Finite Group Databasebeta

← C2×#11750877 #14423243

Subgroups — C2×#11750877 #14423243

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×#6716C211yesmaximal, characteristic, complemented
3C22×#6706C211yesmaximal, characteristic, complemented
4C2×#91786C211yesmaximal, characteristic, complemented
5C2×C3×C5×#102C211yesmaximal, characteristic, complemented
6C2×#91104C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic, complemented
8#11750877C218yesmaximal, direct product factor
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×Dic30C2211yescharacteristic, complemented
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
22C2×#6716—24no—
23C2×#6716C2214yescomplemented
24C2×#6714—21no—
25C2×C4⋊Dic15—21no—
26C22×C3⋊#168C2211yescharacteristic, complemented
27C2×#6706—24no—
28C2×#6706C2214yescomplemented
29#91786—22no—
30#91786C2214yescomplemented
31C3×C5×#102C2214yescomplemented
32#91104C2214yescomplemented
33#91093C2214yescomplemented
34C2×#4776—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×#687—31no—
37C22×#677—31no—
38C2×#4043—31no—
39C2×C5×#102D311yescharacteristic, complemented
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×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—28no—
57C2×#1220—24no—
58C22×Dic15—21no—
59C22×Dic15D411yescharacteristic
60D4×D15—216no—
61D4×D15—28no—
62D4×D15—28no—
63C2×D60—21no—
64C2×D60—22no—
65C2×D60D414yes—
66C2×D60C2312yes—
67C2×C4×D15—22no—
68C2×C4×D15—22no—
69C2×C4×D15D412yes—
70C2×C4×D15C2312yes—
71C2×Dic30—22no—
72C2×Dic30—22no—
73C2×Dic30—21no—
74C2×Dic30C2312yescomplemented
75C2×C3×C5×C8—22no—
76C2×C3×C5×C8C2312yescomplemented
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yescomplemented
79#6716—28no—
80#6714—24no—
81C4⋊Dic15—24no—
82C2×C3⋊#168—22no—
83C2×C3⋊#168C2312yescomplemented
84#6706—28no—
85C22×D3×D4—51no—
86C22×#214—51no—
87C22×#204—51no—
88C2×#897—51no—
89C2×C3×#102D511yescharacteristic, complemented
90C2×(C2×D3)⋊C8—51no—
91C2×#809—51no—
92#4776—58no—
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×Dic10—31no—
103C22×C5×C8C2×D311yescharacteristic, complemented
104C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
105C2×#687—34no—
106C2×#687—64no—
107C2×#685—61no—
108C2×C4⋊Dic5—61no—
109C22×#168—31no—
110C2×#677—34no—
111C2×#677—64no—
112#4043—34no—
113#4043—62no—
114C5×#102C2×D314yescomplemented
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×C5—22no—
139C2×C3×C4×C5—42no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—216no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—42no—
148C2×Dic15C2×D412yes—
149D60—24no—
150D60—22no—
151D60C2×D414yes—
152C4×D15—24no—
153C4×D15—22no—
154C4×D15—22no—
155Dic30—22no—
156Dic30—22no—
157Dic30—42no—
158C3×C5×C8—22no—
159C3⋊#168—22no—
160C24×D3—101no—
161C22×C3×D4C2×D511yescharacteristic
162C22×#67—101no—
163C2×D3×D4—54no—
164C2×D3×D4—102no—
165C2×D3×D4—104no—
166C2×D3×D4—104no—
167C22×D12—51no—
168C22×C4×D3—51no—
169C22×Dic6—51no—
170C22×C3×C8C2×D511yescharacteristic, complemented
171C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
172C2×#214—54no—
173C2×#214—104no—
174C2×(C2×D3)⋊C4—101no—
175C2×C4⋊Dic3—101no—
176C22×C3⋊C8—51no—
177C2×#204—54no—
178C2×#204—104no—
179#897—54no—
180#897—102no—
181C3×#102C2×D514yescomplemented
182(C2×D3)⋊C8—54no—
183#809—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×D4D1214yes—
194C2×C5×D4C22×D312yes—
195C22×C4×C5—21no—
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—64no—
198C2×C22⋊D5—68no—
199C22×Dic5—31no—
200C22×Dic5—61no—
201D4×D5—68no—
202D4×D5—616no—
203D4×D5—68no—
204C2×D20—34no—
205C2×D20—32no—
206C2×D20—62no—
207C2×D20—61no—
208C2×C4×D5—32no—
209C2×C4×D5—32no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—32no—
213C2×Dic10—62no—
214C2×Dic10—62no—
215C2×Dic10—61no—
216C2×C5×C8—22no—
217C2×C5×C8C22×D312yescomplemented
218C5×C4⋊C4—21no—
219C5×C4⋊C4C22×D312yescomplemented
220#687—68no—
221#685—64no—
222C4⋊Dic5—64no—
223C2×#168—32no—
224C2×#168—62no—
225#677—68no—
226C23×D4—151no—
227C22×SD16—151no—
228C22×SD16—151no—
229C2×C22⋊Q8—151no—
230#450—158no—
231C2×#102—151no—
232C2×#102D1511yescharacteristic, complemented
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—42no—
252C3×C4×C5#12012yes—
253C3×C4×C5C22×D411yescharacteristic
254C3×C4×C5C22×D411yescharacteristic
255Dic15—22no—
256Dic15—42no—
257C24×C3—21no—
258C23×D3—51no—
259C23×D3—104no—
260C23×D3—108no—
261C23×D3—101no—
262C23×D3—204no—
263C23×D3—204no—
264C2×C3×D4—22no—
265C2×C3×D4—21no—
266C2×C3×D4D2014yes—
267C2×C3×D4C22×D512yes—
268C22×C3×C4—21no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—104no—
271C2×#67—108no—
272C22×Dic3—51no—
273C22×Dic3—101no—
274D3×D4—108no—
275D3×D4—1016no—
276D3×D4—108no—
277C2×D12—54no—
278C2×D12—52no—
279C2×D12—102no—
280C2×D12—101no—
281C2×C4×D3—52no—
282C2×C4×D3—52no—
283C2×C4×D3—102no—
284C2×C4×D3—102no—
285C2×Dic6—52no—
286C2×Dic6—102no—
287C2×Dic6—102no—
288C2×Dic6—101no—
289C2×C3×C8—22no—
290C2×C3×C8C22×D512yescomplemented
291C3×C4⋊C4—21no—
292C3×C4⋊C4C22×D512yescomplemented
293#214—108no—
294(C2×D3)⋊C4—104no—
295C4⋊Dic3—104no—
296C2×C3⋊C8—52no—
297C2×C3⋊C8—102no—
298#204—108no—
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—128no—
313C22×D5—1232no—
314C22×D5—122no—
315C22×D5—122no—
316C5×D4—24no—
317C5×D4—22no—
318C5×D4C2×D1214yes—
319C2×C4×C5—22no—
320C2×C4×C5—42no—
321C2×C4×C5C2×D1212yes—
322C2×C4×C5D3×D411yescharacteristic
323C2×C4×C5D3×D412yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—616no—
326C2×Dic5—32no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—122no—
330D20—34no—
331D20—64no—
332D20—62no—
333C4×D5—64no—
334C4×D5—62no—
335C4×D5—62no—
336Dic10—62no—
337Dic10—62no—
338Dic10—122no—
339C5×C8—22no—
340#168—62no—
341C25—301no—
342C22×Q8—151no—
343C22×D4—154no—
344C22×D4—151no—
345C22×D4—302no—
346C22×D4—301no—
347C22×D4—304no—
348C22×D4—304no—
349C22×D4C2×D1511yescharacteristic
350C23×C4—151no—
351C2×SD16—154no—
352C2×SD16—154no—
353C2×SD16—304no—
354C2×SD16—304no—
355C22×C8—151no—
356C22×C8C2×D1511yescharacteristic, complemented
357C22⋊Q8—154no—
358C22⋊Q8—302no—
359C2×C4⋊C4—301no—
360C2×C4⋊C4C2×D1511yescharacteristic, complemented
361C2×C22⋊C4—301no—
362#102—154no—
363#102C2×D1514yescomplemented
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×D4—22no—
390C3×D4—24no—
391C3×D4C2×D2014yes—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4C2×D2012yes—
395C2×C3×C4D4×D512yes—
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4C23×D511yescharacteristic
398#67—1016no—
399C2×Dic3—52no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—202no—
403D12—54no—
404D12—102no—
405D12—104no—
406C4×D3—102no—
407C4×D3—102no—
408C4×D3—104no—
409Dic6—102no—
410Dic6—102no—
411Dic6—202no—
412C3×C8—22no—
413C3⋊C8—102no—
414C22×C5—24no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—48no—
418C22×C5#88212yes—
419C22×C5#91112yes—
420C22×C5D3×SD1612yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—34no—
423C2×D5—62no—
424C2×D5—62no—
425C2×D5—68no—
426C2×D5—64no—
427C2×D5—1232no—
428C2×D5—122no—
429C2×D5—122no—
430C2×D5—128no—
431C4×C5—42no—
432C4×C5#88212yes—
433C4×C5C22×D1211yescharacteristic
434C4×C5C2×D3×D411yescharacteristic
435Dic5—62no—
436Dic5—122no—
437C24—21no—
438C24—151no—
439C24—304no—
440C24—308no—
441C24—301no—
442C24—604no—
443C24—604no—
444C2×Q8—152no—
445C2×Q8—301no—
446C2×Q8—302no—
447C2×Q8—302no—
448C2×D4—21no—
449C2×D4—22no—
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×D4D6014yes—
460C2×D4C22×D1512yes—
461C22×C4—21no—
462C22×C4—151no—
463C22×C4—152no—
464C22×C4—152no—
465C22×C4—302no—
466C22×C4—302no—
467C22×C4—301no—
468C22×C4C22×D1511yescharacteristic
469SD16—308no—
470SD16—308no—
471C2×C8—22no—
472C2×C8—152no—
473C2×C8—302no—
474C2×C8C22×D1512yescomplemented
475C4⋊C4—21no—
476C4⋊C4—304no—
477C4⋊C4C22×D1512yescomplemented
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—42no—
498C3×C4#402812yes—
499C3×C4C22×D2011yescharacteristic
500C3×C4C2×D4×D511yescharacteristic
501Dic3—102no—
502Dic3—202no—
503C2×C5—44no—
504C2×C5#477614yescomplemented
505C2×C5C2×#88211yescharacteristic
506C2×C5C2×#91111yescharacteristic
507C2×C5C2×D3×SD1611yescharacteristic
508D5—64no—
509D5—124no—
510C23—24no—
511C23—22no—
512C23—42no—
513C23—42no—
514C23—154no—
515C23—152no—
516C23—3016no—
517C23—302no—
518C23—302no—
519C23—304no—
520C23—302no—
521C23—608no—
522C23—6032no—
523C23—608no—
524C23—602no—
525C23—602no—
526C23D4×D1511yescharacteristic
527Q8—302no—
528Q8—302no—
529Q8—602no—
530D4—24no—
531D4—22no—
532D4—154no—
533D4—3016no—
534D4—304no—
535D4—302no—
536D4C2×D6014yes—
537C2×C4—22no—
538C2×C4—42no—
539C2×C4—152no—
540C2×C4—302no—
541C2×C4—304no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—602no—
546C2×C4C2×D6012yes—
547C2×C4D4×D1511yescharacteristic
548C2×C4D4×D1512yes—
549C2×C4C23×D1511yescharacteristic
550C8—22no—
551C8—302no—
552C2×C3—44no—
553C2×C3#6506514yescomplemented
554C2×C3C2×#402811yescharacteristic
555C2×C3C2×#405711yescharacteristic
556C2×C3C2×D5×SD1611yescharacteristic
557D3—104no—
558D3—204no—
559C5C2×#477611yescharacteristic, 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#9177112yes—
574C22#9180012yes—
575C22SD16×D1512yes—
576C22C2×D4×D1511yescharacteristic
577C4—42no—
578C4—302no—
579C4—602no—
580C4#9177112yes—
581C4C22×D6011yescharacteristic
582C4C2×D4×D1511yescharacteristic
583C3C2×#6506511yescharacteristic, complemented, Sylow
584C2—44no—
585C2—304no—
586C2—604no—
587C2#1175087714yesdirect product factor
588C2C2×#9177111yescharacteristic
589C2C2×#9180011yescharacteristic
590C2C2×SD16×D1511yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC22×D4×D15C2
hypercenterC2×#102D15
hypocenterC3×C5C2×#450
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#6716C2semidirect
3. C22×#6706C2semidirect
4. C2×#91786C2semidirect
5. C2×C3×C5×#102C2semidirect
6. C2×#91104C2semidirect
7. C2×#91093C2semidirect
8. #11750877C2direct (N × H)
19. C22×Dic30C22semidirect
20. C22×C3×C5×C8C22semidirect
21. C2×C3×C5×C4⋊C4C22semidirect
23. C2×#6716C22semidirect
26. C22×C3⋊#168C22semidirect
28. C2×#6706C22semidirect
30. #91786C22semidirect
31. C3×C5×#102C22semidirect
32. #91104C22semidirect
33. #91093C22semidirect
39. C2×C5×#102D3semidirect
74. C2×Dic30C23semidirect
76. C2×C3×C5×C8C23semidirect
78. C3×C5×C4⋊C4C23semidirect
83. C2×C3⋊#168C23semidirect
89. C2×C3×#102D5semidirect
103. C22×C5×C8C2×D3semidirect
104. C2×C5×C4⋊C4C2×D3semidirect
114. C5×#102C2×D3semidirect
133. C22×D15SD16semidirect
170. C22×C3×C8C2×D5semidirect
171. C2×C3×C4⋊C4C2×D5semidirect
181. C3×#102C2×D5semidirect
217. C2×C5×C8C22×D3semidirect
219. C5×C4⋊C4C22×D3semidirect
232. C2×#102D15semidirect
250. C2×D15C2×SD16semidirect
290. C2×C3×C8C22×D5semidirect
292. C3×C4⋊C4C22×D5semidirect
356. C22×C8C2×D15semidirect
360. C2×C4⋊C4C2×D15semidirect
363. #102C2×D15semidirect
366. C2×C3×C5#450semidirect
474. C2×C8C22×D15semidirect
477. C4⋊C4C22×D15semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#4776semidirect
553. C2×C3#65065semidirect
559. C5C2×#4776semidirect
583. C3C2×#65065semidirect
587. C2#11750877direct (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×#67162
C22×#67062
C2×#917862
C2×C3×C5×#1022
C2×#911042
C2×#910932
#117508772
C2×#650653
C2×#47765