Finite Group Databasebeta

← #14424144

Subgroups — #14424144

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic
2C2×#91508C212yesmaximal, complemented
3D5×#924C211yesmaximal, characteristic, complemented
4#11751329C211yesmaximal, characteristic, complemented
5C5×#5228C211yesmaximal, characteristic, complemented
6#11749295C212yesmaximal, complemented
7#11749294C212yesmaximal, complemented
8#11749198C212yesmaximal, complemented
9#11748530C211yesmaximal, characteristic, complemented
10#11748527C211yesmaximal, characteristic, complemented
11#11748499C211yesmaximal, characteristic, complemented
12#10611915—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C3×#713—28no—
15C2×C3×#713—21no—
16C2×C3×#713—21no—
17C2×C3×#713C2212yes—
18C2×C3×#713C2212yes—
19C22×C3×D20—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5—21no—
22C22×C3×C4×D5C2211yescharacteristic
23C2×D5×Dic6C2211yescharacteristic, complemented
24C2×#6718C2212yescomplemented
25#91813C2211yescharacteristic
26C2×C5×#216C2212yescomplemented
27C5×#924C2211yescharacteristic
28#91574—21no—
29D5×#217—21no—
30#91508—28no—
31D5×C4⋊Dic3C2211yescharacteristic, complemented
32D5×Dic3⋊C4—21no—
33#91360C2211yescharacteristic, complemented
34#91359C2211yescharacteristic, complemented
35#91349—21no—
36C2×#6657C2212yescomplemented
37C2×#6655C2212yescomplemented
38C2×#6649C2212yescomplemented
39#91119C2212yescomplemented
40#91114C2211yescharacteristic
41C5×#835C2212yescomplemented
42C5×#830C2211yescharacteristic
43#90965C2212yescomplemented
44#90964C2212yescomplemented
45#90955C2212yescomplemented
46#84084—51nomaximal, Hall
47C22×#713D311yescharacteristic
48C2×#4064—32no—
49D5×C22⋊Q8—31no—
50C5×#451—31no—
51#65517—31no—
52#65476—32no—
53#65335—31no—
54#65099—32no—
55#65092—32no—
56#65020—31no—
57#65015—31no—
58C23×C3×D5—21no—
59C23×C3×D5D411yescharacteristic
60C2×C3×C5×Q8—24no—
61C2×C3×C5×Q8—21no—
62C2×C3×C5×Q8C2312yes—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×Dic30C2311yescharacteristic
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5D411yescharacteristic
68C3×#713—28no—
69C3×#713—28no—
70C3×#713—24no—
71C3×#713—24no—
72C3×#713—24no—
73C3×#713D418yes—
74C2×C3×D20—28no—
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20—21no—
78C2×C3×D20—24no—
79C2×C3×D20C2312yes—
80C2×C3×C4×D5—28no—
81C2×C3×C4×D5—22no—
82C2×C3×C4×D5—22no—
83C2×C3×C4×D5—24no—
84C2×C3×C4×D5D411yescharacteristic
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×#1204—21no—
89C2×D5×Dic3—21no—
90C2×D5×Dic3—21no—
91D5×Dic6—24no—
92#6719—21no—
93#6718—24no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C2×C3⋊#168C2312yes—
97C5×#217—21no—
98C5×#216—24no—
99C5×C4⋊Dic3C2311yescharacteristic
100C5×Dic3⋊C4—21no—
101C2×C5×C3⋊C8C2312yes—
102Dic3⋊Dic5—21no—
103#6669—21no—
104#6668—21no—
105#6665—21no—
106#6665—21no—
107#6657—24no—
108#6655—24no—
109#6649—24no—
110C22×C3×#41—51no—
111C2×#951—52no—
112C2×#924—51no—
113#5239—52no—
114#5239—52no—
115#5232—52no—
116#5228—51no—
117#5228D511yescharacteristic, complemented
118#5218—51no—
119#5218—51no—
120#5207—51no—
121C22×C5×Q8C2×D311yescharacteristic
122C2×#713—28no—
123C2×#713—21no—
124C2×#713—21no—
125C2×#713C2×D312yes—
126C2×#713C2×D312yes—
127C2×Q8×D5—31no—
128C22×D20—21no—
129C22×D20C2×D311yescharacteristic
130C22×C4×D5—21no—
131C22×C4×D5C2×D311yescharacteristic
132C2×C5×Q16—32no—
133C5×C22⋊Q8—31no—
134#4092—31no—
135C2×#689—32no—
136C2×#688—32no—
137#4070—31no—
138#4064—68no—
139C2×#677—32no—
140C2×#676—32no—
141#4043—31no—
142#4042—61no—
143D5×C4⋊C4—31no—
144D5×C4⋊C4—61no—
145D5×C22⋊C4—61no—
146#4024—61no—
147C5×#103—32no—
148C5×C22⋊C8—31no—
149#3967—32no—
150C22⋊#168—31no—
151#3953—32no—
152#3952—32no—
153#3941—32no—
154#3007—151noSylow
155C23×C3×C5C2×D411yescharacteristic
156C22×C3×D5—24no—
157C22×C3×D5—22no—
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5—41no—
161C22×C3×D5—42no—
162C22×C3×D5—42no—
163C22×C3×D5C2×D411yescharacteristic
164C22×C3×D5C2×D411yescharacteristic
165C3×C5×Q8—24no—
166C3×C5×Q8—22no—
167C3×C5×Q8C2×D414yes—
168C2×C3×C4×C5—24no—
169C2×C3×C4×C5—22no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5C2×D411yescharacteristic
172C2×C3×C4×C5C2411yescharacteristic
173C2×Dic15—21no—
174C2×Dic15—21no—
175Dic30—22no—
176C2×C5×Dic3—21no—
177C2×C5×Dic3—21no—
178C5×Dic6—22no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5C2×D411yescharacteristic
181C2×C3×Dic5C2×D411yescharacteristic
182C3×D20—28no—
183C3×D20—24no—
184C3×D20—28no—
185C3×D20—22no—
186C3×D20C2×D414yes—
187C3×C4×D5—28no—
188C3×C4×D5—22no—
189C3×C4×D5—22no—
190C3×C4×D5—28no—
191C3×C4×D5—22no—
192C3×C4×D5C2×D414yes—
193#1204—42no—
194D5×Dic3—42no—
195D5×Dic3—42no—
196C3⋊#168—22no—
197C5×C3⋊C8—22no—
198C2×C3×#41—52no—
199C2×C3×#41—52no—
200C2×C3×#41—101no—
201C2×C3×#41—101no—
202C2×C3×#41—108no—
203C22×C3×Q8C2×D511yescharacteristic
204C22×C3×D4—51no—
205C22×C3×D4—101no—
206C23×C3×C4—51no—
207C23×C3×C4—101no—
208C22×Dic6—51no—
209C2×#217—101no—
210#951—108no—
211C2×#216—52no—
212C2×#216C2×D512yescomplemented
213C2×#214—52no—
214C2×#214—52no—
215C2×C4⋊Dic3—51no—
216#924—51no—
217#924—51no—
218#924—51no—
219#924—101no—
220#924—101no—
221#924C2×D511yescharacteristic
222C2×Dic3⋊C4—101no—
223C2×#208—52no—
224#835—52no—
225#835C2×D512yescomplemented
226#832—52no—
227#832—52no—
228#830—51no—
229#830—52no—
230#830C2×D511yescharacteristic
231C23×D5—21no—
232C23×D5#6711yescharacteristic
233C2×C5×Q8—24no—
234C2×C5×Q8—21no—
235C2×C5×Q8—31no—
236C2×C5×Q8C22×D312yes—
237C22×C4×C5—21no—
238C22×C4×C5C22×D311yescharacteristic
239C22×Dic5#6711yescharacteristic
240#713—28no—
241#713—28no—
242#713—24no—
243#713—24no—
244#713—24no—
245#713#6718yes—
246Q8×D5—64no—
247C2×D20—28no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—21no—
251C2×D20—24no—
252C2×D20C22×D312yes—
253C2×C4×D5—28no—
254C2×C4×D5—22no—
255C2×C4×D5—22no—
256C2×C4×D5—24no—
257C2×C4×D5—61no—
258C2×C4×D5—61no—
259C2×C4×D5#6711yescharacteristic
260C2×C4×D5#6711yescharacteristic
261C2×C4×D5C22×D311yescharacteristic
262C2×C4×D5C22×D311yescharacteristic
263C2×Dic10—31no—
264C2×Dic10—61no—
265C5×Q16—64no—
266C2×C5×C8—32no—
267C5×C4⋊C4—31no—
268C5×C4⋊C4—61no—
269C5×C22⋊C4—61no—
270C22⋊Dic5—61no—
271#689—64no—
272#688—64no—
273#685—61no—
274#685—61no—
275C4⋊Dic5—31no—
276C4⋊Dic5—61no—
277#683—61no—
278#683—61no—
279#683—61no—
280C2×#168—32no—
281#677—64no—
282#676—64no—
283C22×#41—51no—
284C2×#137—152no—
285C2×C22⋊Q8—151no—
286#452—152no—
287#452—152no—
288#451—31no—
289#451—151no—
290#450—151no—
291#450—151no—
292#417—152no—
293#407—151no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5#13712yescomplemented
297C22×C3×C5C22×D411yescharacteristic
298C2×C3×D5—21no—
299C2×C3×D5—21no—
300C2×C3×D5—21no—
301C2×C3×D5—24no—
302C2×C3×D5—21no—
303C2×C3×D5—21no—
304C2×C3×D5—44no—
305C2×C3×D5—48no—
306C2×C3×D5—42no—
307C2×C3×D5—42no—
308C2×C3×D5#12012yes—
309C3×C4×C5—24no—
310C3×C4×C5—21no—
311C3×C4×C5C22×D412yes—
312Dic15—41no—
313Dic15—41no—
314C3×Dic5—21no—
315C3×Dic5#12012yes—
316C5×Dic3—41no—
317C5×Dic3—41no—
318C24×C3—51no—
319C24×C3—101no—
320C3×#41—58no—
321C3×#41—104no—
322C3×#41—104no—
323C3×#41—108no—
324C3×#41—108no—
325C3×#41—104no—
326C2×C3×Q8—24no—
327C2×C3×Q8—21no—
328C2×C3×Q8C22×D512yes—
329C2×C3×D4—52no—
330C2×C3×D4—104no—
331C2×C3×D4—102no—
332C2×C3×D4—102no—
333C2×C3×D4—108no—
334C2×C3×D4—101no—
335C22×C3×C4—21no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—104no—
342C22×C3×C4—102no—
343C22×C3×C4—102no—
344C22×C3×C4—108no—
345C22×C3×C4C22×D511yescharacteristic
346C22×Dic3—101no—
347C22×Dic3—101no—
348C2×Dic6—51no—
349C2×Dic6—104no—
350C2×Dic6—101no—
351C2×Dic6C22×D511yescharacteristic
352#217—21no—
353#217—101no—
354#217—101no—
355#217—101no—
356#216—24no—
357#216—104no—
358#214—104no—
359#214—104no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3C22×D511yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—101no—
365Dic3⋊C4—101no—
366Dic3⋊C4—101no—
367#208—104no—
368C2×C3⋊C8—52no—
369C2×C3⋊C8C22×D512yes—
370C23×C5C2×#6711yescharacteristic
371C22×D5—24no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—41no—
376C22×D5—42no—
377C22×D5—42no—
378C22×D5C2×#6711yescharacteristic
379C22×D5C2×#6711yescharacteristic
380C5×Q8—24no—
381C5×Q8—22no—
382C5×Q8—62no—
383C5×Q8C2×#6714yes—
384C2×C4×C5—24no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—61no—
388C2×C4×C5—61no—
389C2×C4×C5C2×#6711yescharacteristic
390C2×C4×C5C23×D311yescharacteristic
391C2×Dic5—22no—
392C2×Dic5—61no—
393C2×Dic5—61no—
394C2×Dic5C2×#6711yescharacteristic
395C2×Dic5C2×#6711yescharacteristic
396D20—28no—
397D20—24no—
398D20—28no—
399D20—22no—
400D20C2×#6714yes—
401C4×D5—28no—
402C4×D5—22no—
403C4×D5—22no—
404C4×D5—28no—
405C4×D5—22no—
406C4×D5—122no—
407C4×D5—122no—
408C4×D5C2×#6714yes—
409Dic10—62no—
410Dic10—122no—
411C5×C8—62no—
412#168—62no—
413C2×#41—52no—
414C2×#41—52no—
415C2×#41—101no—
416C2×#41—101no—
417C2×#41—108no—
418C22×Q8—151no—
419C22×Q8D3×D511yescharacteristic
420C22×D4—51no—
421C22×D4—101no—
422C23×C4—51no—
423C23×C4—101no—
424#137—308no—
425C2×Q16—32no—
426C2×Q16—152no—
427C2×SD16—152no—
428C2×SD16—152no—
429C2×M16—152no—
430C22⋊Q8—31no—
431C22⋊Q8—151no—
432C22⋊Q8—151no—
433C22⋊Q8—151no—
434C22⋊Q8—301no—
435C22⋊Q8—301no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—301no—
438C2×C22⋊C4—301no—
439#103—32no—
440#103—152no—
441#102—152no—
442#102—152no—
443C22⋊C8—31no—
444C22⋊C8—152no—
445C22⋊C8—151no—
446C2×C3×C5—22no—
447C2×C3×C5C2×#12011yescharacteristic
448C2×C3×C5C2×#13711yescharacteristic
449C2×C3×C5#57511yescharacteristic
450C3×D5—22no—
451C3×D5—41no—
452C3×D5—44no—
453C23×C3—51no—
454C23×C3—51no—
455C23×C3—102no—
456C23×C3—104no—
457C23×C3—102no—
458C23×C3—102no—
459C23×C3—201no—
460C23×C3—202no—
461C23×C3—202no—
462C23×C3D4×D511yescharacteristic
463C3×Q8—24no—
464C3×Q8—22no—
465C3×Q8D4×D514yes—
466C3×D4—54no—
467C3×D4—108no—
468C3×D4—108no—
469C3×D4—104no—
470C3×D4—102no—
471C2×C3×C4—24no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—51no—
475C2×C3×C4—54no—
476C2×C3×C4—51no—
477C2×C3×C4—102no—
478C2×C3×C4—108no—
479C2×C3×C4—102no—
480C2×C3×C4—108no—
481C2×C3×C4—102no—
482C2×C3×C4—102no—
483C2×C3×C4D4×D511yescharacteristic
484C2×C3×C4C23×D511yescharacteristic
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C2×Dic3—202no—
490C2×Dic3—202no—
491Dic6—22no—
492Dic6—102no—
493Dic6—202no—
494C3⋊C8—22no—
495C3⋊C8—102no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5#95112yescomplemented
499C22×C5C22×#6711yescharacteristic
500C2×D5—21no—
501C2×D5—21no—
502C2×D5—21no—
503C2×D5—21no—
504C2×D5—21no—
505C2×D5—24no—
506C2×D5—44no—
507C2×D5—48no—
508C2×D5—42no—
509C2×D5—42no—
510C2×D5#95312yes—
511C4×C5—24no—
512C4×C5—21no—
513C4×C5—121no—
514C4×C5—121no—
515C4×C5C22×#6712yes—
516Dic5—21no—
517Dic5—121no—
518Dic5—121no—
519Dic5#95312yes—
520C24—51no—
521C24—101no—
522#41—58no—
523#41—104no—
524#41—104no—
525#41—108no—
526#41—108no—
527#41—104no—
528C2×Q8—24no—
529C2×Q8—21no—
530C2×Q8—31no—
531C2×Q8—151no—
532C2×Q8—301no—
533C2×Q8—304no—
534C2×Q8C2×D3×D512yes—
535C2×D4—52no—
536C2×D4—104no—
537C2×D4—102no—
538C2×D4—102no—
539C2×D4—108no—
540C2×D4—101no—
541C22×C4—21no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—51no—
547C22×C4—104no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—108no—
551C22×C4—301no—
552C22×C4—301no—
553C22×C4C2×D3×D511yescharacteristic
554Q16—64no—
555Q16—304no—
556SD16—304no—
557SD16—304no—
558M16—304no—
559C2×C8—32no—
560C2×C8—152no—
561C4⋊C4—31no—
562C4⋊C4—61no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C22⋊C4—61no—
569C22⋊C4—301no—
570C22⋊C4—301no—
571C22⋊C4—301no—
572C3×C5#300711yescharacteristic, complemented, Hall
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—52no—
576C22×C3—101no—
577C22×C3—101no—
578C22×C3—101no—
579C22×C3—101no—
580C22×C3—104no—
581C22×C3—101no—
582C22×C3—204no—
583C22×C3—208no—
584C22×C3—202no—
585C22×C3—202no—
586C22×C3#406412yescomplemented
587C22×C3C2×D4×D511yescharacteristic
588C3×C4—24no—
589C3×C4—21no—
590C3×C4—52no—
591C3×C4—101no—
592C3×C4C2×D4×D512yes—
593Dic3—41no—
594Dic3—41no—
595Dic3—201no—
596Dic3—201no—
597C2×C5—22no—
598C2×C5#582211yescharacteristic
599C2×C5C2×#95111yescharacteristic
600C2×C5C2×#95311yescharacteristic
601D5—22no—
602D5—41no—
603D5—44no—
604C23—51no—
605C23—51no—
606C23—102no—
607C23—104no—
608C23—102no—
609C23—102no—
610C23—201no—
611C23—202no—
612C23—202no—
613C23D5×#6711yescharacteristic
614Q8—24no—
615Q8—22no—
616Q8—62no—
617Q8—302no—
618Q8—602no—
619Q8D5×#6714yes—
620D4—54no—
621D4—108no—
622D4—108no—
623D4—104no—
624D4—102no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—51no—
629C2×C4—54no—
630C2×C4—51no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—102no—
634C2×C4—108no—
635C2×C4—102no—
636C2×C4—108no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D5×#6711yescharacteristic
644C2×C4C22×D3×D511yescharacteristic
645C8—62no—
646C8—302no—
647C2×C3—22no—
648C2×C3—102no—
649C2×C3—201no—
650C2×C3—204no—
651C2×C3D5×#12011yescharacteristic
652C2×C3C2×#406411yescharacteristic
653C2×C3#6611111yescharacteristic
654C5#8408411yescharacteristic, complemented, Sylow
655C22—21no—
656C22—21no—
657C22—52no—
658C22—101no—
659C22—101no—
660C22—101no—
661C22—101no—
662C22—104no—
663C22—101no—
664C22—204no—
665C22—208no—
666C22—202no—
667C22—202no—
668C22#9150812yescomplemented
669C22C2×D5×#6711yescharacteristic
670C4—24no—
671C4—21no—
672C4—52no—
673C4—101no—
674C4—121no—
675C4—121no—
676C4—601no—
677C4—601no—
678C4C2×D5×#6712yes—
679C3#1061191511yescharacteristic, complemented, Sylow
680C2—22no—
681C2—102no—
682C2—201no—
683C2—204no—
684C2#1175508411yescharacteristic
685C2C2×#9150811yescharacteristic
686C2D5×#95311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×#713C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91508C2semidirect
3. D5×#924C2semidirect
4. #11751329C2semidirect
5. C5×#5228C2semidirect
6. #11749295C2semidirect
7. #11749294C2semidirect
8. #11749198C2semidirect
9. #11748530C2semidirect
10. #11748527C2semidirect
11. #11748499C2semidirect
23. C2×D5×Dic6C22semidirect
24. C2×#6718C22semidirect
26. C2×C5×#216C22semidirect
31. D5×C4⋊Dic3C22semidirect
33. #91360C22semidirect
34. #91359C22semidirect
36. C2×#6657C22semidirect
37. C2×#6655C22semidirect
38. C2×#6649C22semidirect
39. #91119C22semidirect
41. C5×#835C22semidirect
43. #90965C22semidirect
44. #90964C22semidirect
45. #90955C22semidirect
117. #5228D5semidirect
212. C2×#216C2×D5semidirect
225. #835C2×D5semidirect
296. C22×C3×C5#137semidirect
498. C22×C5#951semidirect
572. C3×C5#3007semidirect
586. C22×C3#4064semidirect
654. C5#84084semidirect
668. C22#91508semidirect
679. C3#10611915semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C2×#915082
D5×#9242
#117513292
C5×#52282
#117492952
#117492942
#117491982
#117485302
#117485272
#117484992
#106119153
#840845