Finite Group Databasebeta

← #14425737

Subgroups — #14425737

Order 1920.

1600 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
1C2×C3×#4144C211yesmaximal, characteristic, complemented
2#11756563C211yesmaximal, characteristic, complemented
3#11755427C212yesmaximal, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C212yesmaximal, complemented
6#11749182C214yesmaximal, complemented
7#11749176C214yesmaximal, complemented
8#10610417—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220C2211yescharacteristic, complemented
11C22×C3×C22⋊D5—21no—
12C22×C3×C22⋊D5C2212yes—
13C3×#4144—22no—
14C3×#4144—24no—
15C3×#4144C2214yes—
16C2×C3×#711—22no—
17C2×C3×D4×D5—22no—
18C2×C3×#709—21no—
19#91842—21no—
20C2×#6719C2211yescharacteristic, complemented
21#91828—22no—
22#91826C2212yescomplemented
23#91824C2212yescomplemented
24#91818—21no—
25C2×C5×#217C2212yescomplemented
26#91572C2214yescomplemented
27#91569—24no—
28#91564—22no—
29#91546—22no—
30#91537C2214yescomplemented
31C5×#834C2214yescomplemented
32#90995C2218yescomplemented
33#84110—51nomaximal, Hall
34C2×#4144D311yescharacteristic, complemented
35#66138—31no—
36#65827—32no—
37C2×C5×#99—31no—
38C2×#3938—32no—
39#65031—34no—
40#65030—34no—
41C24×C3×C5D411yescharacteristic, complemented
42C24×C3×C5C2311yescharacteristic
43C23×D15C2311yescharacteristic, complemented
44C23×C3×D5—21no—
45C23×C3×D5D412yescomplemented
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D412yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5D411yescharacteristic, complemented
51C2×#1220—22no—
52C2×#1220—21no—
53C2×#1220—22no—
54C2×#1220—21no—
55C2×#1220—22no—
56C22×Dic15—21no—
57C22×Dic15C2311yescharacteristic, complemented
58C22×C5×Dic3—22no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—24no—
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5—22no—
63C2×C3×C22⋊D5—22no—
64C2×C3×C22⋊D5—22no—
65C2×C3×C22⋊D5—24no—
66C2×C3×C22⋊D5D414yescomplemented
67C2×C3×C22⋊D5C2314yes—
68C22×C3×Dic5—21no—
69C22×C3×Dic5D412yescomplemented
70C3×#711—28no—
71C3×#711—28no—
72C3×D4×D5—28no—
73C3×D4×D5—28no—
74C3×#709—24no—
75C3×#709—24no—
76C2×C3×D20—21no—
77C2×C3×C4×D5—22no—
78C2×C3×Dic10—21no—
79C2×#1202—24no—
80#6719—21no—
81#6719—22no—
82#6719C2312yescomplemented
83#6714—22no—
84#6712—22no—
85C5×#217—22no—
86C5×#217C2314yescomplemented
87Dic3⋊Dic5—24no—
88#6667—24no—
89#6665—24no—
90C2×C3×H(5,𝔽2)—51no—
91#5804—51no—
92#5804—52no—
93#5244—54no—
94#5243—54no—
95C2×#834—52no—
96C2×#834D511yescharacteristic, complemented
97C22×C5×D4C2×D311yescharacteristic
98C22×C22⋊D5—21no—
99C22×C22⋊D5—31no—
100C22×C22⋊D5C2×D312yes—
101#4144—22no—
102#4144—24no—
103#4144C2×D314yes—
104C2×#711—22no—
105C2×D4×D5—22no—
106C2×#709—21no—
107C2×C5×C22⋊C4—32no—
108#4099—61no—
109C2×C22⋊Dic5—31no—
110#4085—62no—
111#4083—32no—
112#4081—32no—
113#4076—64no—
114#4075—61no—
115#4032—34no—
116#4032—62no—
117#4028—34no—
118#4028—62no—
119C5×#99—34no—
120#3938—38no—
121#3026—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—81no—
125C23×C3×C5—81no—
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C23×C3×C5C2×D412yes—
130C23×C3×C5C2×D412yes—
131C23×C3×C5C2411yescharacteristic
132C22×D15—22no—
133C22×D15—21no—
134C22×D15—81no—
135C22×C3×D5—22no—
136C22×C3×D5—24no—
137C22×C3×D5—22no—
138C22×C3×D5—82no—
139C22×C3×D5—82no—
140C22×C3×D5C2×D414yes—
141C3×C5×D4—24no—
142C3×C5×D4—24no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D412yes—
146#1220—41no—
147#1220—42no—
148#1220—41no—
149#1220—82no—
150C2×Dic15—22no—
151C2×Dic15—21no—
152C2×Dic15—22no—
153C2×Dic15—81no—
154C2×C5×Dic3—24no—
155C2×C5×Dic3—82no—
156C3×C22⋊D5—28no—
157C3×C22⋊D5—24no—
158C3×C22⋊D5—24no—
159C3×C22⋊D5—24no—
160C3×C22⋊D5—24no—
161C2×C3×Dic5—24no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5C2×D414yes—
165C3×D20—24no—
166C3×C4×D5—28no—
167C3×Dic10—24no—
168#1202—84no—
169C3×H(5,𝔽2)—54no—
170C3×H(5,𝔽2)—104no—
171C3×H(5,𝔽2)—102no—
172C2×C3×#41—102no—
173C2×C3×#41—101no—
174C22×C3×D4—52no—
175C22×C3×D4—102no—
176C22×C3×D4—101no—
177C22×C3×D4C2×D511yescharacteristic
178C22×#67—51no—
179#953—102no—
180#953—101no—
181C2×#217—51no—
182C2×#217C2×D512yescomplemented
183#939—104no—
184#939—102no—
185#937—52no—
186#937—54no—
187#935—52no—
188#935—54no—
189#929—102no—
190#929—101no—
191#834—58no—
192#834C2×D514yescomplemented
193C24×C5#6711yescharacteristic, complemented
194C24×C5C22×D311yescharacteristic
195C23×D5—21no—
196C23×D5—31no—
197C23×D5#6712yescomplemented
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4#6712yescomplemented
201C2×C5×D4C22×D312yes—
202C22×C4×C5—62no—
203C22×C4×C5#6711yescharacteristic, complemented
204C2×C22⋊D5—22no—
205C2×C22⋊D5—24no—
206C2×C22⋊D5—22no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5—22no—
209C2×C22⋊D5—22no—
210C2×C22⋊D5—24no—
211C2×C22⋊D5—61no—
212C2×C22⋊D5—62no—
213C2×C22⋊D5—62no—
214C2×C22⋊D5—61no—
215C2×C22⋊D5—62no—
216C2×C22⋊D5#6714yescomplemented
217C2×C22⋊D5C22×D314yes—
218C22×Dic5—21no—
219C22×Dic5—31no—
220C22×Dic5—61no—
221C22×Dic5#6712yescomplemented
222#711—28no—
223#711—28no—
224D4×D5—28no—
225D4×D5—28no—
226#709—24no—
227#709—24no—
228C2×D20—21no—
229C2×D20—64no—
230C2×C4×D5—22no—
231C2×Dic10—21no—
232C5×C22⋊C4—34no—
233C5×C22⋊C4—62no—
234C22⋊Dic5—32no—
235C22⋊Dic5—61no—
236C22⋊Dic5—62no—
237#685—64no—
238#685—62no—
239#685—64no—
240C4⋊Dic5—64no—
241#683—62no—
242C2×H(5,𝔽2)—51no—
243#534—152no—
244#534—151no—
245#458—154no—
246B(4,𝔽2)—154no—
247C2×#99—31no—
248C2×#99—152no—
249C22×C3×C5—22no—
250C22×C3×C5—42no—
251C22×C3×C5—41no—
252C22×C3×C5—42no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5—42no—
256C22×C3×C5—42no—
257C22×C3×C5—81no—
258C22×C3×C5#12011yescharacteristic
259C22×C3×C5#12012yes—
260C22×C3×C5#12011yescharacteristic
261C22×C3×C5C22×D411yescharacteristic
262C22×C3×C5C22×D412yes—
263C2×D15—44no—
264C2×D15—42no—
265C2×D15—41no—
266C2×C3×D5—24no—
267C2×C3×D5—44no—
268C2×C3×D5—44no—
269C2×C3×D5—82no—
270C2×C3×D5—84no—
271C3×C4×C5—22no—
272Dic15—42no—
273Dic15—41no—
274C3×Dic5—24no—
275C5×Dic3—44no—
276C24×C3—52no—
277C24×C3—101no—
278C24×C3D2011yescharacteristic, complemented
279C24×C3C22×D511yescharacteristic
280C23×D3—51no—
281C3×#41—104no—
282C3×#41—108no—
283C3×#41—108no—
284C3×#41—104no—
285C2×C3×Q8—101no—
286C2×C3×D4—22no—
287C2×C3×D4—22no—
288C2×C3×D4—54no—
289C2×C3×D4—54no—
290C2×C3×D4—101no—
291C2×C3×D4—108no—
292C2×C3×D4—108no—
293C2×C3×D4—102no—
294C2×C3×D4—104no—
295C2×C3×D4—102no—
296C2×C3×D4—102no—
297C2×C3×D4—104no—
298C2×C3×D4—102no—
299C2×C3×D4—102no—
300C2×C3×D4D2012yescomplemented
301C2×C3×D4C22×D512yes—
302C22×C3×C4—52no—
303C22×C3×C4—102no—
304C22×C3×C4—101no—
305C22×C3×C4D2011yescharacteristic, complemented
306C2×#67—104no—
307C2×#67—101no—
308C2×#67—101no—
309C2×#67—102no—
310C2×#67—102no—
311C2×#67—102no—
312C22×Dic3—22no—
313C22×Dic3—51no—
314C22×Dic3—101no—
315#217—22no—
316#217—52no—
317#217—104no—
318#217—101no—
319#217—102no—
320#217C22×D514yescomplemented
321(C2×D3)⋊C4—104no—
322(C2×D3)⋊C4—102no—
323Dic3⋊C4—104no—
324Dic3⋊C4—102no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—81no—
328C23×C5—81no—
329C23×C5C2×#6712yes—
330C23×C5C2×#6711yescharacteristic
331C23×C5C2×#6711yescharacteristic
332C23×C5C2×#6712yes—
333C23×C5C2×#6712yes—
334C23×C5C23×D311yescharacteristic
335C22×D5—22no—
336C22×D5—24no—
337C22×D5—22no—
338C22×D5—62no—
339C22×D5—61no—
340C22×D5—82no—
341C22×D5—82no—
342C22×D5—241no—
343C22×D5C2×#6714yes—
344C5×D4—24no—
345C5×D4—24no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—64no—
349C2×C4×C5—242no—
350C2×C4×C5C2×#6712yes—
351C22⋊D5—28no—
352C22⋊D5—24no—
353C22⋊D5—24no—
354C22⋊D5—24no—
355C22⋊D5—24no—
356C22⋊D5—121no—
357C22⋊D5—122no—
358C22⋊D5—121no—
359C22⋊D5—242no—
360C2×Dic5—24no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—61no—
364C2×Dic5—62no—
365C2×Dic5—62no—
366C2×Dic5—241no—
367C2×Dic5C2×#6714yes—
368D20—24no—
369D20—244no—
370C4×D5—28no—
371Dic10—24no—
372H(5,𝔽2)—54no—
373H(5,𝔽2)—104no—
374H(5,𝔽2)—102no—
375C2×#41—102no—
376C2×#41—101no—
377C22×D4—52no—
378C22×D4—102no—
379C22×D4—101no—
380C22×D4—151no—
381C22×D4D3×D511yescharacteristic
382#123—154no—
383#123—152no—
384#123—302no—
385#123—301no—
386#121—304no—
387#121—302no—
388#120—154no—
389#120—152no—
390#120—302no—
391#120—301no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—151no—
394#99—34no—
395#99—158no—
396C2×C3×C5—22no—
397C2×C3×C5—21no—
398C2×C3×C5—21no—
399C2×C3×C5—22no—
400C2×C3×C5—21no—
401C2×C3×C5—42no—
402C2×C3×C5C2×#12011yescharacteristic
403D15—81no—
404C3×D5—44no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—54no—
408C23×C3—81no—
409C23×C3—81no—
410C23×C3—104no—
411C23×C3—102no—
412C23×C3—102no—
413C23×C3—402no—
414C23×C3—402no—
415C23×C3C2×D2012yes—
416C23×C3C2×D2011yescharacteristic
417C23×C3C2×D2011yescharacteristic
418C23×C3D4×D512yes—
419C23×C3D4×D512yes—
420C23×C3C23×D511yescharacteristic
421C22×D3—101no—
422C22×D3—102no—
423C22×D3—401no—
424C3×Q8—104no—
425C3×D4—24no—
426C3×D4—24no—
427C3×D4—104no—
428C3×D4—108no—
429C3×D4—104no—
430C3×D4—104no—
431C3×D4—104no—
432C3×D4—104no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—54no—
436C2×C3×C4—108no—
437C2×C3×C4—104no—
438C2×C3×C4—102no—
439C2×C3×C4—102no—
440C2×C3×C4C2×D2012yes—
441#67—201no—
442#67—201no—
443#67—202no—
444#67—404no—
445#67—402no—
446C2×Dic3—24no—
447C2×Dic3—82no—
448C2×Dic3—101no—
449C2×Dic3—102no—
450C2×Dic3—102no—
451C2×Dic3—401no—
452C22×C5—22no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—42no—
459C22×C5—42no—
460C22×C5—81no—
461C22×C5#95311yescharacteristic
462C22×C5#95312yes—
463C22×C5#95311yescharacteristic
464C22×C5C22×#6711yescharacteristic
465C22×C5C22×#6712yes—
466C2×D5—24no—
467C2×D5—44no—
468C2×D5—44no—
469C2×D5—82no—
470C2×D5—84no—
471C2×D5—124no—
472C2×D5—122no—
473C2×D5—121no—
474C4×C5—22no—
475C4×C5—124no—
476Dic5—24no—
477Dic5—122no—
478Dic5—121no—
479C24—52no—
480C24—101no—
481C24—151no—
482C24#120211yescharacteristic, complemented
483C24C2×D3×D511yescharacteristic
484#41—104no—
485#41—108no—
486#41—108no—
487#41—104no—
488C2×Q8—101no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—54no—
492C2×D4—54no—
493C2×D4—101no—
494C2×D4—108no—
495C2×D4—108no—
496C2×D4—102no—
497C2×D4—104no—
498C2×D4—102no—
499C2×D4—102no—
500C2×D4—104no—
501C2×D4—102no—
502C2×D4—102no—
503C2×D4—304no—
504C2×D4—301no—
505C2×D4—301no—
506C2×D4—302no—
507C2×D4—302no—
508C2×D4—302no—
509C2×D4#120212yescomplemented
510C2×D4C2×D3×D512yes—
511C22×C4—52no—
512C22×C4—62no—
513C22×C4—102no—
514C22×C4—101no—
515C22×C4—151no—
516C22×C4—301no—
517C22×C4#120211yescharacteristic, complemented
518C4⋊C4—304no—
519C4⋊C4—302no—
520C22⋊C4—34no—
521C22⋊C4—62no—
522C22⋊C4—152no—
523C22⋊C4—304no—
524C22⋊C4—304no—
525C22⋊C4—301no—
526C22⋊C4—302no—
527C22⋊C4—302no—
528C3×C5#302611yescharacteristic, complemented, Hall
529C22×C3—22no—
530C22×C3—42no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—81no—
538C22×C3—104no—
539C22×C3—204no—
540C22×C3—204no—
541C22×C3—402no—
542C22×C3—404no—
543C22×C3#402811yescharacteristic
544C22×C3#402811yescharacteristic
545C22×C3#402812yes—
546C22×C3C22×D2011yescharacteristic
547C22×C3C2×D4×D512yes—
548C2×D3—204no—
549C2×D3—202no—
550C2×D3—201no—
551C3×C4—22no—
552C3×C4—104no—
553Dic3—44no—
554Dic3—202no—
555Dic3—201no—
556C2×C5—21no—
557C2×C5—22no—
558C2×C5—21no—
559C2×C5—22no—
560C2×C5—21no—
561C2×C5—42no—
562C2×C5C2×#95311yescharacteristic
563D5—44no—
564D5—241no—
565C23—21no—
566C23—21no—
567C23—54no—
568C23—81no—
569C23—81no—
570C23—104no—
571C23—102no—
572C23—102no—
573C23—301no—
574C23—302no—
575C23—402no—
576C23—402no—
577C23—1201no—
578C23C2×#120212yes—
579C23C2×#120211yescharacteristic
580C23C2×#120211yescharacteristic
581C23D5×#6712yes—
582C23D5×#6712yes—
583C23C22×D3×D511yescharacteristic
584Q8—104no—
585D4—24no—
586D4—24no—
587D4—104no—
588D4—108no—
589D4—104no—
590D4—104no—
591D4—104no—
592D4—104no—
593D4—601no—
594D4—601no—
595D4—602no—
596D4—1204no—
597D4—1202no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—54no—
601C2×C4—64no—
602C2×C4—108no—
603C2×C4—104no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—242no—
607C2×C4—302no—
608C2×C4—301no—
609C2×C4—302no—
610C2×C4—1201no—
611C2×C4C2×#120212yes—
612C2×C3—22no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—22no—
617C2×C3—42no—
618C2×C3—204no—
619C2×C3C2×#402811yescharacteristic
620D3—401no—
621C5#8411011yescharacteristic, complemented, Sylow
622C22—22no—
623C22—42no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—41no—
628C22—42no—
629C22—42no—
630C22—81no—
631C22—104no—
632C22—204no—
633C22—204no—
634C22—402no—
635C22—404no—
636C22—604no—
637C22—602no—
638C22—601no—
639C22#9156411yescharacteristic
640C22#9156411yescharacteristic
641C22#9156412yes—
642C22C22×#120211yescharacteristic
643C22C2×D5×#6712yes—
644C4—22no—
645C4—104no—
646C4—124no—
647C4—602no—
648C4—601no—
649C3#1061041711yescharacteristic, complemented, Sylow
650C2—22no—
651C2—21no—
652C2—21no—
653C2—21no—
654C2—22no—
655C2—42no—
656C2—204no—
657C2—1201no—
658C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C2×#120
hypercenterC22×D4D3×D5
hypocenterC3×C5#3026
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4144C2semidirect
2. #11756563C2semidirect
3. #11755427C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. #11749182C2semidirect
7. #11749176C2semidirect
10. C22×#1220C22semidirect
20. C2×#6719C22semidirect
22. #91826C22semidirect
23. #91824C22semidirect
25. C2×C5×#217C22semidirect
26. #91572C22semidirect
30. #91537C22semidirect
31. C5×#834C22semidirect
32. #90995C22semidirect
34. C2×#4144D3semidirect
41. C24×C3×C5D4semidirect
43. C23×D15C23semidirect
45. C23×C3×D5D4semidirect
48. C2×C3×C5×D4D4semidirect
50. C22×C3×C4×C5D4semidirect
57. C22×Dic15C23semidirect
66. C2×C3×C22⋊D5D4semidirect
69. C22×C3×Dic5D4semidirect
82. #6719C23semidirect
86. C5×#217C23semidirect
96. C2×#834D5semidirect
182. C2×#217C2×D5semidirect
192. #834C2×D5semidirect
193. C24×C5#67semidirect
197. C23×D5#67semidirect
200. C2×C5×D4#67semidirect
203. C22×C4×C5#67semidirect
216. C2×C22⋊D5#67semidirect
221. C22×Dic5#67semidirect
278. C24×C3D20semidirect
300. C2×C3×D4D20semidirect
305. C22×C3×C4D20semidirect
320. #217C22×D5semidirect
482. C24#1202semidirect
509. C2×D4#1202semidirect
517. C22×C4#1202semidirect
528. C3×C5#3026semidirect
621. C5#84110semidirect
649. C3#10610417semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41442
#117565632
#117554272
C2×C5×#8342
C2×#909952
#117491822
#117491762
#106104173
#841105