Finite Group Databasebeta

← C2×#11749151 #14423205

Subgroups — C2×#11749151 #14423205

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×D12C211yesmaximal, characteristic, complemented
2C22×#6715C211yesmaximal, characteristic, complemented
3C22×C5×#213C211yesmaximal, characteristic, complemented
4C2×C3×#4084C211yesmaximal, characteristic, complemented
5#11749151C218yesmaximal, direct product factor
6C2×#90968C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65445—31nomaximal, Hall
10C23×D3×D5—21no—
11C22×C3×C5×D4C2211yescharacteristic, complemented
12C22×D60C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C22×C3×C22⋊D5—21no—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1203—21no—
17C2×D5×D12—24no—
18C2×D5×D12—24no—
19C2×D5×D12—22no—
20C2×D5×D12C2214yescomplemented
21C2×#6715—24no—
22C2×#6715C2214yescomplemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C2×C5×#213—24no—
25C2×C5×#213C2214yescomplemented
26C22×C5×C3⋊C8C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5—21no—
28C3×#4084—22no—
29C3×#4084C2214yescomplemented
30C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
31#90968C2214yescomplemented
32#90966C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5036—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×C5×D8—31no—
37C2×#4084D311yescharacteristic, complemented
38C22×#686—31no—
39C2×#3964—31no—
40#65445—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C24×C3×C5—21no—
44C23×D15—21no—
45C23×C5×D3—21no—
46C23×C3×D5D411yescharacteristic
47C22×D3×D5—28no—
48C22×D3×D5—24no—
49C22×D3×D5—44no—
50C22×D3×D5—44no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4C2312yescomplemented
55C22×C3×C4×C5C2311yescharacteristic
56C2×D60—21no—
57C2×D60—22no—
58C2×D60D414yescomplemented
59C2×D60C2312yes—
60C2×C5×D12—21no—
61C2×C5×D12—22no—
62C2×C5×D12D414yescomplemented
63C2×C5×D12C2312yes—
64C2×C3×C22⋊D5—24no—
65C2×C3×C22⋊D5—44no—
66C22×C3×Dic5—21no—
67C22×C3×Dic5D411yescharacteristic
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5D412yes—
71C2×C3×C4×D5C2312yes—
72C2×#1203—28no—
73C2×#1203—24no—
74D5×D12—216no—
75D5×D12—28no—
76D5×D12—28no—
77#6715—28no—
78C2×C3⋊#168—22no—
79C2×C3⋊#168C2312yescomplemented
80C5×#213—28no—
81C2×C5×C3⋊C8—22no—
82C2×C5×C3⋊C8C2312yescomplemented
83C3×C22⋊Dic5—24no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2312yescomplemented
86C23×D12—51no—
87C2×C3×#121—51no—
88C22×#213—51no—
89C22×#213D511yescharacteristic, complemented
90C2×#830—51no—
91#5036—58no—
92C2×#809—51no—
93C2×#809—51no—
94C24×D5—61no—
95C22×C5×D4—31no—
96C22×C5×D4C2×D311yescharacteristic, complemented
97C22×C22⋊D5—21no—
98C22×C22⋊D5—61no—
99C2×D4×D5—34no—
100C2×D4×D5—64no—
101C2×D4×D5—64no—
102C2×D4×D5—62no—
103C22×D20—31no—
104C22×C4×D5C2×D311yescharacteristic
105C2×C5×D8—34no—
106C2×C5×D8—64no—
107C22×C5×C8—31no—
108C2×C22⋊Dic5—21no—
109#4084—22no—
110#4084C2×D314yescomplemented
111C2×#686—34no—
112C2×#686—64no—
113C2×C4⋊Dic5C2×D311yescharacteristic, complemented
114C22×#168—31no—
115#3964—34no—
116#3953—34no—
117#3952—34no—
118C2×#447—151noSylow
119C23×C3×C5—22no—
120C23×C3×C5—42no—
121C23×C3×C5—42no—
122C23×C3×C5—42no—
123C23×C3×C5C2×D411yescharacteristic
124C22×D15—24no—
125C22×D15—22no—
126C22×D15—42no—
127C22×D15—42no—
128C22×C5×D3—24no—
129C22×C5×D3—22no—
130C22×C5×D3—42no—
131C22×C5×D3—42no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5D814yescomplemented
135C22×C3×D5C2×D412yes—
136C2×D3×D5—216no—
137C2×D3×D5—48no—
138C2×D3×D5—432no—
139C2×D3×D5—48no—
140C3×C5×D4—22no—
141C3×C5×D4—22no—
142C3×C5×D4—42no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147D60—24no—
148D60—22no—
149D60C2×D414yescomplemented
150C5×D12—24no—
151C5×D12—22no—
152C5×D12C2×D414yescomplemented
153C3×C22⋊D5—48no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—42no—
157C2×C3×Dic5C2×D412yes—
158C3×C4×D5—24no—
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161#1203—216no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C24×D3—101no—
165C22×C3×D4—101no—
166C22×C3×D4C2×D511yescharacteristic, complemented
167C23×C3×C4—51no—
168C22×D12—51no—
169C22×D12—54no—
170C22×D12—104no—
171C22×D12—102no—
172C22×D12—101no—
173C22×D12—104no—
174C22×D12C2×D511yescharacteristic
175C3×#121—54no—
176C3×#121—102no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C22⋊C4—101no—
179C2×#213—24no—
180C2×#213—54no—
181C2×#213—104no—
182C2×#213C2×D514yescomplemented
183C22×C3⋊C8—51no—
184C22×C3⋊C8C2×D511yescharacteristic, complemented
185#830—54no—
186#809—54no—
187#809—54no—
188C24×C5—21no—
189C24×C5—61no—
190C23×D5—68no—
191C23×D5—61no—
192C23×D5—64no—
193C23×D5—124no—
194C23×D5—124no—
195C23×D5#6711yescharacteristic
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4—21no—
199C2×C5×D4—34no—
200C2×C5×D4—32no—
201C2×C5×D4—62no—
202C2×C5×D4—61no—
203C2×C5×D4C22×D312yescomplemented
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—24no—
206C2×C22⋊D5—44no—
207C2×C22⋊D5—68no—
208C2×C22⋊D5—64no—
209C22×Dic5—21no—
210C22×Dic5#6711yescharacteristic
211D4×D5—68no—
212D4×D5—68no—
213D4×D5—616no—
214C2×D20—34no—
215C2×D20—32no—
216C2×D20—62no—
217C2×D20—61no—
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5#6712yes—
221C2×C4×D5C22×D312yes—
222C5×D8—68no—
223C2×C5×C8—32no—
224C2×C5×C8—62no—
225C22⋊Dic5—24no—
226#686—68no—
227C4⋊Dic5—21no—
228C4⋊Dic5C22×D312yescomplemented
229C2×#168—32no—
230C2×#168—62no—
231C23×D4—151no—
232C22×D8—31no—
233C22×D8—151no—
234C2×#121—51no—
235#447—158no—
236C2×#102—151no—
237C2×#102—151no—
238C2×C22⋊C8—151no—
239C22×C3×C5—42no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—84no—
243C22×C3×C5#12012yes—
244C22×C3×C5C2×D812yes—
245C22×C3×C5AGL(1,ℤ/8)12yes—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—24no—
248C2×D15—42no—
249C2×D15—42no—
250C2×D15—48no—
251C2×C5×D3—24no—
252C2×C5×D3—42no—
253C2×C5×D3—42no—
254C2×C5×D3—48no—
255C2×C3×D5—22no—
256C2×C3×D5—22no—
257C2×C3×D5—28no—
258C2×C3×D5C2×D814yescomplemented
259D3×D5—432no—
260C3×C4×C5#12012yes—
261C3×C4×C5C22×D411yescharacteristic
262C3×C4×C5C22×D411yescharacteristic
263C3×Dic5—22no—
264C3×Dic5—42no—
265C24×C3—21no—
266C24×C3—51no—
267C23×D3—21no—
268C23×D3—104no—
269C23×D3—108no—
270C23×D3—101no—
271C23×D3—204no—
272C23×D3—204no—
273C2×C3×D4—22no—
274C2×C3×D4—21no—
275C2×C3×D4—22no—
276C2×C3×D4—104no—
277C2×C3×D4—204no—
278C2×C3×D4C22×D512yescomplemented
279C22×C3×C4—51no—
280C22×C3×C4—52no—
281C22×C3×C4—52no—
282C22×C3×C4—102no—
283C22×C3×C4—102no—
284C22×C3×C4—101no—
285C22×C3×C4C22×D511yescharacteristic
286C2×D12—21no—
287C2×D12—22no—
288C2×D12—54no—
289C2×D12—52no—
290C2×D12—108no—
291C2×D12—1016no—
292C2×D12—104no—
293C2×D12—108no—
294C2×D12—101no—
295C2×D12—102no—
296C2×D12—108no—
297C2×D12C22⋊D514yescomplemented
298C2×D12C22×D512yes—
299C3×C4⋊C4—52no—
300C3×C4⋊C4—101no—
301C3×C22⋊C4—104no—
302#213—28no—
303#213—108no—
304C2×C3⋊C8—22no—
305C2×C3⋊C8—52no—
306C2×C3⋊C8—102no—
307C2×C3⋊C8C22×D512yescomplemented
308C23×C5—22no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5—42no—
312C23×C5—64no—
313C23×C5—62no—
314C23×C5—122no—
315C23×C5—122no—
316C23×C5C2×#6711yescharacteristic
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—616no—
320C22×D5—64no—
321C22×D5—62no—
322C22×D5—1232no—
323C22×D5—128no—
324C22×D5—122no—
325C22×D5—122no—
326C22×D5—128no—
327C22×D5#21314yescomplemented
328C22×D5C2×#6712yes—
329C5×D4—22no—
330C5×D4—22no—
331C5×D4—34no—
332C5×D4—42no—
333C5×D4—64no—
334C5×D4—62no—
335C2×C4×C5D3×D412yes—
336C2×C4×C5D3×D412yes—
337C2×C4×C5C2×#6711yescharacteristic
338C2×C4×C5C23×D311yescharacteristic
339C22⋊D5—48no—
340C22⋊D5—616no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—42no—
344C2×Dic5C2×#6712yes—
345D20—34no—
346D20—64no—
347D20—62no—
348C4×D5—24no—
349C4×D5—22no—
350C4×D5—22no—
351C5×C8—62no—
352#168—62no—
353C25—301no—
354C22×D4—31no—
355C22×D4—101no—
356C22×D4—154no—
357C22×D4—151no—
358C22×D4—302no—
359C22×D4—301no—
360C22×D4—304no—
361C22×D4—304no—
362C22×D4D3×D511yescharacteristic, complemented
363C23×C4—51no—
364C2×D8—34no—
365C2×D8—64no—
366C2×D8—154no—
367C2×D8—304no—
368C22×C8—31no—
369C22×C8—151no—
370#121—54no—
371#121—102no—
372C2×C4⋊C4—51no—
373C2×C22⋊C4—101no—
374#102—154no—
375#102—154no—
376C22⋊C8—154no—
377C2×C3×C5—82no—
378C2×C3×C5#44714yescomplemented
379C2×C3×C5C2×#12011yescharacteristic
380C2×C3×C5C22×D811yescharacteristic
381C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
382D15—44no—
383C3×D5—24no—
384C5×D3—44no—
385C23×C3—22no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—52no—
390C23×C3—54no—
391C23×C3—102no—
392C23×C3—102no—
393C23×C3D4×D511yescharacteristic
394C22×D3—22no—
395C22×D3—24no—
396C22×D3—42no—
397C22×D3—42no—
398C22×D3—1016no—
399C22×D3—102no—
400C22×D3—104no—
401C22×D3—208no—
402C22×D3—208no—
403C22×D3—2032no—
404C22×D3—202no—
405C22×D3—202no—
406C3×D4—22no—
407C3×D4—22no—
408C3×D4—42no—
409C3×D4—208no—
410C2×C3×C4—52no—
411C2×C3×C4—102no—
412C2×C3×C4—102no—
413C2×C3×C4—102no—
414C2×C3×C4—104no—
415C2×C3×C4—102no—
416C2×C3×C4—202no—
417C2×C3×C4D4×D511yescharacteristic
418C2×C3×C4D4×D512yes—
419C2×C3×C4C2×C22⋊D512yes—
420C2×C3×C4C23×D511yescharacteristic
421D12—22no—
422D12—24no—
423D12—54no—
424D12—1016no—
425D12—102no—
426D12—104no—
427D12C2×C22⋊D514yescomplemented
428C3⋊C8—22no—
429C3⋊C8—102no—
430C22×C5—42no—
431C22×C5—42no—
432C22×C5—42no—
433C22×C5—64no—
434C22×C5—84no—
435C22×C5—122no—
436C22×C5—128no—
437C22×C5—122no—
438C22×C5C2×#21312yes—
439C22×C5#93712yes—
440C22×C5#94912yes—
441C22×C5C22×#6711yescharacteristic
442C2×D5—22no—
443C2×D5—28no—
444C2×D5—22no—
445C2×D5—64no—
446C2×D5—1232no—
447C2×D5—122no—
448C2×D5—128no—
449C2×D5—122no—
450C2×D5C2×#21314yescomplemented
451C4×C5#93712yes—
452C4×C5C2×D3×D411yescharacteristic
453C4×C5C2×D3×D411yescharacteristic
454Dic5—22no—
455Dic5—42no—
456C24—21no—
457C24—51no—
458C24—61no—
459C24—304no—
460C24—308no—
461C24—301no—
462C24—604no—
463C24—604no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—34no—
468C2×D4—32no—
469C2×D4—61no—
470C2×D4—62no—
471C2×D4—104no—
472C2×D4—154no—
473C2×D4—152no—
474C2×D4—204no—
475C2×D4—304no—
476C2×D4—308no—
477C2×D4—308no—
478C2×D4—3016no—
479C2×D4—308no—
480C2×D4—301no—
481C2×D4—302no—
482C2×D4C2×D3×D512yescomplemented
483C22×C4—51no—
484C22×C4—52no—
485C22×C4—52no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—101no—
489C22×C4C2×D3×D511yescharacteristic
490D8—68no—
491D8—308no—
492C2×C8—32no—
493C2×C8—62no—
494C2×C8—152no—
495C2×C8—302no—
496C4⋊C4—52no—
497C4⋊C4—101no—
498C22⋊C4—104no—
499C3×C5C2×#44711yescharacteristic, complemented, Hall
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—54no—
504C22×C3—84no—
505C22×C3—102no—
506C22×C3—102no—
507C22×C3—108no—
508C22×C3D5×D812yes—
509C22×C3#405712yes—
510C22×C3#408312yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—24no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—48no—
516C2×D3—104no—
517C2×D3—2032no—
518C2×D3—202no—
519C2×D3—202no—
520C2×D3—208no—
521C3×C4—102no—
522C3×C4—202no—
523C3×C4#408312yes—
524C3×C4C2×D4×D511yescharacteristic
525C3×C4C22×C22⋊D511yescharacteristic
526C2×C5—82no—
527C2×C5—124no—
528C2×C5#503614yescomplemented
529C2×C5C22×#21311yescharacteristic
530C2×C5C2×#93711yescharacteristic
531C2×C5C2×#94911yescharacteristic
532D5—24no—
533D5—124no—
534C23—22no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—54no—
539C23—52no—
540C23—62no—
541C23—64no—
542C23—102no—
543C23—102no—
544C23—122no—
545C23—122no—
546C23—3016no—
547C23—302no—
548C23—304no—
549C23—608no—
550C23—6032no—
551C23—608no—
552C23—602no—
553C23—602no—
554C23D5×#6711yescharacteristic
555D4—22no—
556D4—22no—
557D4—34no—
558D4—42no—
559D4—62no—
560D4—64no—
561D4—154no—
562D4—208no—
563D4—3016no—
564D4—302no—
565D4—304no—
566C2×C4—52no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—104no—
571C2×C4—102no—
572C2×C4—202no—
573C2×C4D5×#6711yescharacteristic
574C2×C4D3×C22⋊D512yes—
575C2×C4#679012yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—62no—
578C8—302no—
579C2×C3—82no—
580C2×C3—104no—
581C2×C3#6544514yescomplemented
582C2×C3C2×D5×D811yescharacteristic
583C2×C3C2×#405711yescharacteristic
584C2×C3C2×#408311yescharacteristic
585D3—44no—
586D3—204no—
587C5C2×#503611yescharacteristic, complemented, Sylow
588C22—42no—
589C22—42no—
590C22—42no—
591C22—54no—
592C22—64no—
593C22—84no—
594C22—108no—
595C22—102no—
596C22—102no—
597C22—128no—
598C22—122no—
599C22—122no—
600C22—304no—
601C22—6032no—
602C22—608no—
603C22—602no—
604C22—602no—
605C22D5×#21312yes—
606C22#9147812yes—
607C22#9157712yes—
608C22C2×D5×#6711yescharacteristic
609C4—102no—
610C4—202no—
611C4#9157712yes—
612C4C2×D3×C22⋊D511yescharacteristic
613C4C2×#679011yescharacteristic
614C3C2×#6544511yescharacteristic, complemented, Sylow
615C2—82no—
616C2—104no—
617C2—124no—
618C2—604no—
619C2#1174915114yesdirect product factor
620C2C2×D5×#21311yescharacteristic
621C2C2×#9147811yescharacteristic
622C2C2×#9157711yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#447
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D5×D12C2semidirect
2. C22×#6715C2semidirect
3. C22×C5×#213C2semidirect
4. C2×C3×#4084C2semidirect
5. #11749151C2direct (N × H)
6. C2×#90968C2semidirect
7. C2×#90966C2semidirect
8. C2×#90955C2semidirect
11. C22×C3×C5×D4C22semidirect
20. C2×D5×D12C22semidirect
22. C2×#6715C22semidirect
23. C22×C3⋊#168C22semidirect
25. C2×C5×#213C22semidirect
26. C22×C5×C3⋊C8C22semidirect
29. C3×#4084C22semidirect
30. C2×C3×C4⋊Dic5C22semidirect
31. #90968C22semidirect
32. #90966C22semidirect
33. #90955C22semidirect
37. C2×#4084D3semidirect
54. C2×C3×C5×D4C23semidirect
58. C2×D60D4semidirect
62. C2×C5×D12D4semidirect
79. C2×C3⋊#168C23semidirect
82. C2×C5×C3⋊C8C23semidirect
85. C3×C4⋊Dic5C23semidirect
89. C22×#213D5semidirect
96. C22×C5×D4C2×D3semidirect
110. #4084C2×D3semidirect
113. C2×C4⋊Dic5C2×D3semidirect
134. C22×C3×D5D8semidirect
149. D60C2×D4semidirect
152. C5×D12C2×D4semidirect
166. C22×C3×D4C2×D5semidirect
182. C2×#213C2×D5semidirect
184. C22×C3⋊C8C2×D5semidirect
203. C2×C5×D4C22×D3semidirect
228. C4⋊Dic5C22×D3semidirect
258. C2×C3×D5C2×D8semidirect
278. C2×C3×D4C22×D5semidirect
297. C2×D12C22⋊D5semidirect
307. C2×C3⋊C8C22×D5semidirect
327. C22×D5#213semidirect
362. C22×D4D3×D5semidirect
378. C2×C3×C5#447semidirect
427. D12C2×C22⋊D5semidirect
450. C2×D5C2×#213semidirect
482. C2×D4C2×D3×D5semidirect
499. C3×C5C2×#447semidirect
528. C2×C5#5036semidirect
581. C2×C3#65445semidirect
587. C5C2×#5036semidirect
614. C3C2×#65445semidirect
619. C2#11749151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D122
C22×#67152
C22×C5×#2132
C2×C3×#40842
#117491512
C2×#909682
C2×#909662
C2×#909552
C2×#654453
C2×#50365