Finite Group Databasebeta

← C2×#11749044 #14423265

Subgroups — C2×#11749044 #14423265

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C22×C5×#214C211yesmaximal, characteristic, complemented
3C2×#91359C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×#91116C211yesmaximal, characteristic, complemented
6#11749044C218yesmaximal, direct product factor
7C2×#90965C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65458—31nomaximal, Hall
10C24×C3×D5—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic, complemented
13C22×C3×C22⋊D5—21no—
14C2×C3×D4×D5—24no—
15C2×C3×D4×D5—24no—
16C2×C3×D4×D5—22no—
17C2×C3×D4×D5C2214yes—
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic, complemented
21C22×C3⋊#168C2211yescharacteristic, complemented
22C2×C5×#214—24no—
23C2×C5×#214C2214yescomplemented
24C22×C5×C3⋊C8C2211yescharacteristic, complemented
25C2×#6669—21no—
26C2×#6665—21no—
27#91359—22no—
28#91359C2214yescomplemented
29C2×#6655—24no—
30C2×#6655C2214yescomplemented
31#91116C2214yescomplemented
32#90965C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5218—51nomaximal, Hall
35C22×D4×D5D311yescharacteristic
36C22×C5×SD16—31no—
37C2×#4092—31no—
38C22×#688—31no—
39C2×#3964—31no—
40#65458—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C24×C3×C5—21no—
44C23×C3×D5—28no—
45C23×C3×D5—21no—
46C23×C3×D5—24no—
47C23×C3×D5—44no—
48C23×C3×D5—44no—
49C23×C3×D5D411yescharacteristic
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4D414yes—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—21no—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—22no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6C2312yescomplemented
61C2×C3×C22⋊D5—28no—
62C2×C3×C22⋊D5—24no—
63C22×C3×Dic5D411yescharacteristic
64C3×D4×D5—216no—
65C3×D4×D5—28no—
66C3×D4×D5—28no—
67C2×C3×D20—21no—
68C2×C3×D20—22no—
69C2×C3×D20D414yes—
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5D412yes—
74C2×C3×C4×D5C2312yes—
75C4⋊Dic15—21no—
76C4⋊Dic15C2312yescomplemented
77C2×C3⋊#168—22no—
78C2×C3⋊#168C2312yescomplemented
79C5×#214—28no—
80C2×C5×C3⋊C8—22no—
81C2×C5×C3⋊C8C2312yescomplemented
82#6669—24no—
83#6665—24no—
84#6655—28no—
85C23×C3×D4—51no—
86C22×#214—51no—
87C22×#214D511yescharacteristic, complemented
88C2×#924—51no—
89#5218—58no—
90C2×#832—51no—
91C2×#832—51no—
92C2×#830—51no—
93C24×D5—21no—
94C22×C5×Q8—31no—
95C22×C5×D4C2×D311yescharacteristic
96C22×C22⋊D5—21no—
97C2×D4×D5—24no—
98C2×D4×D5—24no—
99C2×D4×D5—22no—
100C2×D4×D5C2×D314yes—
101C22×D20C2×D311yescharacteristic
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×SD16—34no—
104C2×C5×SD16—64no—
105C22×C5×C8—31no—
106#4092—34no—
107#4092—62no—
108C2×#688—34no—
109C2×#688—64no—
110C2×#685—61no—
111C2×C4⋊Dic5—31no—
112C2×#683—61no—
113C22×#168—31no—
114#3964—34no—
115#3953—34no—
116#3952—34no—
117C2×#450—151noSylow
118C23×C3×C5—24no—
119C23×C3×C5—22no—
120C23×C3×C5—42no—
121C23×C3×C5—42no—
122C23×C3×C5C2×D411yescharacteristic
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—216no—
126C22×C3×D5—24no—
127C22×C3×D5—22no—
128C22×C3×D5—48no—
129C22×C3×D5—432no—
130C22×C3×D5—42no—
131C22×C3×D5—42no—
132C22×C3×D5—48no—
133C22×C3×D5SD1614yescomplemented
134C22×C3×D5C2×D412yes—
135C3×C5×D4—24no—
136C3×C5×D4—22no—
137C3×C5×D4C2×D414yes—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143C2×Dic15—42no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—42no—
146C5×Dic6—22no—
147C5×Dic6—22no—
148C5×Dic6—42no—
149C3×C22⋊D5—216no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5C2×D412yes—
152C3×D20—24no—
153C3×D20—22no—
154C3×D20C2×D414yes—
155C3×C4×D5—24no—
156C3×C4×D5—22no—
157C3×C4×D5—22no—
158C3⋊#168—22no—
159C5×C3⋊C8—22no—
160C25×C3—101no—
161C22×C3×D4—54no—
162C22×C3×D4—51no—
163C22×C3×D4—102no—
164C22×C3×D4—101no—
165C22×C3×D4—104no—
166C22×C3×D4—104no—
167C22×C3×D4C2×D511yescharacteristic
168C23×C3×C4—51no—
169C22×Dic6C2×D511yescharacteristic, complemented
170C2×#217—101no—
171C2×#214—24no—
172C2×#214—54no—
173C2×#214—104no—
174C2×#214C2×D514yescomplemented
175C2×C4⋊Dic3—51no—
176#924—54no—
177#924—102no—
178C2×Dic3⋊C4—101no—
179C22×C3⋊C8—51no—
180C22×C3⋊C8C2×D511yescharacteristic, complemented
181#832—54no—
182#832—54no—
183#830—54no—
184C24×C5—21no—
185C23×D5—28no—
186C23×D5—21no—
187C23×D5—24no—
188C23×D5—44no—
189C23×D5—44no—
190C23×D5#6711yescharacteristic
191C2×C5×Q8—32no—
192C2×C5×Q8—61no—
193C2×C5×Q8—62no—
194C2×C5×Q8—62no—
195C2×C5×D4—21no—
196C2×C5×D4—22no—
197C2×C5×D4#6714yes—
198C2×C5×D4C22×D312yes—
199C22×C4×C5—61no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—28no—
202C2×C22⋊D5—24no—
203C22×Dic5—61no—
204C22×Dic5#6711yescharacteristic
205D4×D5—216no—
206D4×D5—28no—
207D4×D5—28no—
208C2×D20—22no—
209C2×D20—21no—
210C2×D20#6714yes—
211C2×D20C22×D312yes—
212C2×C4×D5—22no—
213C2×C4×D5—22no—
214C2×C4×D5#6712yes—
215C2×C4×D5C22×D312yes—
216C5×SD16—68no—
217C2×C5×C8—32no—
218C2×C5×C8—62no—
219#688—68no—
220#685—64no—
221C4⋊Dic5—32no—
222C4⋊Dic5—61no—
223#683—64no—
224C2×#168—32no—
225C2×#168—62no—
226C23×D4—51no—
227C22×SD16—31no—
228C22×SD16—151no—
229C2×C22⋊Q8—151no—
230#450—158no—
231C2×#102—151no—
232C2×#102—151no—
233C2×C22⋊C8—151no—
234C22×C3×C5—24no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—48no—
238C22×C3×C5#12012yes—
239C22×C3×C5C2×SD1612yes—
240C22×C3×C5AGL(1,ℤ/8)12yes—
241C22×C3×C5C22×D411yescharacteristic
242C2×C3×D5—22no—
243C2×C3×D5—22no—
244C2×C3×D5—28no—
245C2×C3×D5—24no—
246C2×C3×D5—432no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—48no—
250C2×C3×D5C2×SD1614yescomplemented
251C3×C4×C5#12012yes—
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254Dic15—42no—
255C3×Dic5—22no—
256C5×Dic3—42no—
257C24×C3—21no—
258C24×C3—51no—
259C24×C3—104no—
260C24×C3—108no—
261C24×C3—101no—
262C24×C3—204no—
263C24×C3—204no—
264C2×C3×D4—22no—
265C2×C3×D4—21no—
266C2×C3×D4—54no—
267C2×C3×D4—52no—
268C2×C3×D4—104no—
269C2×C3×D4—108no—
270C2×C3×D4—1016no—
271C2×C3×D4—108no—
272C2×C3×D4—108no—
273C2×C3×D4—101no—
274C2×C3×D4—102no—
275C2×C3×D4C22⋊D514yes—
276C2×C3×D4C22×D512yes—
277C22×C3×C4—51no—
278C22×C3×C4—52no—
279C22×C3×C4—52no—
280C22×C3×C4—102no—
281C22×C3×C4—102no—
282C22×C3×C4C22×D511yescharacteristic
283C22×Dic3—21no—
284C22×Dic3—101no—
285C2×Dic6—22no—
286C2×Dic6—22no—
287C2×Dic6—21no—
288C2×Dic6C22×D512yescomplemented
289#217—104no—
290#214—28no—
291#214—108no—
292C4⋊Dic3—52no—
293C4⋊Dic3—101no—
294Dic3⋊C4—104no—
295C2×C3⋊C8—22no—
296C2×C3⋊C8—52no—
297C2×C3⋊C8—102no—
298C2×C3⋊C8C22×D512yescomplemented
299C23×C5—24no—
300C23×C5—22no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5C2×#6711yescharacteristic
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—216no—
307C22×D5—24no—
308C22×D5—22no—
309C22×D5—432no—
310C22×D5—48no—
311C22×D5—42no—
312C22×D5—42no—
313C22×D5—48no—
314C22×D5#21414yescomplemented
315C22×D5C2×#6712yes—
316C5×Q8—62no—
317C5×Q8—62no—
318C5×Q8—122no—
319C5×D4—24no—
320C5×D4—22no—
321C5×D4C2×#6714yes—
322C2×C4×C5—62no—
323C2×C4×C5—122no—
324C2×C4×C5C2×#6712yes—
325C2×C4×C5C2×#6711yescharacteristic
326C2×C4×C5C2×#6712yes—
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—216no—
329C2×Dic5—22no—
330C2×Dic5—62no—
331C2×Dic5—122no—
332C2×Dic5C2×#6712yes—
333D20—24no—
334D20—22no—
335D20C2×#6714yes—
336C4×D5—24no—
337C4×D5—22no—
338C4×D5—22no—
339C5×C8—62no—
340#168—62no—
341C25—101no—
342C22×Q8—31no—
343C22×D4—54no—
344C22×D4—51no—
345C22×D4—102no—
346C22×D4—101no—
347C22×D4—104no—
348C22×D4—104no—
349C22×D4D3×D511yescharacteristic
350C23×C4—51no—
351C2×SD16—34no—
352C2×SD16—64no—
353C2×SD16—154no—
354C2×SD16—304no—
355C22×C8—31no—
356C22×C8—151no—
357C22⋊Q8—154no—
358C22⋊Q8—302no—
359C2×C4⋊C4—151no—
360C2×C4⋊C4—301no—
361C2×C22⋊C4—301no—
362#102—154no—
363#102—154no—
364C22⋊C8—154no—
365C2×C3×C5—44no—
366C2×C3×C5#45014yescomplemented
367C2×C3×C5C2×#12011yescharacteristic
368C2×C3×C5C22×SD1611yescharacteristic
369C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
370C3×D5—24no—
371C3×D5—44no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—52no—
377C23×C3—54no—
378C23×C3—1016no—
379C23×C3—102no—
380C23×C3—102no—
381C23×C3—102no—
382C23×C3—104no—
383C23×C3—208no—
384C23×C3—208no—
385C23×C3—2032no—
386C23×C3—202no—
387C23×C3—202no—
388C23×C3D4×D511yescharacteristic
389C3×D4—22no—
390C3×D4—24no—
391C3×D4—54no—
392C3×D4—1016no—
393C3×D4—102no—
394C3×D4—104no—
395C3×D4C2×C22⋊D514yes—
396C2×C3×C4—52no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—102no—
400C2×C3×C4—104no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405C2×Dic3—22no—
406C2×Dic3—42no—
407C2×Dic3—102no—
408C2×Dic3—202no—
409Dic6—22no—
410Dic6—22no—
411Dic6—42no—
412C3⋊C8—22no—
413C3⋊C8—102no—
414C22×C5—24no—
415C22×C5—48no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5#93212yes—
419C22×C5C2×#21412yes—
420C22×C5#95312yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—28no—
423C2×D5—22no—
424C2×D5—22no—
425C2×D5—24no—
426C2×D5—432no—
427C2×D5—48no—
428C2×D5—42no—
429C2×D5—42no—
430C2×D5C2×#21414yescomplemented
431C4×C5—122no—
432C4×C5#95312yes—
433C4×C5C22×#6711yescharacteristic
434C4×C5C22×#6711yescharacteristic
435Dic5—22no—
436Dic5—122no—
437C24—21no—
438C24—51no—
439C24—104no—
440C24—108no—
441C24—101no—
442C24—204no—
443C24—204no—
444C2×Q8—32no—
445C2×Q8—61no—
446C2×Q8—62no—
447C2×Q8—62no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—54no—
451C2×D4—52no—
452C2×D4—104no—
453C2×D4—108no—
454C2×D4—1016no—
455C2×D4—108no—
456C2×D4—108no—
457C2×D4—102no—
458C2×D4—101no—
459C2×D4#120114yes—
460C2×D4C2×D3×D512yes—
461C22×C4—51no—
462C22×C4—52no—
463C22×C4—52no—
464C22×C4—61no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—301no—
468C22×C4C2×D3×D511yescharacteristic
469SD16—68no—
470SD16—308no—
471C2×C8—32no—
472C2×C8—62no—
473C2×C8—152no—
474C2×C8—302no—
475C4⋊C4—152no—
476C4⋊C4—304no—
477C4⋊C4—301no—
478C22⋊C4—304no—
479C3×C5C2×#45011yescharacteristic, complemented, Hall
480C22×C3—24no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—48no—
484C22×C3—54no—
485C22×C3—102no—
486C22×C3—102no—
487C22×C3—108no—
488C22×C3—104no—
489C22×C3—2032no—
490C22×C3—202no—
491C22×C3—202no—
492C22×C3—208no—
493C22×C3D5×SD1612yes—
494C22×C3#406012yes—
495C22×C3#408312yes—
496C22×C3C2×D4×D511yescharacteristic
497C3×C4—102no—
498C3×C4#408312yes—
499C3×C4C2×D4×D511yescharacteristic
500C3×C4C22×C22⋊D511yescharacteristic
501Dic3—42no—
502Dic3—202no—
503C2×C5—44no—
504C2×C5#521814yescomplemented
505C2×C5C2×#93211yescharacteristic
506C2×C5C22×#21411yescharacteristic
507C2×C5C2×#95311yescharacteristic
508D5—24no—
509D5—44no—
510C23—22no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—54no—
515C23—52no—
516C23—1016no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—104no—
521C23—208no—
522C23—2032no—
523C23—208no—
524C23—202no—
525C23—202no—
526C23D5×#6711yescharacteristic
527Q8—62no—
528Q8—62no—
529Q8—122no—
530D4—22no—
531D4—24no—
532D4—54no—
533D4—1016no—
534D4—102no—
535D4—104no—
536D4C2×#120114yes—
537C2×C4—52no—
538C2×C4—62no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—104no—
543C2×C4—122no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4C2×#120112yes—
547C2×C4D5×#6712yes—
548C2×C4D5×#6711yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—44no—
553C2×C3—104no—
554C2×C3—204no—
555C2×C3#6545814yescomplemented
556C2×C3C2×D5×SD1611yescharacteristic
557C2×C3C2×#406011yescharacteristic
558C2×C3C2×#408311yescharacteristic
559C5C2×#521811yescharacteristic, complemented, Sylow
560C22—24no—
561C22—48no—
562C22—42no—
563C22—42no—
564C22—54no—
565C22—102no—
566C22—108no—
567C22—102no—
568C22—104no—
569C22—2032no—
570C22—208no—
571C22—202no—
572C22—202no—
573C22D5×#21412yes—
574C22#9149112yes—
575C22#9156312yes—
576C22C2×D5×#6711yescharacteristic
577C4—102no—
578C4—122no—
579C4—602no—
580C4#9156312yes—
581C4C22×#120111yescharacteristic
582C4C2×D5×#6711yescharacteristic
583C3C2×#6545811yescharacteristic, complemented, Sylow
584C2—44no—
585C2—104no—
586C2—204no—
587C2#1174904414yesdirect product factor
588C2C2×D5×#21411yescharacteristic
589C2C2×#9149111yescharacteristic
590C2C2×#9156311yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D4×D5C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#450
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
2. C22×C5×#214C2semidirect
3. C2×#91359C2semidirect
4. C22×#6655C2semidirect
5. C2×#91116C2semidirect
6. #11749044C2direct (N × H)
7. C2×#90965C2semidirect
8. C2×#90955C2semidirect
12. C22×C5×Dic6C22semidirect
20. C2×C4⋊Dic15C22semidirect
21. C22×C3⋊#168C22semidirect
23. C2×C5×#214C22semidirect
24. C22×C5×C3⋊C8C22semidirect
28. #91359C22semidirect
30. C2×#6655C22semidirect
31. #91116C22semidirect
32. #90965C22semidirect
33. #90955C22semidirect
60. C2×C5×Dic6C23semidirect
76. C4⋊Dic15C23semidirect
78. C2×C3⋊#168C23semidirect
81. C2×C5×C3⋊C8C23semidirect
87. C22×#214D5semidirect
133. C22×C3×D5SD16semidirect
169. C22×Dic6C2×D5semidirect
174. C2×#214C2×D5semidirect
180. C22×C3⋊C8C2×D5semidirect
250. C2×C3×D5C2×SD16semidirect
288. C2×Dic6C22×D5semidirect
298. C2×C3⋊C8C22×D5semidirect
314. C22×D5#214semidirect
366. C2×C3×C5#450semidirect
430. C2×D5C2×#214semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#5218semidirect
555. C2×C3#65458semidirect
559. C5C2×#5218semidirect
583. C3C2×#65458semidirect
587. C2#11749044direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C22×C5×#2142
C2×#913592
C22×#66552
C2×#911162
#117490442
C2×#909652
C2×#909552
C2×#654583
C2×#52185