Finite Group Databasebeta

← C2×#11749176 #14425620

Subgroups — C2×#11749176 #14425620

Order 1920.

2036 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4144C211yesmaximal, characteristic, complemented
2C2×#91826C211yesmaximal, characteristic, complemented
3C2×#91572C212yesmaximal, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C212yesmaximal, complemented
6#11749176C218yesmaximal, direct product factor
7C2×#65030—31nomaximal, Hall
8C24×D15C2211yescharacteristic, complemented
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C22×C3×C22⋊D5—21no—
12C22×C3×C22⋊D5C2212yes—
13C3×#4144—22no—
14C3×#4144—24no—
15C3×#4144C2214yescomplemented
16C2×C3×#711—22no—
17C2×C3×D4×D5—22no—
18C2×C3×#709—21no—
19C22×#1202—22no—
20C2×#6719C2211yescharacteristic, complemented
21#91826—22no—
22#91826C2214yescomplemented
23C2×#6714—21no—
24C2×C5×#217C2212yescomplemented
25#91572—24no—
26#91572C2218yescomplemented
27C2×#6667—22no—
28C5×#834C2214yescomplemented
29#90995C2218yescomplemented
30C2×#5244—51nomaximal, Hall
31C2×#4144D311yescharacteristic, complemented
32C2×#4083—31no—
33C2×#4028—32no—
34C2×C5×#99—31no—
35C2×#3938—32no—
36#65030—38no—
37C24×C3×C5D411yescharacteristic, complemented
38C24×C3×C5C2311yescharacteristic
39C23×D15—22no—
40C23×D15—21no—
41C23×D15—21no—
42C23×D15—22no—
43C23×D15—44no—
44C23×D15C2312yescomplemented
45C23×C3×D5—21no—
46C23×C3×D5D412yescomplemented
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4—22no—
49C2×C3×C5×D4D412yescomplemented
50C2×C3×C5×D4C2312yes—
51C22×C3×C4×C5D411yescharacteristic, complemented
52C2×#1220—24no—
53C2×#1220—44no—
54C22×Dic15—21no—
55C22×C5×Dic3—22no—
56C2×C3×C22⋊D5—22no—
57C2×C3×C22⋊D5—24no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5D414yescomplemented
64C2×C3×C22⋊D5C2314yes—
65C22×C3×Dic5—21no—
66C22×C3×Dic5D412yescomplemented
67C3×#711—28no—
68C3×#711—28no—
69C3×D4×D5—28no—
70C3×D4×D5—28no—
71C3×#709—24no—
72C3×#709—24no—
73C2×C3×D20—21no—
74C2×C3×C4×D5—22no—
75C2×C3×Dic10—21no—
76C2×#1202—28no—
77C2×#1202—48no—
78#6719—21no—
79#6719C2312yescomplemented
80#6714—24no—
81C5×#217—22no—
82C5×#217C2314yescomplemented
83#6667—28no—
84C2×C3×H(5,𝔽2)—51no—
85C2×#937—51no—
86C2×#937—52no—
87#5244—58no—
88C2×#834—52no—
89C2×#834D511yescharacteristic, complemented
90C24×D5—31no—
91C22×C5×D4C2×D311yescharacteristic
92C22×C22⋊D5—21no—
93C22×C22⋊D5—61no—
94C22×C22⋊D5C2×D312yes—
95#4144—22no—
96#4144—24no—
97#4144C2×D314yescomplemented
98C2×#711—22no—
99C2×D4×D5—22no—
100C2×#709—21no—
101C22×D20—62no—
102C2×C5×C22⋊C4—32no—
103C2×C22⋊Dic5—31no—
104#4083—34no—
105#4083—62no—
106C2×#685—61no—
107C2×#685—62no—
108#4028—38no—
109#4028—64no—
110C5×#99—34no—
111#3938—38no—
112C2×B(4,𝔽2)—151noSylow
113C23×C3×C5—21no—
114C23×C3×C5—21no—
115C23×C3×C5—42no—
116C23×C3×C5—42no—
117C23×C3×C5C2×D411yescharacteristic
118C23×C3×C5C2×D412yes—
119C23×C3×C5C2×D411yescharacteristic
120C23×C3×C5C2×D412yes—
121C23×C3×C5C2×D412yescomplemented
122C23×C3×C5C2411yescharacteristic
123C22×D15—28no—
124C22×D15—24no—
125C22×D15—24no—
126C22×D15—22no—
127C22×D15—44no—
128C22×D15—48no—
129C22×D15—44no—
130C22×D15—44no—
131C22×D15—42no—
132C22×D15—42no—
133C22×D15—41no—
134C22×D15—41no—
135C22×C3×D5—22no—
136C22×C3×D5—24no—
137C22×C3×D5—22no—
138C22×C3×D5—44no—
139C22×C3×D5—82no—
140C22×C3×D5C2×D414yescomplemented
141C3×C5×D4—24no—
142C3×C5×D4—24no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D412yescomplemented
146#1220—48no—
147C2×Dic15—22no—
148C2×Dic15—42no—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—44no—
151C3×C22⋊D5—28no—
152C3×C22⋊D5—24no—
153C3×C22⋊D5—24no—
154C3×C22⋊D5—24no—
155C3×C22⋊D5—24no—
156C2×C3×Dic5—24no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5C2×D414yescomplemented
160C3×D20—24no—
161C3×C4×D5—28no—
162C3×Dic10—24no—
163#1202—416no—
164C24×D3—51no—
165C3×H(5,𝔽2)—54no—
166C3×H(5,𝔽2)—104no—
167C3×H(5,𝔽2)—102no—
168C2×C3×#41—102no—
169C2×C3×#41—101no—
170C22×C3×D4—52no—
171C22×C3×D4—102no—
172C22×C3×D4—101no—
173C22×C3×D4C2×D511yescharacteristic
174C22×#67—102no—
175C22×#67—101no—
176C2×#217—51no—
177C2×#217C2×D512yescomplemented
178#937—54no—
179#937—58no—
180#937—104no—
181#937—102no—
182C2×(C2×D3)⋊C4—102no—
183C2×(C2×D3)⋊C4—101no—
184#834—58no—
185#834C2×D514yescomplemented
186C24×C5#6711yescharacteristic, complemented
187C24×C5C22×D311yescharacteristic
188C23×D5—21no—
189C23×D5—32no—
190C23×D5—62no—
191C23×D5—61no—
192C23×D5—62no—
193C23×D5—61no—
194C23×D5—124no—
195C23×D5#6712yescomplemented
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4#6712yescomplemented
199C2×C5×D4C22×D312yes—
200C22×C4×C5—62no—
201C22×C4×C5#6711yescharacteristic, complemented
202C2×C22⋊D5—22no—
203C2×C22⋊D5—24no—
204C2×C22⋊D5—22no—
205C2×C22⋊D5—22no—
206C2×C22⋊D5—22no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5—24no—
209C2×C22⋊D5—64no—
210C2×C22⋊D5—124no—
211C2×C22⋊D5#6714yescomplemented
212C2×C22⋊D5C22×D314yes—
213C22×Dic5—21no—
214C22×Dic5—61no—
215C22×Dic5#6712yescomplemented
216#711—28no—
217#711—28no—
218D4×D5—28no—
219D4×D5—28no—
220#709—24no—
221#709—24no—
222C2×D20—21no—
223C2×D20—68no—
224C2×D20—128no—
225C2×C4×D5—22no—
226C2×Dic10—21no—
227C5×C22⋊C4—34no—
228C5×C22⋊C4—62no—
229C22⋊Dic5—32no—
230C22⋊Dic5—61no—
231#685—64no—
232#685—68no—
233C2×H(5,𝔽2)—51no—
234C2×#120—152no—
235C2×#120—151no—
236B(4,𝔽2)—158no—
237C2×#99—31no—
238C2×#99—152no—
239C22×C3×C5—24no—
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5—41no—
243C22×C3×C5—42no—
244C22×C3×C5—41no—
245C22×C3×C5—42no—
246C22×C3×C5—42no—
247C22×C3×C5—81no—
248C22×C3×C5#12012yes—
249C22×C3×C5#12011yescharacteristic
250C22×C3×C5#12011yescharacteristic
251C22×C3×C5C22×D411yescharacteristic
252C22×C3×C5C22×D412yes—
253C2×D15—28no—
254C2×D15—24no—
255C2×D15—44no—
256C2×D15—42no—
257C2×D15—48no—
258C2×D15—44no—
259C2×D15—42no—
260C2×D15—44no—
261C2×C3×D5—24no—
262C2×C3×D5—44no—
263C2×C3×D5—44no—
264C2×C3×D5—82no—
265C2×C3×D5—84no—
266C3×C4×C5—22no—
267Dic15—42no—
268C3×Dic5—24no—
269C5×Dic3—44no—
270C24×C3—52no—
271C24×C3—101no—
272C24×C3D2011yescharacteristic, complemented
273C24×C3C22×D511yescharacteristic
274C23×D3—52no—
275C23×D3—101no—
276C23×D3—102no—
277C23×D3—101no—
278C23×D3—102no—
279C23×D3—204no—
280C3×#41—104no—
281C3×#41—108no—
282C3×#41—108no—
283C3×#41—104no—
284C2×C3×Q8—101no—
285C2×C3×D4—22no—
286C2×C3×D4—22no—
287C2×C3×D4—54no—
288C2×C3×D4—54no—
289C2×C3×D4—101no—
290C2×C3×D4—108no—
291C2×C3×D4—108no—
292C2×C3×D4—102no—
293C2×C3×D4—104no—
294C2×C3×D4—102no—
295C2×C3×D4—102no—
296C2×C3×D4—104no—
297C2×C3×D4—102no—
298C2×C3×D4—102no—
299C2×C3×D4D2012yescomplemented
300C2×C3×D4C22×D512yes—
301C22×C3×C4—52no—
302C22×C3×C4—102no—
303C22×C3×C4—101no—
304C22×C3×C4D2011yescharacteristic, complemented
305C2×#67—108no—
306C2×#67—104no—
307C2×#67—208no—
308C2×#67—204no—
309C22×Dic3—22no—
310C22×Dic3—101no—
311#217—22no—
312#217—52no—
313#217—101no—
314#217C22×D514yescomplemented
315(C2×D3)⋊C4—108no—
316(C2×D3)⋊C4—104no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—42no—
320C23×C5—42no—
321C23×C5C2×#6711yescharacteristic
322C23×C5C2×#6711yescharacteristic
323C23×C5C2×#6712yes—
324C23×C5C2×#6712yes—
325C23×C5C2×#6712yescomplemented
326C23×C5C23×D311yescharacteristic
327C22×D5—22no—
328C22×D5—24no—
329C22×D5—22no—
330C22×D5—44no—
331C22×D5—68no—
332C22×D5—64no—
333C22×D5—64no—
334C22×D5—62no—
335C22×D5—82no—
336C22×D5—124no—
337C22×D5—128no—
338C22×D5—124no—
339C22×D5—122no—
340C22×D5—124no—
341C22×D5—122no—
342C22×D5—121no—
343C22×D5—121no—
344C22×D5C2×#6714yescomplemented
345C5×D4—24no—
346C5×D4—24no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—64no—
350C2×C4×C5—124no—
351C2×C4×C5C2×#6712yescomplemented
352C22⋊D5—28no—
353C22⋊D5—24no—
354C22⋊D5—24no—
355C22⋊D5—24no—
356C22⋊D5—24no—
357C22⋊D5—128no—
358C2×Dic5—24no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—62no—
362C2×Dic5—122no—
363C2×Dic5C2×#6714yescomplemented
364D20—24no—
365D20—1216no—
366C4×D5—28no—
367Dic10—24no—
368C25—151no—
369H(5,𝔽2)—54no—
370H(5,𝔽2)—104no—
371H(5,𝔽2)—102no—
372C2×#41—102no—
373C2×#41—101no—
374C22×D4—52no—
375C22×D4—102no—
376C22×D4—101no—
377C22×D4—302no—
378C22×D4—301no—
379C22×D4D3×D511yescharacteristic
380#120—158no—
381#120—154no—
382#120—304no—
383#120—302no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—302no—
387C2×C22⋊C4—301no—
388#99—34no—
389#99—158no—
390C2×C3×C5—22no—
391C2×C3×C5—21no—
392C2×C3×C5—22no—
393C2×C3×C5—21no—
394C2×C3×C5—42no—
395C2×C3×C5B(4,𝔽2)12yescomplemented
396C2×C3×C5C2×#12011yescharacteristic
397D15—44no—
398C3×D5—44no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—54no—
404C23×C3—104no—
405C23×C3—102no—
406C23×C3—102no—
407C23×C3—204no—
408C23×C3—402no—
409C23×C3C2×D2011yescharacteristic
410C23×C3C2×D2011yescharacteristic
411C23×C3C2×D2012yescomplemented
412C23×C3D4×D512yes—
413C23×C3D4×D512yes—
414C23×C3C23×D511yescharacteristic
415C22×D3—108no—
416C22×D3—104no—
417C22×D3—102no—
418C22×D3—104no—
419C22×D3—204no—
420C22×D3—204no—
421C22×D3—208no—
422C22×D3—204no—
423C22×D3—202no—
424C22×D3—201no—
425C22×D3—202no—
426C22×D3—201no—
427C3×Q8—104no—
428C3×D4—24no—
429C3×D4—24no—
430C3×D4—104no—
431C3×D4—108no—
432C3×D4—104no—
433C3×D4—104no—
434C3×D4—104no—
435C3×D4—104no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—54no—
439C2×C3×C4—108no—
440C2×C3×C4—104no—
441C2×C3×C4—102no—
442C2×C3×C4—102no—
443C2×C3×C4C2×D2012yescomplemented
444#67—2016no—
445#67—208no—
446C2×Dic3—24no—
447C2×Dic3—44no—
448C2×Dic3—102no—
449C2×Dic3—202no—
450C22×C5—22no—
451C22×C5—24no—
452C22×C5—22no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—41no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—81no—
459C22×C5#95312yes—
460C22×C5#95311yescharacteristic
461C22×C5#95311yescharacteristic
462C22×C5C22×#6711yescharacteristic
463C22×C5C22×#6712yes—
464C2×D5—24no—
465C2×D5—44no—
466C2×D5—44no—
467C2×D5—68no—
468C2×D5—64no—
469C2×D5—82no—
470C2×D5—84no—
471C2×D5—122no—
472C2×D5—124no—
473C2×D5—128no—
474C2×D5—124no—
475C2×D5—124no—
476C2×D5—122no—
477C4×C5—22no—
478C4×C5—124no—
479Dic5—24no—
480Dic5—122no—
481C24—52no—
482C24—101no—
483C24—152no—
484C24—301no—
485C24—302no—
486C24—301no—
487C24—302no—
488C24—604no—
489C24#120211yescharacteristic, complemented
490C24C2×D3×D511yescharacteristic
491#41—104no—
492#41—108no—
493#41—108no—
494#41—104no—
495C2×Q8—101no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—54no—
499C2×D4—54no—
500C2×D4—101no—
501C2×D4—108no—
502C2×D4—108no—
503C2×D4—102no—
504C2×D4—104no—
505C2×D4—102no—
506C2×D4—102no—
507C2×D4—104no—
508C2×D4—102no—
509C2×D4—102no—
510C2×D4—308no—
511C2×D4—304no—
512C2×D4—608no—
513C2×D4—604no—
514C2×D4#120212yescomplemented
515C2×D4C2×D3×D512yes—
516C22×C4—52no—
517C22×C4—62no—
518C22×C4—102no—
519C22×C4—101no—
520C22×C4—301no—
521C22×C4#120211yescharacteristic, complemented
522C22⋊C4—34no—
523C22⋊C4—62no—
524C22⋊C4—152no—
525C22⋊C4—308no—
526C22⋊C4—301no—
527C22⋊C4—304no—
528C3×C5C2×B(4,𝔽2)11yescharacteristic, complemented, Hall
529C22×C3—24no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—41no—
533C22×C3—42no—
534C22×C3—41no—
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#402812yes—
545C22×C3#402811yescharacteristic
546C22×C3C22×D2011yescharacteristic
547C22×C3C2×D4×D512yes—
548C2×D3—108no—
549C2×D3—104no—
550C2×D3—204no—
551C2×D3—202no—
552C2×D3—204no—
553C2×D3—208no—
554C2×D3—204no—
555C2×D3—202no—
556C3×C4—22no—
557C3×C4—104no—
558Dic3—44no—
559Dic3—202no—
560C2×C5—21no—
561C2×C5—22no—
562C2×C5—22no—
563C2×C5—21no—
564C2×C5—42no—
565C2×C5#524412yescomplemented
566C2×C5C2×#95311yescharacteristic
567D5—44no—
568D5—124no—
569C23—21no—
570C23—21no—
571C23—42no—
572C23—42no—
573C23—54no—
574C23—104no—
575C23—102no—
576C23—102no—
577C23—204no—
578C23—308no—
579C23—304no—
580C23—302no—
581C23—304no—
582C23—402no—
583C23—604no—
584C23—602no—
585C23—604no—
586C23—604no—
587C23—608no—
588C23—601no—
589C23—602no—
590C23—601no—
591C23C2×#120211yescharacteristic
592C23C2×#120211yescharacteristic
593C23C2×#120212yescomplemented
594C23D5×#6712yes—
595C23D5×#6712yes—
596C23C22×D3×D511yescharacteristic
597Q8—104no—
598D4—24no—
599D4—24no—
600D4—104no—
601D4—108no—
602D4—104no—
603D4—104no—
604D4—104no—
605D4—104no—
606D4—6016no—
607D4—608no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—54no—
611C2×C4—64no—
612C2×C4—108no—
613C2×C4—104no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—124no—
617C2×C4—302no—
618C2×C4—602no—
619C2×C4C2×#120212yescomplemented
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—22no—
624C2×C3—42no—
625C2×C3—204no—
626C2×C3#6503012yescomplemented
627C2×C3C2×#402811yescharacteristic
628D3—204no—
629C5C2×#524411yescharacteristic, complemented, Sylow
630C22—24no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—81no—
639C22—104no—
640C22—204no—
641C22—204no—
642C22—308no—
643C22—304no—
644C22—402no—
645C22—404no—
646C22—604no—
647C22—602no—
648C22—604no—
649C22—608no—
650C22—604no—
651C22—602no—
652C22#9156411yescharacteristic
653C22#9156412yes—
654C22#9156411yescharacteristic
655C22C22×#120211yescharacteristic
656C22C2×D5×#6712yes—
657C4—22no—
658C4—104no—
659C4—124no—
660C4—602no—
661C3C2×#6503011yescharacteristic, complemented, Sylow
662C2—22no—
663C2—21no—
664C2—21no—
665C2—22no—
666C2—42no—
667C2—204no—
668C2—604no—
669C2#1174917612yesdirect product factor
670C2C2×#9156411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#120
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×B(4,𝔽2)
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4144C2semidirect
2. C2×#91826C2semidirect
3. C2×#91572C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. #11749176C2direct (N × H)
8. C24×D15C22semidirect
15. C3×#4144C22semidirect
20. C2×#6719C22semidirect
22. #91826C22semidirect
24. C2×C5×#217C22semidirect
26. #91572C22semidirect
28. C5×#834C22semidirect
29. #90995C22semidirect
31. C2×#4144D3semidirect
37. C24×C3×C5D4semidirect
44. C23×D15C23semidirect
46. C23×C3×D5D4semidirect
49. C2×C3×C5×D4D4semidirect
51. C22×C3×C4×C5D4semidirect
63. C2×C3×C22⋊D5D4semidirect
66. C22×C3×Dic5D4semidirect
79. #6719C23semidirect
82. C5×#217C23semidirect
89. C2×#834D5semidirect
97. #4144C2×D3semidirect
121. C23×C3×C5C2×D4semidirect
140. C22×C3×D5C2×D4semidirect
145. C2×C3×C4×C5C2×D4semidirect
159. C2×C3×Dic5C2×D4semidirect
177. C2×#217C2×D5semidirect
185. #834C2×D5semidirect
186. C24×C5#67semidirect
195. C23×D5#67semidirect
198. C2×C5×D4#67semidirect
201. C22×C4×C5#67semidirect
211. C2×C22⋊D5#67semidirect
215. C22×Dic5#67semidirect
272. C24×C3D20semidirect
299. C2×C3×D4D20semidirect
304. C22×C3×C4D20semidirect
314. #217C22×D5semidirect
325. C23×C5C2×#67semidirect
344. C22×D5C2×#67semidirect
351. C2×C4×C5C2×#67semidirect
363. C2×Dic5C2×#67semidirect
395. C2×C3×C5B(4,𝔽2)semidirect
411. C23×C3C2×D20semidirect
443. C2×C3×C4C2×D20semidirect
489. C24#1202semidirect
514. C2×D4#1202semidirect
521. C22×C4#1202semidirect
528. C3×C5C2×B(4,𝔽2)semidirect
565. C2×C5#5244semidirect
593. C23C2×#1202semidirect
619. C2×C4C2×#1202semidirect
626. C2×C3#65030semidirect
629. C5C2×#5244semidirect
661. C3C2×#65030semidirect
669. C2#11749176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C2×#918262
C2×#915722
C2×C5×#8342
C2×#909952
#117491762
C2×#650303
C2×#52445