Finite Group Databasebeta

← C2×#11749064 #14423269

Subgroups — C2×#11749064 #14423269

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×D4×D15C211yesmaximal, characteristic
2C22×C3×#687C211yesmaximal, characteristic, complemented
3C2×#91390C211yesmaximal, characteristic, complemented
4C22×#6658C211yesmaximal, characteristic, complemented
5C2×C5×#832C211yesmaximal, characteristic, complemented
6#11749064C218yesmaximal, direct product factor
7C2×#90969C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65065—31nomaximal, Hall
10C24×D15—21no—
11C22×C3×C5×D4C2211yescharacteristic
12C22×#1220—21no—
13C2×D4×D15—24no—
14C2×D4×D15—24no—
15C2×D4×D15—22no—
16C2×D4×D15C2214yes—
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic, complemented
20C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
21C22×C5×C3⋊C8C2211yescharacteristic, complemented
22C2×C3×#687—24no—
23C2×C3×#687C2214yescomplemented
24C22×C3×#168C2211yescharacteristic, complemented
25C2×Dic3⋊Dic5—21no—
26C2×#6667—21no—
27#91390—22no—
28#91390C2214yescomplemented
29C2×#6658—24no—
30C2×#6658C2214yescomplemented
31C5×#832C2214yescomplemented
32#90969C2214yescomplemented
33#90957C2214yescomplemented
34C2×#5169—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×#687D311yescharacteristic, complemented
37C22×#677—31no—
38C2×#4043—31no—
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3941—31no—
42#65065—38no—
43C24×C3×C5—21no—
44C23×D15—28no—
45C23×D15—21no—
46C23×D15—24no—
47C23×D15—44no—
48C23×D15—44no—
49C23×D15D411yescharacteristic
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4D414yes—
53C2×C3×C5×D4C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—28no—
56C2×#1220—24no—
57C22×Dic15D411yescharacteristic
58D4×D15—216no—
59D4×D15—28no—
60D4×D15—28no—
61C2×D60—21no—
62C2×D60—22no—
63C2×D60D414yes—
64C2×D60C2312yes—
65C2×C4×D15—22no—
66C2×C4×D15—22no—
67C2×C4×D15D412yes—
68C2×C4×D15C2312yes—
69C22×C5×Dic3—21no—
70C22×C3×Dic5—21no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10—22no—
73C2×C3×Dic10—21no—
74C2×C3×Dic10C2312yescomplemented
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2312yescomplemented
77C2×C5×C3⋊C8—22no—
78C2×C5×C3⋊C8C2312yescomplemented
79C3×#687—28no—
80C2×C3×#168—22no—
81C2×C3×#168C2312yescomplemented
82Dic3⋊Dic5—24no—
83#6667—24no—
84#6658—28no—
85C22×D3×D4—51no—
86C22×C3×SD16—51no—
87C2×#946—51no—
88C22×#215—51no—
89C2×#832D511yescharacteristic, complemented
90#5169—58no—
91C2×#821—51no—
92C2×(C2×D3)⋊C8—51no—
93C24×D5—61no—
94C22×C5×D4C2×D311yescharacteristic
95C22×C22⋊D5—61no—
96C2×D4×D5—34no—
97C2×D4×D5—62no—
98C2×D4×D5—64no—
99C2×D4×D5—64no—
100C22×D20—31no—
101C22×C4×D5—31no—
102C22×Dic10C2×D311yescharacteristic, complemented
103C22×C5×C8—31no—
104C2×C5×C4⋊C4—31no—
105C2×#687—24no—
106C2×#687C2×D314yescomplemented
107C2×#685—61no—
108C2×C4⋊Dic5—61no—
109C22×#168C2×D311yescharacteristic, complemented
110C2×#677—34no—
111C2×#677—64no—
112#4043—34no—
113#4043—62no—
114C5×#102—34no—
115#3952—34no—
116#3941—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×D15—22no—
124C22×D15—22no—
125C22×D15—216no—
126C22×D15—24no—
127C22×D15—22no—
128C22×D15—48no—
129C22×D15—432no—
130C22×D15—42no—
131C22×D15—42no—
132C22×D15—48no—
133C22×D15SD1614yescomplemented
134C22×D15C2×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
142#1220—216no—
143C2×Dic15—22no—
144C2×Dic15C2×D412yes—
145D60—24no—
146D60—22no—
147D60C2×D414yes—
148C4×D15—24no—
149C4×D15—22no—
150C4×D15—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—42no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—42no—
155C3×Dic10—22no—
156C3×Dic10—22no—
157C3×Dic10—42no—
158C3×#168—22no—
159C5×C3⋊C8—22no—
160C24×D3—101no—
161C22×C3×Q8—51no—
162C22×C3×D4C2×D511yescharacteristic
163C22×#67—101no—
164C2×D3×D4—54no—
165C2×D3×D4—102no—
166C2×D3×D4—104no—
167C2×D3×D4—104no—
168C22×D12—51no—
169C22×C4×D3—51no—
170C2×C3×SD16—54no—
171C2×C3×SD16—104no—
172C22×C3×C8—51no—
173#946—54no—
174#946—102no—
175C2×#215—54no—
176C2×#215—104no—
177C2×(C2×D3)⋊C4—101no—
178C2×C4⋊Dic3C2×D511yescharacteristic, complemented
179C2×Dic3⋊C4—101no—
180C22×C3⋊C8C2×D511yescharacteristic, complemented
181#832C2×D514yescomplemented
182#821—54no—
183(C2×D3)⋊C8—54no—
184C24×C5—21no—
185C23×D5—31no—
186C23×D5—64no—
187C23×D5—68no—
188C23×D5—61no—
189C23×D5—124no—
190C23×D5—124no—
191C2×C5×D4—21no—
192C2×C5×D4—22no—
193C2×C5×D4#6714yes—
194C2×C5×D4C22×D312yes—
195C22×C4×C5—61no—
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—64no—
198C2×C22⋊D5—68no—
199C22×Dic5—21no—
200C22×Dic5—31no—
201D4×D5—68no—
202D4×D5—616no—
203D4×D5—68no—
204C2×D20—34no—
205C2×D20—32no—
206C2×D20—61no—
207C2×D20—62no—
208C2×C4×D5—32no—
209C2×C4×D5—32no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—22no—
213C2×Dic10—22no—
214C2×Dic10—21no—
215C2×Dic10C22×D312yescomplemented
216C2×C5×C8—32no—
217C2×C5×C8—62no—
218C5×C4⋊C4—32no—
219C5×C4⋊C4—61no—
220#687—28no—
221#685—64no—
222C4⋊Dic5—64no—
223C2×#168—22no—
224C2×#168C22×D312yescomplemented
225#677—68no—
226C23×D4—151no—
227C22×SD16—51no—
228C22×SD16—151no—
229C2×C22⋊Q8—151no—
230#450—158no—
231C2×#102—31no—
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×D15—22no—
243C2×D15—22no—
244C2×D15—28no—
245C2×D15—24no—
246C2×D15—432no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—48no—
250C2×D15C2×SD1614yescomplemented
251C3×C4×C5#12012yes—
252C3×C4×C5C22×D411yescharacteristic
253C3×C4×C5C22×D411yescharacteristic
254Dic15—22no—
255C3×Dic5—42no—
256C5×Dic3—42no—
257C24×C3—21no—
258C23×D3—51no—
259C23×D3—104no—
260C23×D3—108no—
261C23×D3—101no—
262C23×D3—204no—
263C23×D3—204no—
264C2×C3×Q8—52no—
265C2×C3×Q8—101no—
266C2×C3×Q8—102no—
267C2×C3×Q8—102no—
268C2×C3×D4—22no—
269C2×C3×D4—21no—
270C2×C3×D4D2014yes—
271C2×C3×D4C22×D512yes—
272C22×C3×C4—101no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—104no—
275C2×#67—108no—
276C22×Dic3—21no—
277C22×Dic3—51no—
278D3×D4—108no—
279D3×D4—1016no—
280D3×D4—108no—
281C2×D12—54no—
282C2×D12—52no—
283C2×D12—102no—
284C2×D12—101no—
285C2×C4×D3—52no—
286C2×C4×D3—52no—
287C2×C4×D3—102no—
288C2×C4×D3—102no—
289C3×SD16—108no—
290C2×C3×C8—52no—
291C2×C3×C8—102no—
292#215—108no—
293(C2×D3)⋊C4—104no—
294C4⋊Dic3—21no—
295C4⋊Dic3C22×D512yescomplemented
296Dic3⋊C4—104no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8C22×D512yescomplemented
299C23×C5—24no—
300C23×C5—22no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5D3×D411yescharacteristic
304C22×D5—34no—
305C22×D5—32no—
306C22×D5—62no—
307C22×D5—62no—
308C22×D5—616no—
309C22×D5—64no—
310C22×D5—62no—
311C22×D5—128no—
312C22×D5—1232no—
313C22×D5—128no—
314C22×D5—122no—
315C22×D5—122no—
316C5×D4—24no—
317C5×D4—22no—
318C5×D4C2×#6714yes—
319C2×C4×C5—62no—
320C2×C4×C5—122no—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5D3×D412yes—
323C2×C4×C5C2×#6712yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—616no—
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—42no—
329C2×Dic5—62no—
330D20—34no—
331D20—64no—
332D20—62no—
333C4×D5—64no—
334C4×D5—62no—
335C4×D5—62no—
336Dic10—22no—
337Dic10—22no—
338Dic10—42no—
339C5×C8—62no—
340#168—22no—
341C25—301no—
342C22×Q8—51no—
343C22×D4—154no—
344C22×D4—151no—
345C22×D4—302no—
346C22×D4—301no—
347C22×D4—304no—
348C22×D4—304no—
349C22×D4D3×D511yescharacteristic
350C23×C4—151no—
351C2×SD16—54no—
352C2×SD16—104no—
353C2×SD16—154no—
354C2×SD16—304no—
355C22×C8—31no—
356C22×C8—51no—
357C22⋊Q8—154no—
358C22⋊Q8—302no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—301no—
361C2×C22⋊C4—301no—
362#102—34no—
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
370D15—24no—
371D15—44no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3D4×D511yescharacteristic
377C22×D3—52no—
378C22×D3—54no—
379C22×D3—102no—
380C22×D3—102no—
381C22×D3—1016no—
382C22×D3—102no—
383C22×D3—104no—
384C22×D3—208no—
385C22×D3—208no—
386C22×D3—2032no—
387C22×D3—202no—
388C22×D3—202no—
389C3×Q8—102no—
390C3×Q8—102no—
391C3×Q8—202no—
392C3×D4—22no—
393C3×D4—24no—
394C3×D4C2×D2014yes—
395C2×C3×C4—102no—
396C2×C3×C4—202no—
397C2×C3×C4C2×D2012yes—
398C2×C3×C4D4×D512yes—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4C23×D511yescharacteristic
401#67—1016no—
402C2×Dic3—22no—
403C2×Dic3—42no—
404C2×Dic3—52no—
405C2×Dic3—102no—
406D12—54no—
407D12—102no—
408D12—104no—
409C4×D3—102no—
410C4×D3—102no—
411C4×D3—104no—
412C3×C8—102no—
413C3⋊C8—22no—
414C22×C5—24no—
415C22×C5—48no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5D3×SD1612yes—
419C22×C5#91412yes—
420C22×C5#93712yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—34no—
423C2×D5—68no—
424C2×D5—62no—
425C2×D5—62no—
426C2×D5—64no—
427C2×D5—1232no—
428C2×D5—128no—
429C2×D5—122no—
430C2×D5—122no—
431C4×C5—122no—
432C4×C5#93712yes—
433C4×C5C2×D3×D411yescharacteristic
434C4×C5C22×#6711yescharacteristic
435Dic5—42no—
436Dic5—62no—
437C24—21no—
438C24—151no—
439C24—304no—
440C24—308no—
441C24—301no—
442C24—604no—
443C24—604no—
444C2×Q8—52no—
445C2×Q8—101no—
446C2×Q8—102no—
447C2×Q8—102no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—154no—
451C2×D4—152no—
452C2×D4—304no—
453C2×D4—308no—
454C2×D4—3016no—
455C2×D4—308no—
456C2×D4—308no—
457C2×D4—302no—
458C2×D4—301no—
459C2×D4#120214yes—
460C2×D4C2×D3×D512yes—
461C22×C4—61no—
462C22×C4—101no—
463C22×C4—151no—
464C22×C4—152no—
465C22×C4—152no—
466C22×C4—302no—
467C22×C4—302no—
468C22×C4C2×D3×D511yescharacteristic
469SD16—108no—
470SD16—308no—
471C2×C8—32no—
472C2×C8—52no—
473C2×C8—62no—
474C2×C8—102no—
475C4⋊C4—32no—
476C4⋊C4—61no—
477C4⋊C4—304no—
478C22⋊C4—304no—
479C3×C5C2×#45011yescharacteristic, complemented, Hall
480C22×C3—24no—
481C22×C3—42no—
482C22×C3—48no—
483C22×C3—42no—
484C22×C3#402812yes—
485C22×C3#405712yes—
486C22×C3D5×SD1612yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—54no—
489C2×D3—102no—
490C2×D3—102no—
491C2×D3—108no—
492C2×D3—104no—
493C2×D3—2032no—
494C2×D3—202no—
495C2×D3—208no—
496C2×D3—202no—
497C3×C4—202no—
498C3×C4#402812yes—
499C3×C4C22×D2011yescharacteristic
500C3×C4C2×D4×D511yescharacteristic
501Dic3—42no—
502Dic3—102no—
503C2×C5—44no—
504C2×C5#516914yescomplemented
505C2×C5C2×D3×SD1611yescharacteristic
506C2×C5C2×#91411yescharacteristic
507C2×C5C2×#93711yescharacteristic
508D5—64no—
509D5—124no—
510C23—22no—
511C23—24no—
512C23—42no—
513C23—42no—
514C23—154no—
515C23—152no—
516C23—3016no—
517C23—302no—
518C23—302no—
519C23—302no—
520C23—304no—
521C23—608no—
522C23—6032no—
523C23—608no—
524C23—602no—
525C23—602no—
526C23#679011yescharacteristic
527Q8—102no—
528Q8—102no—
529Q8—202no—
530D4—22no—
531D4—24no—
532D4—154no—
533D4—3016no—
534D4—302no—
535D4—304no—
536D4C2×#120214yes—
537C2×C4—62no—
538C2×C4—102no—
539C2×C4—122no—
540C2×C4—152no—
541C2×C4—202no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—304no—
546C2×C4C2×#120212yes—
547C2×C4#679012yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—44no—
553C2×C3#6506514yescomplemented
554C2×C3C2×#402811yescharacteristic
555C2×C3C2×#405711yescharacteristic
556C2×C3C2×D5×SD1611yescharacteristic
557D3—104no—
558D3—204no—
559C5C2×#516911yescharacteristic, complemented, Sylow
560C22—24no—
561C22—48no—
562C22—42no—
563C22—42no—
564C22—154no—
565C22—302no—
566C22—308no—
567C22—302no—
568C22—304no—
569C22—6032no—
570C22—608no—
571C22—602no—
572C22—602no—
573C22#9148712yes—
574C22#9150012yes—
575C22#9157212yes—
576C22C2×#679011yescharacteristic
577C4—122no—
578C4—202no—
579C4—302no—
580C4#9157212yes—
581C4C22×#120211yescharacteristic
582C4C2×#679011yescharacteristic
583C3C2×#6506511yescharacteristic, complemented, Sylow
584C2—44no—
585C2—304no—
586C2—604no—
587C2#1174906414yesdirect product factor
588C2C2×#9148711yescharacteristic
589C2C2×#9150011yescharacteristic
590C2C2×#9157211yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×D4×D15C2
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×C3×#687C2semidirect
3. C2×#91390C2semidirect
4. C22×#6658C2semidirect
5. C2×C5×#832C2semidirect
6. #11749064C2direct (N × H)
7. C2×#90969C2semidirect
8. C2×#90957C2semidirect
19. C22×C3×Dic10C22semidirect
20. C2×C5×C4⋊Dic3C22semidirect
21. C22×C5×C3⋊C8C22semidirect
23. C2×C3×#687C22semidirect
24. C22×C3×#168C22semidirect
28. #91390C22semidirect
30. C2×#6658C22semidirect
31. C5×#832C22semidirect
32. #90969C22semidirect
33. #90957C22semidirect
36. C22×#687D3semidirect
74. C2×C3×Dic10C23semidirect
76. C5×C4⋊Dic3C23semidirect
78. C2×C5×C3⋊C8C23semidirect
81. C2×C3×#168C23semidirect
89. C2×#832D5semidirect
102. C22×Dic10C2×D3semidirect
106. C2×#687C2×D3semidirect
109. C22×#168C2×D3semidirect
133. C22×D15SD16semidirect
178. C2×C4⋊Dic3C2×D5semidirect
180. C22×C3⋊C8C2×D5semidirect
181. #832C2×D5semidirect
215. C2×Dic10C22×D3semidirect
224. C2×#168C22×D3semidirect
250. C2×D15C2×SD16semidirect
295. C4⋊Dic3C22×D5semidirect
298. C2×C3⋊C8C22×D5semidirect
366. C2×C3×C5#450semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#5169semidirect
553. C2×C3#65065semidirect
559. C5C2×#5169semidirect
583. C3C2×#65065semidirect
587. C2#11749064direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D152
C22×C3×#6872
C2×#913902
C22×#66582
C2×C5×#8322
#117490642
C2×#909692
C2×#909572
C2×#650653
C2×#51695