Finite Group Databasebeta

← C2×#11749179 #14425619

Subgroups — C2×#11749179 #14425619

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×#92095C211yesmaximal, characteristic, complemented
2C2×C3×#4083C211yesmaximal, characteristic, complemented
3C2×#91564C212yesmaximal, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90997C212yesmaximal, complemented
6#11749179C218yesmaximal, direct product factor
7C2×#65030—31nomaximal, Hall
8C24×C3×D5C2211yescharacteristic, complemented
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C22×#1220C2212yes—
12#92095—22no—
13#92095—24no—
14#92095C2214yescomplemented
15C2×#6819—22no—
16C2×D4×D15—22no—
17C2×#6817—21no—
18C22×C3×C22⋊D5—21no—
19C22×#1202—22no—
20C2×C5×#217C2212yescomplemented
21C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
22C3×#4083—22no—
23C3×#4083C2214yescomplemented
24C2×C3×#685—21no—
25#91564—24no—
26#91564C2218yescomplemented
27C2×#6665—22no—
28C5×#834C2214yescomplemented
29#90997C2218yescomplemented
30C2×#5032—51nomaximal, Hall
31C2×#4144—31no—
32C2×#4083D311yescharacteristic, complemented
33C2×#4028—32no—
34C2×C5×#99—31no—
35C2×#3938—32no—
36#65030—38no—
37C24×C3×C5D411yescharacteristic, complemented
38C24×C3×C5C2311yescharacteristic
39C23×D15—21no—
40C23×D15D412yescomplemented
41C23×C3×D5—22no—
42C23×C3×D5—21no—
43C23×C3×D5—21no—
44C23×C3×D5—22no—
45C23×C3×D5—44no—
46C23×C3×D5C2312yescomplemented
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—22no—
53C2×#1220—24no—
54C2×#1220—22no—
55C2×#1220—22no—
56C2×#1220—22no—
57C2×#1220—22no—
58C2×#1220—24no—
59C2×#1220D414yescomplemented
60C2×#1220C2314yes—
61C22×Dic15—21no—
62C22×Dic15D412yescomplemented
63#6819—28no—
64#6819—28no—
65D4×D15—28no—
66D4×D15—28no—
67#6817—24no—
68#6817—24no—
69C2×D60—21no—
70C2×C4×D15—22no—
71C2×Dic30—21no—
72C22×C5×Dic3—22no—
73C2×C3×C22⋊D5—24no—
74C2×C3×C22⋊D5—44no—
75C22×C3×Dic5—21no—
76C2×#1202—28no—
77C2×#1202—48no—
78C5×#217—22no—
79C5×#217C2314yescomplemented
80C3×C22⋊Dic5—21no—
81C3×C22⋊Dic5C2312yescomplemented
82C3×#685—24no—
83#6665—28no—
84C2×#1004—51no—
85C2×C3×#120—51no—
86C2×#953—52no—
87C2×#834D511yescharacteristic, complemented
88#5032—58no—
89C2×#806—52no—
90C24×D5C2×D311yescharacteristic, complemented
91C22×C5×D4C2×D311yescharacteristic
92C22×C22⋊D5—21no—
93C22×C22⋊D5—32no—
94C22×C22⋊D5—61no—
95#4144—34no—
96#4144—64no—
97#4144—62no—
98C2×#711—62no—
99C2×D4×D5—62no—
100C2×#709—61no—
101C22×D20—62no—
102C2×C5×C22⋊C4—32no—
103C2×C22⋊Dic5C2×D311yescharacteristic, complemented
104#4083—22no—
105#4083C2×D314yescomplemented
106C2×#685—21no—
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—22no—
124C22×D15—24no—
125C22×D15—22no—
126C22×D15—44no—
127C22×D15—82no—
128C22×D15C2×D414yescomplemented
129C22×C3×D5—28no—
130C22×C3×D5—24no—
131C22×C3×D5—24no—
132C22×C3×D5—22no—
133C22×C3×D5—44no—
134C22×C3×D5—48no—
135C22×C3×D5—44no—
136C22×C3×D5—42no—
137C22×C3×D5—44no—
138C22×C3×D5—42no—
139C22×C3×D5—41no—
140C22×C3×D5—41no—
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—28no—
147#1220—24no—
148#1220—24no—
149#1220—24no—
150#1220—24no—
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15C2×D414yescomplemented
155D60—24no—
156C4×D15—28no—
157Dic30—24no—
158C2×C5×Dic3—24no—
159C2×C5×Dic3—44no—
160C3×C22⋊D5—48no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—42no—
163#1202—416no—
164C25×C3—51no—
165C22×C3×D4—101no—
166C22×C3×D4C2×D511yescharacteristic
167C22×#67—52no—
168C22×#67—102no—
169C22×#67—101no—
170#1004—54no—
171#1004—104no—
172#1004—102no—
173C2×#237—102no—
174C2×D3×D4—102no—
175C2×#235—101no—
176C3×#120—54no—
177C3×#120—102no—
178C2×C3×C22⋊C4—51no—
179C2×C3×C22⋊C4—101no—
180#953—58no—
181#953—104no—
182C2×#217—102no—
183C2×#217C2×D512yescomplemented
184#834C2×D514yescomplemented
185#806—58no—
186C24×C5#6711yescharacteristic, complemented
187C24×C5C22×D311yescharacteristic
188C23×D5—22no—
189C23×D5—21no—
190C23×D5—22no—
191C23×D5—21no—
192C23×D5—32no—
193C23×D5—44no—
194C23×D5—61no—
195C23×D5C22×D312yescomplemented
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—24no—
203C2×C22⋊D5—34no—
204C2×C22⋊D5—34no—
205C2×C22⋊D5—44no—
206C2×C22⋊D5—62no—
207C2×C22⋊D5—64no—
208C2×C22⋊D5—62no—
209C2×C22⋊D5—62no—
210C2×C22⋊D5—62no—
211C2×C22⋊D5—62no—
212C2×C22⋊D5—64no—
213C22×Dic5—21no—
214C22×Dic5—32no—
215C22×Dic5—61no—
216#711—68no—
217#711—68no—
218D4×D5—68no—
219D4×D5—68no—
220#709—64no—
221#709—64no—
222C2×D20—61no—
223C2×D20—68no—
224C2×D20—128no—
225C2×C4×D5—62no—
226C2×Dic10—61no—
227C5×C22⋊C4—34no—
228C5×C22⋊C4—62no—
229C22⋊Dic5—21no—
230C22⋊Dic5C22×D312yescomplemented
231#685—24no—
232#685—68no—
233C2×H(5,𝔽2)—151no—
234C2×#120—51no—
235C2×#120—152no—
236B(4,𝔽2)—158no—
237C2×#99—31no—
238C2×#99—152no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
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—24no—
254C2×D15—44no—
255C2×D15—44no—
256C2×D15—82no—
257C2×D15—84no—
258C2×C3×D5—28no—
259C2×C3×D5—24no—
260C2×C3×D5—44no—
261C2×C3×D5—42no—
262C2×C3×D5—48no—
263C2×C3×D5—44no—
264C2×C3×D5—42no—
265C2×C3×D5—44no—
266C3×C4×C5—22no—
267Dic15—24no—
268C3×Dic5—42no—
269C5×Dic3—44no—
270C24×C3—52no—
271C24×C3—101no—
272C24×C3—102no—
273C24×C3—101no—
274C24×C3—102no—
275C24×C3—204no—
276C24×C3D2011yescharacteristic, complemented
277C24×C3C22×D511yescharacteristic
278C23×D3—52no—
279C23×D3—101no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—104no—
283C2×C3×D4—204no—
284C2×C3×D4D2012yescomplemented
285C2×C3×D4C22×D512yes—
286C22×C3×C4—101no—
287C22×C3×C4D2011yescharacteristic, complemented
288C2×#67—54no—
289C2×#67—54no—
290C2×#67—108no—
291C2×#67—102no—
292C2×#67—104no—
293C2×#67—102no—
294C2×#67—102no—
295C2×#67—104no—
296C2×#67—102no—
297C2×#67—102no—
298C2×#67—208no—
299C22×Dic3—22no—
300C22×Dic3—52no—
301C22×Dic3—101no—
302#237—108no—
303#237—108no—
304D3×D4—108no—
305D3×D4—108no—
306#235—104no—
307#235—104no—
308C2×D12—101no—
309C2×C4×D3—102no—
310C2×Dic6—101no—
311C3×C22⋊C4—52no—
312C3×C22⋊C4—101no—
313C3×C22⋊C4—104no—
314#217—22no—
315#217—108no—
316#217C22×D514yescomplemented
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—42no—
320C23×C5—42no—
321C23×C5D3×D412yes—
322C23×C5D3×D412yes—
323C23×C5C2×#6711yescharacteristic
324C23×C5C2×#6711yescharacteristic
325C23×C5C2×#6712yescomplemented
326C23×C5C23×D311yescharacteristic
327C22×D5—28no—
328C22×D5—24no—
329C22×D5—24no—
330C22×D5—22no—
331C22×D5—34no—
332C22×D5—44no—
333C22×D5—48no—
334C22×D5—44no—
335C22×D5—42no—
336C22×D5—44no—
337C22×D5—42no—
338C22×D5—41no—
339C22×D5—41no—
340C22×D5—62no—
341C22×D5—64no—
342C22×D5—62no—
343C22×D5—124no—
344C22×D5—242no—
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—48no—
353C22⋊D5—68no—
354C22⋊D5—64no—
355C22⋊D5—64no—
356C22⋊D5—64no—
357C22⋊D5—64no—
358C2×Dic5—22no—
359C2×Dic5—34no—
360C2×Dic5—42no—
361C2×Dic5—64no—
362C2×Dic5—62no—
363C2×Dic5—62no—
364D20—64no—
365D20—1216no—
366C4×D5—68no—
367Dic10—64no—
368C25—51no—
369H(5,𝔽2)—154no—
370H(5,𝔽2)—304no—
371H(5,𝔽2)—302no—
372C2×#41—302no—
373C2×#41—301no—
374C22×D4—101no—
375C22×D4—152no—
376C22×D4—302no—
377C22×D4—302no—
378C22×D4—301no—
379C22×D4D3×D511yescharacteristic
380#120—54no—
381#120—102no—
382#120—158no—
383#120—304no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—51no—
386C2×C22⋊C4—101no—
387C2×C22⋊C4—302no—
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—108no—
404C23×C3—104no—
405C23×C3—102no—
406C23×C3—104no—
407C23×C3—204no—
408C23×C3—202no—
409C23×C3—204no—
410C23×C3—204no—
411C23×C3—208no—
412C23×C3—202no—
413C23×C3—201no—
414C23×C3—201no—
415C23×C3C2×D2011yescharacteristic
416C23×C3C2×D2011yescharacteristic
417C23×C3C2×D2012yescomplemented
418C23×C3D4×D512yes—
419C23×C3D4×D512yes—
420C23×C3C23×D511yescharacteristic
421C22×D3—54no—
422C22×D3—102no—
423C22×D3—104no—
424C22×D3—102no—
425C22×D3—204no—
426C22×D3—402no—
427C3×D4—24no—
428C3×D4—24no—
429C3×D4—208no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—102no—
433C2×C3×C4—202no—
434C2×C3×C4C2×D2012yescomplemented
435#67—108no—
436#67—104no—
437#67—104no—
438#67—104no—
439#67—104no—
440#67—2016no—
441C2×Dic3—24no—
442C2×Dic3—44no—
443C2×Dic3—54no—
444C2×Dic3—104no—
445C2×Dic3—102no—
446C2×Dic3—102no—
447D12—104no—
448C4×D3—108no—
449Dic6—104no—
450C22×C5—22no—
451C22×C5—24no—
452C22×C5—22no—
453C22×C5—42no—
454C22×C5—41no—
455C22×C5—41no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—81no—
459C22×C5#93712yes—
460C22×C5#93711yescharacteristic
461C22×C5#93711yescharacteristic
462C22×C5C2×D3×D412yes—
463C22×C5C22×#6711yescharacteristic
464C2×D5—28no—
465C2×D5—24no—
466C2×D5—42no—
467C2×D5—44no—
468C2×D5—48no—
469C2×D5—44no—
470C2×D5—42no—
471C2×D5—44no—
472C2×D5—64no—
473C2×D5—124no—
474C2×D5—124no—
475C2×D5—242no—
476C2×D5—244no—
477C4×C5—22no—
478C4×C5—124no—
479Dic5—42no—
480Dic5—64no—
481C24—52no—
482C24—101no—
483C24—102no—
484C24—101no—
485C24—102no—
486C24—152no—
487C24—204no—
488C24—301no—
489C24#120211yescharacteristic, complemented
490C24C2×D3×D511yescharacteristic
491#41—304no—
492#41—308no—
493#41—308no—
494#41—304no—
495C2×Q8—301no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—104no—
499C2×D4—154no—
500C2×D4—154no—
501C2×D4—204no—
502C2×D4—301no—
503C2×D4—308no—
504C2×D4—308no—
505C2×D4—308no—
506C2×D4—302no—
507C2×D4—304no—
508C2×D4—302no—
509C2×D4—302no—
510C2×D4—304no—
511C2×D4—302no—
512C2×D4—302no—
513C2×D4—608no—
514C2×D4#120212yescomplemented
515C2×D4C2×D3×D512yes—
516C22×C4—62no—
517C22×C4—101no—
518C22×C4—152no—
519C22×C4—302no—
520C22×C4—301no—
521C22×C4#120211yescharacteristic, complemented
522C22⋊C4—34no—
523C22⋊C4—52no—
524C22⋊C4—62no—
525C22⋊C4—101no—
526C22⋊C4—104no—
527C22⋊C4—308no—
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—108no—
539C22×C3—104no—
540C22×C3—204no—
541C22×C3—202no—
542C22×C3—208no—
543C22×C3—204no—
544C22×C3—204no—
545C22×C3—202no—
546C22×C3#402812yes—
547C22×C3#402811yescharacteristic
548C22×C3#402811yescharacteristic
549C22×C3C22×D2011yescharacteristic
550C22×C3C2×D4×D512yes—
551C2×D3—104no—
552C2×D3—204no—
553C2×D3—204no—
554C2×D3—402no—
555C2×D3—404no—
556C3×C4—22no—
557C3×C4—202no—
558Dic3—44no—
559Dic3—104no—
560C2×C5—21no—
561C2×C5—22no—
562C2×C5—22no—
563C2×C5—21no—
564C2×C5—42no—
565C2×C5#503212yescomplemented
566C2×C5C2×#93711yescharacteristic
567D5—44no—
568D5—124no—
569C23—21no—
570C23—21no—
571C23—42no—
572C23—42no—
573C23—104no—
574C23—108no—
575C23—102no—
576C23—104no—
577C23—154no—
578C23—204no—
579C23—202no—
580C23—204no—
581C23—204no—
582C23—208no—
583C23—201no—
584C23—202no—
585C23—201no—
586C23—304no—
587C23—302no—
588C23—302no—
589C23—604no—
590C23—1202no—
591C23C2×#120211yescharacteristic
592C23C2×#120211yescharacteristic
593C23C2×#120212yescomplemented
594C23#679012yes—
595C23#679012yes—
596C23C22×D3×D511yescharacteristic
597Q8—304no—
598D4—24no—
599D4—24no—
600D4—208no—
601D4—304no—
602D4—308no—
603D4—304no—
604D4—304no—
605D4—304no—
606D4—304no—
607D4—6016no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—64no—
611C2×C4—102no—
612C2×C4—124no—
613C2×C4—154no—
614C2×C4—202no—
615C2×C4—308no—
616C2×C4—304no—
617C2×C4—302no—
618C2×C4—302no—
619C2×C4C2×#120212yescomplemented
620C2×C3—22no—
621C2×C3—21no—
622C2×C3—22no—
623C2×C3—21no—
624C2×C3—42no—
625C2×C3—204no—
626C2×C3#6503012yescomplemented
627C2×C3C2×#402811yescharacteristic
628D3—204no—
629C5C2×#503211yescharacteristic, complemented, Sylow
630C22—24no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—81no—
639C22—104no—
640C22—108no—
641C22—204no—
642C22—202no—
643C22—204no—
644C22—208no—
645C22—204no—
646C22—202no—
647C22—304no—
648C22—604no—
649C22—604no—
650C22—1202no—
651C22—1204no—
652C22#9157211yescharacteristic
653C22#9157212yes—
654C22#9157211yescharacteristic
655C22C22×#120211yescharacteristic
656C22C2×#679012yes—
657C4—22no—
658C4—124no—
659C4—202no—
660C4—304no—
661C3C2×#6503011yescharacteristic, complemented, Sylow
662C2—22no—
663C2—21no—
664C2—21no—
665C2—22no—
666C2—42no—
667C2—204no—
668C2—604no—
669C2#1174917912yesdirect product factor
670C2C2×#9157211yescharacteristic
subgroupG/H
centerC22#91572
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×#92095C2semidirect
2. C2×C3×#4083C2semidirect
3. C2×#91564C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90997C2semidirect
6. #11749179C2direct (N × H)
8. C24×C3×D5C22semidirect
14. #92095C22semidirect
20. C2×C5×#217C22semidirect
21. C2×C3×C22⋊Dic5C22semidirect
23. C3×#4083C22semidirect
26. #91564C22semidirect
28. C5×#834C22semidirect
29. #90997C22semidirect
32. C2×#4083D3semidirect
37. C24×C3×C5D4semidirect
40. C23×D15D4semidirect
46. C23×C3×D5C23semidirect
49. C2×C3×C5×D4D4semidirect
51. C22×C3×C4×C5D4semidirect
59. C2×#1220D4semidirect
62. C22×Dic15D4semidirect
79. C5×#217C23semidirect
81. C3×C22⋊Dic5C23semidirect
87. C2×#834D5semidirect
90. C24×D5C2×D3semidirect
103. C2×C22⋊Dic5C2×D3semidirect
105. #4083C2×D3semidirect
121. C23×C3×C5C2×D4semidirect
128. C22×D15C2×D4semidirect
145. C2×C3×C4×C5C2×D4semidirect
154. C2×Dic15C2×D4semidirect
183. C2×#217C2×D5semidirect
184. #834C2×D5semidirect
186. C24×C5#67semidirect
195. C23×D5C22×D3semidirect
198. C2×C5×D4#67semidirect
201. C22×C4×C5#67semidirect
230. C22⋊Dic5C22×D3semidirect
276. C24×C3D20semidirect
284. C2×C3×D4D20semidirect
287. C22×C3×C4D20semidirect
316. #217C22×D5semidirect
325. C23×C5C2×#67semidirect
351. C2×C4×C5C2×#67semidirect
395. C2×C3×C5B(4,𝔽2)semidirect
417. C23×C3C2×D20semidirect
434. 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#5032semidirect
593. C23C2×#1202semidirect
619. C2×C4C2×#1202semidirect
626. C2×C3#65030semidirect
629. C5C2×#5032semidirect
661. C3C2×#65030semidirect
669. C2#11749179direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920952
C2×C3×#40832
C2×#915642
C2×C5×#8342
C2×#909972
#117491792
C2×#650303
C2×#50325