Finite Group Databasebeta

← C2×#11751339 #14423414

Subgroups — C2×#11751339 #14423414

Order 1920.

1624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C22×#6717C211yesmaximal, characteristic, complemented
3C22×#6715C211yesmaximal, characteristic, complemented
4C2×#91819C211yesmaximal, characteristic, complemented
5#11751339C218yesmaximal, direct product factor
6C2×#91119C211yesmaximal, characteristic, complemented
7C2×#91116C211yesmaximal, characteristic, complemented
8C2×#91114C211yesmaximal, characteristic, complemented
9C2×#65527—31nomaximal, Hall
10C2×C3×C5×#41—24no—
11C2×C3×C5×#41—24no—
12C2×C3×C5×#41—22no—
13C2×C3×C5×#41C2214yescomplemented
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C3×C5×D4—21no—
16C22×C3×C5×D4C2211yescharacteristic
17C23×C3×C4×C5—21no—
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220—21no—
20C22×D60C2211yescharacteristic
21C2×#6717—24no—
22C2×#6717C2214yescomplemented
23C2×#6715—24no—
24C2×#6715C2214yescomplemented
25#91819—22no—
26#91819C2214yescomplemented
27C2×#6714—21no—
28C2×C4⋊Dic15C2211yescharacteristic
29C22×C3⋊#168C2211yescharacteristic
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91116C2214yescomplemented
33#91114C2214yescomplemented
34C2×#5238—51nomaximal, Hall
35C22×C5×#41D311yescharacteristic, complemented
36C22×#688—31no—
37C22×#686—31no—
38C2×#4076—31no—
39#65527—38no—
40C2×#3967—31no—
41C2×#3964—31no—
42C2×C22⋊#168—31no—
43C24×C3×C5—21no—
44C24×C3×C5D411yescharacteristic
45C23×D15—21no—
46C3×C5×#41—216no—
47C3×C5×#41—28no—
48C3×C5×#41—28no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8D414yescomplemented
52C2×C3×C5×Q8C2312yes—
53C2×C3×C5×D4—28no—
54C2×C3×C5×D4—24no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4D414yescomplemented
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5—28no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D411yescharacteristic
65C22×C3×C4×C5D412yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—24no—
69C2×#1220—44no—
70C22×Dic15—21no—
71C2×D60—22no—
72C2×D60—22no—
73C2×D60—21no—
74C2×D60C2312yes—
75#6717—28no—
76#6715—28no—
77#6714—24no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80C2×C3⋊#168—22no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83C2×C3⋊#168C2312yes—
84C22×C3×#41D511yescharacteristic, complemented
85C22×#215—51no—
86C22×#213—51no—
87C2×#930—51no—
88#5238—58no—
89C2×#835—51no—
90C2×#832—51no—
91C2×#830—51no—
92C2×C5×#41—24no—
93C2×C5×#41—24no—
94C2×C5×#41—22no—
95C2×C5×#41C2×D314yescomplemented
96C22×C5×Q8C2×D311yescharacteristic
97C22×C5×D4—21no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5—21no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—61no—
102C22×D20—31no—
103C2×#688—34no—
104C2×#688—64no—
105C2×#686—34no—
106C2×#686—64no—
107#4076—34no—
108#4076—62no—
109C2×#685—61no—
110C2×C4⋊Dic5—31no—
111C22×#168—31no—
112C22×#168—31no—
113#3967—34no—
114#3964—34no—
115C22⋊#168—34no—
116C2×#449—151noSylow
117C23×C3×C5—22no—
118C23×C3×C5—24no—
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—22no—
122C23×C3×C5—42no—
123C23×C3×C5—42no—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D411yescharacteristic
126C22×D15—22no—
127C22×D15—42no—
128C22×D15—42no—
129C22×D15—42no—
130C3×C5×Q8—24no—
131C3×C5×Q8—22no—
132C3×C5×Q8C2×D414yescomplemented
133C3×C5×D4—216no—
134C3×C5×D4—24no—
135C3×C5×D4—22no—
136C3×C5×D4C2×D414yescomplemented
137C2×C3×C4×C5—216no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—24no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—24no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—48no—
150C2×Dic15—22no—
151C2×Dic15—42no—
152D60—22no—
153D60—22no—
154D60—42no—
155C3⋊#168—22no—
156C3⋊#168—22no—
157C2×C3×#41—24no—
158C2×C3×#41—24no—
159C2×C3×#41—22no—
160C2×C3×#41C2×D514yescomplemented
161C22×C3×Q8C2×D511yescharacteristic
162C22×C3×D4—21no—
163C22×C3×D4C2×D511yescharacteristic
164C23×C3×C4—21no—
165C23×C3×C4C2×D511yescharacteristic
166C22×#67—101no—
167C22×D12—51no—
168C2×#215—54no—
169C2×#215—104no—
170C2×#213—54no—
171C2×#213—104no—
172#930—54no—
173#930—102no—
174C2×(C2×D3)⋊C4—101no—
175C2×C4⋊Dic3—51no—
176C22×C3⋊C8—51no—
177C22×C3⋊C8—51no—
178#835—54no—
179#832—54no—
180#830—54no—
181C24×C5—21no—
182C24×C5#6711yescharacteristic
183C23×D5—61no—
184C5×#41—216no—
185C5×#41—28no—
186C5×#41—28no—
187C2×C5×Q8—22no—
188C2×C5×Q8—21no—
189C2×C5×Q8#6714yescomplemented
190C2×C5×Q8C22×D312yes—
191C2×C5×D4—28no—
192C2×C5×D4—24no—
193C2×C5×D4—21no—
194C2×C5×D4—22no—
195C2×C5×D4#6714yescomplemented
196C2×C5×D4C22×D312yes—
197C22×C4×C5—28no—
198C22×C4×C5—21no—
199C22×C4×C5—24no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5#6711yescharacteristic
203C22×C4×C5#6712yes—
204C22×C4×C5C22×D312yes—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—64no—
207C2×C22⋊D5—124no—
208C22×Dic5—61no—
209C2×D20—32no—
210C2×D20—62no—
211C2×D20—62no—
212C2×D20—61no—
213#688—68no—
214#686—68no—
215#685—64no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C2×#168—32no—
219C2×#168—32no—
220C2×#168—62no—
221C2×#168—62no—
222C22×#41D1511yescharacteristic, complemented
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—44no—
237C22×C3×C5—48no—
238C22×C3×C5#12012yes—
239C22×C3×C5#13512yes—
240C22×C3×C5AGL(1,ℤ/8)12yes—
241C22×C3×C5C22×D411yescharacteristic
242C2×D15—42no—
243C2×D15—42no—
244C2×D15—42no—
245C2×D15—84no—
246C3×C4×C5—22no—
247C3×C4×C5—24no—
248C3×C4×C5#12012yes—
249C3×C4×C5C22×D411yescharacteristic
250C3×C4×C5C22×D411yescharacteristic
251Dic15—42no—
252C24×C3—21no—
253C24×C3C22⋊D511yescharacteristic
254C23×D3—101no—
255C3×#41—216no—
256C3×#41—28no—
257C3×#41—28no—
258C2×C3×Q8—22no—
259C2×C3×Q8—21no—
260C2×C3×Q8C22⋊D514yescomplemented
261C2×C3×Q8C22×D512yes—
262C2×C3×D4—28no—
263C2×C3×D4—24no—
264C2×C3×D4—21no—
265C2×C3×D4—22no—
266C2×C3×D4C22⋊D514yescomplemented
267C2×C3×D4C22×D512yes—
268C22×C3×C4—28no—
269C22×C3×C4—21no—
270C22×C3×C4—24no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4C22⋊D511yescharacteristic
274C22×C3×C4C22⋊D512yes—
275C22×C3×C4C22×D512yes—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—104no—
278C2×#67—204no—
279C22×Dic3—101no—
280C2×D12—52no—
281C2×D12—102no—
282C2×D12—102no—
283C2×D12—101no—
284#215—108no—
285#213—108no—
286(C2×D3)⋊C4—104no—
287C4⋊Dic3—52no—
288C4⋊Dic3—101no—
289C2×C3⋊C8—52no—
290C2×C3⋊C8—52no—
291C2×C3⋊C8—102no—
292C2×C3⋊C8—102no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—24no—
297C23×C5—22no—
298C23×C5—42no—
299C23×C5—42no—
300C23×C5C2×#6712yes—
301C23×C5C2×#6711yescharacteristic
302C22×D5—62no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5—122no—
306C5×Q8—24no—
307C5×Q8—22no—
308C5×Q8C2×#6714yescomplemented
309C5×D4—216no—
310C5×D4—24no—
311C5×D4—22no—
312C5×D4C2×#6714yescomplemented
313C2×C4×C5—216no—
314C2×C4×C5—22no—
315C2×C4×C5—24no—
316C2×C4×C5—22no—
317C2×C4×C5—24no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5C2×#6712yes—
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C2×#6712yes—
323C2×C4×C5C2×#6712yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—128no—
326C2×Dic5—62no—
327C2×Dic5—122no—
328D20—62no—
329D20—62no—
330D20—122no—
331#168—62no—
332#168—62no—
333C2×#41—24no—
334C2×#41—24no—
335C2×#41—22no—
336C2×#41C2×D1514yescomplemented
337C22×Q8C2×D1511yescharacteristic
338C22×D4—21no—
339C22×D4—151no—
340C22×D4—301no—
341C22×D4C2×D1511yescharacteristic
342C23×C4—21no—
343C23×C4C2×D1511yescharacteristic
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—151no—
349C22×C8—151no—
350#121—154no—
351#121—302no—
352C2×C4⋊C4—151no—
353C2×C22⋊C4—301no—
354#103—154no—
355#102—154no—
356C22⋊C8—154no—
357C2×C3×C5—42no—
358C2×C3×C5—44no—
359C2×C3×C5#44914yescomplemented
360C2×C3×C5C2×#12011yescharacteristic
361C2×C3×C5C2×#13511yescharacteristic
362C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
363D15—82no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—24no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3C2×C22⋊D512yes—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—102no—
374C22×D3—202no—
375C22×D3—202no—
376C22×D3—202no—
377C3×Q8—24no—
378C3×Q8—22no—
379C3×Q8C2×C22⋊D514yescomplemented
380C3×D4—216no—
381C3×D4—24no—
382C3×D4—22no—
383C3×D4C2×C22⋊D514yescomplemented
384C2×C3×C4—216no—
385C2×C3×C4—22no—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4C2×C22⋊D512yes—
392C2×C3×C4C2×C22⋊D511yescharacteristic
393C2×C3×C4C2×C22⋊D512yes—
394C2×C3×C4C2×C22⋊D512yes—
395C2×C3×C4C23×D511yescharacteristic
396#67—208no—
397C2×Dic3—102no—
398C2×Dic3—202no—
399D12—102no—
400D12—102no—
401D12—202no—
402C3⋊C8—102no—
403C3⋊C8—102no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—24no—
408C22×C5—44no—
409C22×C5—48no—
410C22×C5—42no—
411C22×C5—42no—
412C22×C5#94912yes—
413C22×C5#95012yes—
414C22×C5#95312yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—244no—
420C4×C5—22no—
421C4×C5—24no—
422C4×C5#95312yes—
423C4×C5C22×#6711yescharacteristic
424C4×C5C22×#6711yescharacteristic
425Dic5—122no—
426C24—21no—
427C24—301no—
428C24#122011yescharacteristic
429#41—216no—
430#41—28no—
431#41—28no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8#122014yescomplemented
435C2×Q8C22×D1512yes—
436C2×D4—28no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—152no—
441C2×D4—304no—
442C2×D4—302no—
443C2×D4—302no—
444C2×D4—301no—
445C2×D4—604no—
446C2×D4#122014yescomplemented
447C2×D4C22×D1512yes—
448C22×C4—28no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—301no—
454C22×C4#122012yes—
455C22×C4#122011yescharacteristic
456C22×C4C22×D1512yes—
457C22×C4C22×D1511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—152no—
461C2×C8—152no—
462C2×C8—302no—
463C2×C8—302no—
464C4⋊C4—152no—
465C4⋊C4—301no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—44no—
475C22×C3—48no—
476C22×C3#409512yes—
477C22×C3#409612yes—
478C22×C3#409912yes—
479C22×C3C22×C22⋊D511yescharacteristic
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—404no—
484C3×C4—22no—
485C3×C4—24no—
486C3×C4#409912yes—
487C3×C4C22×C22⋊D511yescharacteristic
488C3×C4C22×C22⋊D511yescharacteristic
489Dic3—202no—
490C2×C5—42no—
491C2×C5—44no—
492C2×C5#523814yescomplemented
493C2×C5C2×#94911yescharacteristic
494C2×C5C2×#95011yescharacteristic
495C2×C5C2×#95311yescharacteristic
496D5—242no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—24no—
501C23—22no—
502C23—42no—
503C23—42no—
504C23—302no—
505C23—602no—
506C23—602no—
507C23—602no—
508C23C2×#122012yes—
509C23C2×#122011yescharacteristic
510Q8—24no—
511Q8—22no—
512Q8C2×#122014yescomplemented
513D4—216no—
514D4—24no—
515D4—22no—
516D4—302no—
517D4—302no—
518D4—608no—
519D4—602no—
520D4C2×#122014yescomplemented
521C2×C4—216no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—302no—
529C2×C4—602no—
530C2×C4C2×#122012yes—
531C2×C4C2×#122011yescharacteristic
532C2×C4C2×#122012yes—
533C2×C4C2×#122012yes—
534C2×C4C23×D1511yescharacteristic
535C8—302no—
536C8—302no—
537C2×C3—42no—
538C2×C3—44no—
539C2×C3#6552714yescomplemented
540C2×C3C2×#409511yescharacteristic
541C2×C3C2×#409611yescharacteristic
542C2×C3C2×#409911yescharacteristic
543D3—402no—
544C5C2×#523811yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—24no—
549C22—42no—
550C22—42no—
551C22—44no—
552C22—48no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—1204no—
557C22#9183812yes—
558C22#9183912yes—
559C22#9184212yes—
560C22C22×#122011yescharacteristic
561C4—22no—
562C4—24no—
563C4—602no—
564C4#9184212yes—
565C4C22×#122011yescharacteristic
566C4C22×#122011yescharacteristic
567C3C2×#6552711yescharacteristic, complemented, Sylow
568C2—42no—
569C2—44no—
570C2—1202no—
571C2#1175133914yesdirect product factor
572C2C2×#9183811yescharacteristic
573C2C2×#9183911yescharacteristic
574C2C2×#9184211yescharacteristic
subgroupG/H
centerC23C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×#41C2
socleC23×C3×C5C2×D4
hypercenterC22×#41D15
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C22×#6717C2semidirect
3. C22×#6715C2semidirect
4. C2×#91819C2semidirect
5. #11751339C2direct (N × H)
6. C2×#91119C2semidirect
7. C2×#91116C2semidirect
8. C2×#91114C2semidirect
13. C2×C3×C5×#41C22semidirect
22. C2×#6717C22semidirect
24. C2×#6715C22semidirect
26. #91819C22semidirect
31. #91119C22semidirect
32. #91116C22semidirect
33. #91114C22semidirect
35. C22×C5×#41D3semidirect
51. C2×C3×C5×Q8D4semidirect
57. C2×C3×C5×D4D4semidirect
84. C22×C3×#41D5semidirect
95. C2×C5×#41C2×D3semidirect
132. C3×C5×Q8C2×D4semidirect
136. C3×C5×D4C2×D4semidirect
160. C2×C3×#41C2×D5semidirect
189. C2×C5×Q8#67semidirect
195. C2×C5×D4#67semidirect
222. C22×#41D15semidirect
260. C2×C3×Q8C22⋊D5semidirect
266. C2×C3×D4C22⋊D5semidirect
308. C5×Q8C2×#67semidirect
312. C5×D4C2×#67semidirect
336. C2×#41C2×D15semidirect
359. C2×C3×C5#449semidirect
379. C3×Q8C2×C22⋊D5semidirect
383. C3×D4C2×C22⋊D5semidirect
434. C2×Q8#1220semidirect
446. C2×D4#1220semidirect
467. C3×C5C2×#449semidirect
492. C2×C5#5238semidirect
512. Q8C2×#1220semidirect
520. D4C2×#1220semidirect
539. C2×C3#65527semidirect
544. C5C2×#5238semidirect
567. C3C2×#65527semidirect
571. C2#11751339direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×#67172
C22×#67152
C2×#918192
#117513392
C2×#911192
C2×#911162
C2×#911142
C2×#655273
C2×#52385