Finite Group Databasebeta

← C2×#11749035 #14423447

Subgroups — C2×#11749035 #14423447

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×C5×#237C211yesmaximal, characteristic, complemented
2C22×C3×#686C211yesmaximal, characteristic, complemented
3C2×#91456C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×#91116C211yesmaximal, characteristic, complemented
6#11749035C218yesmaximal, direct product factor
7C2×#90973C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊#168C211yesmaximal, characteristic, complemented
9C2×#65527—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×C5×#67—21no—
12C23×C5×Dic3—21no—
13C2×C5×#237—24no—
14C2×C5×#237—22no—
15C2×C5×#237—24no—
16C2×C5×#237C2214yescomplemented
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×#1201—21no—
21C2×C4⋊Dic15C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C2×C3×#686—24no—
24C2×C3×#686C2214yescomplemented
25C22×C3×#168C2211yescharacteristic
26C2×#6665—21no—
27#91456—22no—
28#91456C2214yescomplemented
29C2×#6655—24no—
30C2×#6655C2214yescomplemented
31#91116C2214yescomplemented
32#90973C2214yescomplemented
33(C2×D3)⋊#168C2214yescomplemented
34C2×#5158—51nomaximal, Hall
35C22×C5×#41—31no—
36C22×#688—31no—
37C22×#686D311yescharacteristic, complemented
38C2×#4076—31no—
39#65527—38no—
40C2×#3967—31no—
41C2×#3964—31no—
42C2×C22⋊#168—31no—
43C24×C3×C5—21no—
44C23×C5×D3D411yescharacteristic
45C23×C3×D5—21no—
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D414yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C2×C5×#67—28no—
53C2×C5×#67—24no—
54C22×C5×Dic3—28no—
55C22×C5×Dic3—21no—
56C22×C5×Dic3—24no—
57C22×C5×Dic3D411yescharacteristic
58C5×#237—216no—
59C5×#237—28no—
60C5×#237—28no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3D412yes—
64C2×C4×C5×D3C2312yes—
65C2×C5×Dic6—21no—
66C2×C5×Dic6—22no—
67C2×C5×Dic6D414yescomplemented
68C2×C5×Dic6C2312yes—
69C2×C3×D20—22no—
70C2×C3×D20—22no—
71C2×C3×D20—21no—
72C2×C3×D20C2312yes—
73C2×#1201—24no—
74C2×#1201—44no—
75C4⋊Dic15—21no—
76C4⋊Dic15C2312yes—
77C2×C3⋊#168—22no—
78C2×C3⋊#168C2312yes—
79C3×#686—28no—
80C2×C3×#168—22no—
81C2×C3×#168C2312yes—
82#6665—24no—
83#6655—28no—
84C22×#237D511yescharacteristic, complemented
85C22×C3×D8—51no—
86C2×#938—51no—
87C22×#214—51no—
88C2×#832—51no—
89#5158—58no—
90C2×(C2×D3)⋊C8—51no—
91C2×#816—51no—
92C2×C5×#41—34no—
93C2×C5×#41—62no—
94C2×C5×#41—64no—
95C2×C5×#41—64no—
96C22×C5×Q8—31no—
97C22×C5×D4—61no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5—31no—
100C23×C4×C5—61no—
101C22×C22⋊D5—61no—
102C22×D20C2×D311yescharacteristic
103C2×#688—34no—
104C2×#688—64no—
105C2×#686—24no—
106C2×#686C2×D314yescomplemented
107#4076—34no—
108#4076—62no—
109C2×#685—61no—
110C2×C4⋊Dic5—31no—
111C22×#168—31no—
112C22×#168C2×D311yescharacteristic
113#3967—34no—
114#3964—34no—
115C22⋊#168—34no—
116C2×#449—151noSylow
117C23×C3×C5—24no—
118C23×C3×C5—22no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C2×D411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3C2×D412yes—
126C22×C3×D5—22no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
130C3×C5×D4—24no—
131C3×C5×D4—22no—
132C3×C5×D4C2×D414yescomplemented
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138C2×Dic15—42no—
139C5×#67—216no—
140C2×C5×Dic3—216no—
141C2×C5×Dic3—24no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C2×D412yes—
145C4×C5×D3—24no—
146C4×C5×D3—22no—
147C4×C5×D3—22no—
148C5×Dic6—24no—
149C5×Dic6—22no—
150C5×Dic6C2×D414yescomplemented
151C3×D20—22no—
152C3×D20—22no—
153C3×D20—42no—
154#1201—48no—
155C3⋊#168—22no—
156C3×#168—22no—
157C22×C3×D4—51no—
158C22×C3×D4C2×D511yescharacteristic
159C22×#67—21no—
160C22×#67—101no—
161C23×Dic3—21no—
162C2×#237—24no—
163C2×#237—22no—
164C2×#237—24no—
165C2×#237C2×D514yescomplemented
166C22×C4×D3C2×D511yescharacteristic
167C22×Dic6C2×D511yescharacteristic
168C2×C3×D8—54no—
169C2×C3×D8—104no—
170C22×C3×C8—51no—
171C2×#217—101no—
172#938—54no—
173#938—102no—
174C2×#214—54no—
175C2×#214—104no—
176C2×C4⋊Dic3—51no—
177C22×C3⋊C8—51no—
178#832—54no—
179(C2×D3)⋊C8—54no—
180#816—54no—
181C24×C5—21no—
182C24×C5—31no—
183C23×D5—21no—
184C5×#41—68no—
185C5×#41—616no—
186C5×#41—68no—
187C2×C5×Q8—34no—
188C2×C5×Q8—32no—
189C2×C5×Q8—61no—
190C2×C5×Q8—62no—
191C2×C5×D4—21no—
192C2×C5×D4—22no—
193C2×C5×D4—64no—
194C2×C5×D4—68no—
195C2×C5×D4#6714yescomplemented
196C2×C5×D4C22×D312yes—
197C22×C4×C5—31no—
198C22×C4×C5—32no—
199C22×C4×C5—32no—
200C22×C4×C5—64no—
201C22×C4×C5—68no—
202C22×C4×C5—61no—
203C22×C4×C5—62no—
204C22×C4×C5—62no—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—64no—
207C2×C22⋊D5—124no—
208C22×Dic5—61no—
209C2×D20—22no—
210C2×D20—22no—
211C2×D20—21no—
212C2×D20C22×D312yes—
213#688—68no—
214#686—28no—
215#685—64no—
216C4⋊Dic5—32no—
217C4⋊Dic5—61no—
218C2×#168—22no—
219C2×#168—32no—
220C2×#168—62no—
221C2×#168C22×D312yes—
222C22×#41—31no—
223C22×SD16—151no—
224C22×D8—51no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5—24no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—48no—
234C22×C3×C5#12012yes—
235C22×C3×C5#13512yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×C5×D3—22no—
239C2×C5×D3—22no—
240C2×C5×D3—22no—
241C2×C5×D3—44no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5#12012yes—
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249Dic15—42no—
250C5×Dic3—24no—
251C5×Dic3—22no—
252C24×C3—21no—
253C24×C3—101no—
254C23×D3C22⋊D511yescharacteristic
255C2×C3×D4—21no—
256C2×C3×D4—22no—
257C2×C3×D4—52no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C2×C3×D4—101no—
261C2×C3×D4C22⋊D514yescomplemented
262C2×C3×D4C22×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C2×#67—28no—
265C2×#67—24no—
266C2×#67—104no—
267C2×#67—204no—
268C22×Dic3—28no—
269C22×Dic3—21no—
270C22×Dic3—24no—
271C22×Dic3—101no—
272C22×Dic3C22⋊D511yescharacteristic
273#237—216no—
274#237—28no—
275#237—28no—
276C2×C4×D3—22no—
277C2×C4×D3—22no—
278C2×C4×D3C22⋊D512yes—
279C2×C4×D3C22×D512yes—
280C2×Dic6—22no—
281C2×Dic6—21no—
282C2×Dic6C22⋊D514yescomplemented
283C2×Dic6C22×D512yes—
284C3×D8—108no—
285C2×C3×C8—52no—
286C2×C3×C8—102no—
287#217—104no—
288#214—108no—
289C4⋊Dic3—52no—
290C4⋊Dic3—101no—
291C2×C3⋊C8—52no—
292C2×C3⋊C8—102no—
293C23×C5—24no—
294C23×C5—22no—
295C23×C5—32no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5—62no—
299C23×C5—62no—
300C23×C5—62no—
301C23×C5D3×D411yescharacteristic
302C22×D5—22no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C5×Q8—34no—
307C5×Q8—64no—
308C5×Q8—62no—
309C5×D4—24no—
310C5×D4—22no—
311C5×D4—616no—
312C5×D4C2×#6714yescomplemented
313C2×C4×C5—32no—
314C2×C4×C5—616no—
315C2×C4×C5—62no—
316C2×C4×C5—64no—
317C2×C4×C5—62no—
318C2×C4×C5—64no—
319C2×C4×C5—62no—
320C2×C4×C5—62no—
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5D3×D412yes—
323C2×C4×C5C2×#6712yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—128no—
326C2×Dic5—62no—
327C2×Dic5—122no—
328D20—22no—
329D20—22no—
330D20—42no—
331#168—22no—
332#168—62no—
333C2×#41—34no—
334C2×#41—62no—
335C2×#41—64no—
336C2×#41—64no—
337C22×Q8—31no—
338C22×D4—51no—
339C22×D4—61no—
340C22×D4—301no—
341C22×D4D3×D511yescharacteristic
342C23×C4—31no—
343C23×C4—61no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—54no—
347C2×D8—104no—
348C22×C8—51no—
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—44no—
358C2×C3×C5#44914yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×#13511yescharacteristic
361C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
362C3×D5—82no—
363C5×D3—42no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—102no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3—202no—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3C2×C22⋊D512yes—
377C3×D4—24no—
378C3×D4—22no—
379C3×D4—102no—
380C3×D4—102no—
381C3×D4—202no—
382C3×D4C2×C22⋊D514yescomplemented
383C2×C3×C4C2×C22⋊D512yes—
384C2×C3×C4C2×C22⋊D511yescharacteristic
385C2×C3×C4C2×C22⋊D512yes—
386C2×C3×C4C23×D511yescharacteristic
387#67—216no—
388#67—208no—
389C2×Dic3—216no—
390C2×Dic3—24no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—102no—
394C2×Dic3—202no—
395C2×Dic3C2×C22⋊D512yes—
396C4×D3—24no—
397C4×D3—22no—
398C4×D3—22no—
399Dic6—24no—
400Dic6—22no—
401Dic6C2×C22⋊D514yescomplemented
402C3×C8—102no—
403C3⋊C8—102no—
404C22×C5—24no—
405C22×C5—48no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5—62no—
409C22×C5—62no—
410C22×C5—62no—
411C22×C5—124no—
412C22×C5#91112yes—
413C22×C5#91212yes—
414C22×C5#93712yes—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—84no—
420C4×C5—62no—
421C4×C5—64no—
422C4×C5#93712yes—
423C4×C5C2×D3×D411yescharacteristic
424C4×C5C22×#6711yescharacteristic
425Dic5—122no—
426C24—21no—
427C24—31no—
428C24—101no—
429#41—68no—
430#41—616no—
431#41—68no—
432C2×Q8—34no—
433C2×Q8—32no—
434C2×Q8—62no—
435C2×Q8—61no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—52no—
439C2×D4—64no—
440C2×D4—68no—
441C2×D4—102no—
442C2×D4—102no—
443C2×D4—101no—
444C2×D4—304no—
445C2×D4—604no—
446C2×D4#120114yescomplemented
447C2×D4C2×D3×D512yes—
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—64no—
452C22×C4—68no—
453C22×C4—61no—
454C22×C4—62no—
455C22×C4—62no—
456C22×C4—301no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—108no—
460C2×C8—52no—
461C2×C8—102no—
462C2×C8—152no—
463C2×C8—302no—
464C4⋊C4—152no—
465C4⋊C4—301no—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—24no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—48no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—404no—
476C22×C3#409512yes—
477C22×C3#409612yes—
478C22×C3#409912yes—
479C22×C3C22×C22⋊D511yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—44no—
484C3×C4#409912yes—
485C3×C4C22×C22⋊D511yescharacteristic
486C3×C4C22×C22⋊D511yescharacteristic
487Dic3—24no—
488Dic3—22no—
489Dic3—202no—
490C2×C5—44no—
491C2×C5—122no—
492C2×C5#515814yescomplemented
493C2×C5C2×#91111yescharacteristic
494C2×C5C2×#91211yescharacteristic
495C2×C5C2×#93711yescharacteristic
496D5—82no—
497C23—22no—
498C23—24no—
499C23—32no—
500C23—42no—
501C23—42no—
502C23—62no—
503C23—62no—
504C23—62no—
505C23—102no—
506C23—202no—
507C23—202no—
508C23—202no—
509C23D3×C22⋊D511yescharacteristic
510Q8—34no—
511Q8—62no—
512Q8—64no—
513D4—22no—
514D4—24no—
515D4—616no—
516D4—102no—
517D4—102no—
518D4—202no—
519D4—608no—
520D4C2×#120114yescomplemented
521C2×C4—32no—
522C2×C4—616no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—64no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—302no—
530C2×C4—602no—
531C2×C4C2×#120112yes—
532C2×C4D3×C22⋊D512yes—
533C2×C4D3×C22⋊D511yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—102no—
536C8—302no—
537C2×C3—44no—
538C2×C3—402no—
539C2×C3#6552714yescomplemented
540C2×C3C2×#409511yescharacteristic
541C2×C3C2×#409611yescharacteristic
542C2×C3C2×#409911yescharacteristic
543D3—42no—
544C5C2×#515811yescharacteristic, complemented, Sylow
545C22—24no—
546C22—48no—
547C22—42no—
548C22—42no—
549C22—62no—
550C22—62no—
551C22—62no—
552C22—124no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—404no—
557C22#9148012yes—
558C22#9149312yes—
559C22#9156812yes—
560C22C2×D3×C22⋊D511yescharacteristic
561C4—62no—
562C4—64no—
563C4—602no—
564C4#9156812yes—
565C4C22×#120111yescharacteristic
566C4C2×D3×C22⋊D511yescharacteristic
567C3C2×#6552711yescharacteristic, complemented, Sylow
568C2—44no—
569C2—122no—
570C2—402no—
571C2#1174903514yesdirect product factor
572C2C2×#9148011yescharacteristic
573C2C2×#9149311yescharacteristic
574C2C2×#9156811yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#449
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×C5×#237C2semidirect
2. C22×C3×#686C2semidirect
3. C2×#91456C2semidirect
4. C22×#6655C2semidirect
5. C2×#91116C2semidirect
6. #11749035C2direct (N × H)
7. C2×#90973C2semidirect
8. C2×(C2×D3)⋊#168C2semidirect
16. C2×C5×#237C22semidirect
24. C2×C3×#686C22semidirect
28. #91456C22semidirect
30. C2×#6655C22semidirect
31. #91116C22semidirect
32. #90973C22semidirect
33. (C2×D3)⋊#168C22semidirect
37. C22×#686D3semidirect
48. C2×C3×C5×D4D4semidirect
67. C2×C5×Dic6D4semidirect
84. C22×#237D5semidirect
106. C2×#686C2×D3semidirect
132. C3×C5×D4C2×D4semidirect
150. C5×Dic6C2×D4semidirect
165. C2×#237C2×D5semidirect
195. C2×C5×D4#67semidirect
261. C2×C3×D4C22⋊D5semidirect
282. C2×Dic6C22⋊D5semidirect
312. C5×D4C2×#67semidirect
358. C2×C3×C5#449semidirect
382. C3×D4C2×C22⋊D5semidirect
401. Dic6C2×C22⋊D5semidirect
446. C2×D4#1201semidirect
467. C3×C5C2×#449semidirect
492. C2×C5#5158semidirect
520. D4C2×#1201semidirect
539. C2×C3#65527semidirect
544. C5C2×#5158semidirect
567. C3C2×#65527semidirect
571. C2#11749035direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2372
C22×C3×#6862
C2×#914562
C22×#66552
C2×#911162
#117490352
C2×#909732
C2×(C2×D3)⋊#1682
C2×#655273
C2×#51585