—
467#41—301no—
468#41—301no—
469#41—301no—
470C2×Q8—151no—
471C2×D4—151no—
472C2×D4—301no—
473C2×D4—301no—
474C2×D4—301no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—61no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—301no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488M16—21no—
489M16—52no—
490M16—104no—
491M16—101no—
492M16#120212yescomplemented
493C2×C8—21no—
494C2×C8—104no—
495C2×C8—101no—
496C4⋊C4—31no—
497C4⋊C4—31no—
498C4⋊C4—301no—
499C4⋊C4—301no—
500C22⋊C4—61no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C22⋊C4—301no—
504C22⋊C4—301no—
505C22⋊C4—304no—
506C42—61no—
507C42—61no—
508C42—61no—
509C42—301no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—52no—
515C22×C3—101no—
516C22×C3—101no—
517C22×C3—101no—
518C22×C3—101no—
519C22×C3—101no—
520C22×C3—202no—
521C22×C3—202no—
522C22×C3D5×C22⋊C411yescharacteristic
523C22×C3#403011yescharacteristic
524C22×C3#404111yescharacteristic
525C2×D3—201no—
526C2×D3—201no—
527C2×D3—201no—
528C3×C4—101no—
529C3×C4—101no—
530C3×C4C4×D2011yescharacteristic
531C3×C4#402811yescharacteristic
532C3×C4#403911yescharacteristic
533C3×C4#404011yescharacteristic
534Dic3—42no—
535Dic3—41no—
536Dic3—41no—
537Dic3—202no—
538Dic3—201no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5C2×#82511yescharacteristic
542C2×C5#513911yescharacteristic
543C2×C5#521311yescharacteristic
544D5—22no—
545D5—41no—
546D5—241no—
547C23—51no—
548C23—51no—
549C23—102no—
550C23—101no—
551C23—101no—
552C23—201no—
553C23—301no—
554C23D5×D1211yescharacteristic
555Q8—301no—
556Q8—301no—
557D4—301no—
558D4—301no—
559D4—602no—
560D4—602no—
561D4—601no—
562D4—601no—
563C2×C4—51no—
564C2×C4—51no—
565C2×C4—62no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—121no—
579C2×C4—121no—
580C2×C4—302no—
581C2×C4—301no—
582C2×C4—601no—
583C2×C4—601no—
584C2×C4—601no—
585C2×C4—601no—
586C2×C4#677111yescharacteristic
587C2×C4#677311yescharacteristic
588C2×C4C4×D3×D511yescharacteristic
589C2×C4C2×#120211yescharacteristic
590C2×C4D5×#6711yescharacteristic
591C2×C4D5×#6711yescharacteristic
592C8—22no—
593C8—102no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—102no—
597C2×C3—201no—
598C2×C3#6495411yescharacteristic
599C2×C3D5×#10411yescharacteristic
600C2×C3#6511011yescharacteristic
601D3—401no—
602C5#7198411yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—52no—
606C22—101no—
607C22—101no—
608C22—101no—
609C22—101no—
610C22—101no—
611C22—202no—
612C22—202no—
613C22—601no—
614C22—601no—
615C22—601no—
616C22#9144811yescharacteristic
617C22#9145011yescharacteristic
618C22D5×(C2×D3)⋊C411yescharacteristic
619C4—101no—
620C4—101no—
621C4—122no—
622C4—121no—
623C4—121no—
624C4—602no—
625C4—601no—
626C4#9134811yescharacteristic
627C4C4×#120211yescharacteristic
628C4#9144411yescharacteristic
629C4#9156411yescharacteristic
630C3#1059954811yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—102no—
634C2—201no—
635C2—1201no—
636C2D5×#82511yescharacteristic
637C2#1174822911yescharacteristic
638C2#1174890711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754564C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×M16C2semidirect
3. C2×#91109C2semidirect
4. C4×#6665C2semidirect
5. C2×#90980C2semidirect
6. C5×#4555C2semidirect
7. #11745975C2semidirect
23. #91450C4semidirect
24. #91450C4semidirect
27. #91360C4semidirect
28. #91360C4semidirect
33. C2×D5×M16D3semidirect
64. C3×C5×M16D4semidirect
75. C3×#681D4semidirect
92. #4555D5semidirect
211. C5×M16#67semidirect
229. #681#67semidirect
255. C2×C3×D5#104semidirect
294. C3×M16D20semidirect
453. C2×D5#825semidirect
492. M16#1202semidirect
511. C3×C5#1871semidirect
602. C5#71984semidirect
630. C3#10599548semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×M162
#117545642
C2×#911092
C4×#66652
C2×#909802
C5×#45552
#117459752
#105995483
#719845