Finite Group Databasebeta

← C2×#11748517 #14423453

Subgroups — C2×#11748517 #14423453

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×#235C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic, complemented
3C22×#6655C211yesmaximal, characteristic, complemented
4C22×#6652C211yesmaximal, characteristic, complemented
5C2×#91114C211yesmaximal, characteristic, complemented
6#11748517C218yesmaximal, direct product factor
7C2×#90972C211yesmaximal, characteristic, complemented
8C2×#90966C211yesmaximal, characteristic, complemented
9C2×#65527—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C5×#67—21no—
12C2×C5×#235—22no—
13C2×C5×#235—24no—
14C2×C5×#235—24no—
15C2×C5×#235C2214yescomplemented
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3—21no—
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×C22⋊D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C3×#4076—22no—
24C3×#4076C2214yescomplemented
25C2×C3×#685—21no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×#6655—24no—
28C2×#6655C2214yescomplemented
29C2×#6652—24no—
30C2×#6652C2214yescomplemented
31#91114C2214yescomplemented
32#90972C2214yescomplemented
33#90966C2214yescomplemented
34C2×#5037—51nomaximal, Hall
35C22×C5×#41—31no—
36C22×#688—31no—
37C22×#686—31no—
38C2×#4076D311yescharacteristic, complemented
39#65527—38no—
40C2×#3967—31no—
41C2×#3964—31no—
42C2×C22⋊#168—31no—
43C24×C3×C5D411yescharacteristic
44C23×C5×D3—21no—
45C23×C3×D5—21no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5D412yes—
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C2×C5×#67—28no—
53C2×C5×#67—24no—
54C22×C5×Dic3—21no—
55C5×#235—216no—
56C5×#235—28no—
57C5×#235—28no—
58C2×C5×D12—21no—
59C2×C5×D12—22no—
60C2×C5×D12D414yescomplemented
61C2×C5×D12C2312yes—
62C2×C4×C5×D3—28no—
63C2×C4×C5×D3—24no—
64C2×C5×Dic6—21no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6D414yescomplemented
67C2×C5×Dic6C2312yes—
68C2×C3×C22⋊D5—24no—
69C2×C3×C22⋊D5—44no—
70C22×C3×Dic5—21no—
71C2×C3×D20—22no—
72C2×C3×D20—22no—
73C2×C3×D20—21no—
74C2×C3×D20C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168—22no—
77C2×C3⋊#168C2312yes—
78C2×C3⋊#168C2312yes—
79C3×#685—24no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82#6655—28no—
83#6652—28no—
84C22×#235D511yescharacteristic, complemented
85C2×C3×#121—51no—
86C22×#214—51no—
87C22×#213—51no—
88C2×#830—51no—
89#5037—58no—
90C2×#810—51no—
91C2×#809—51no—
92C2×C5×#41—34no—
93C2×C5×#41—64no—
94C2×C5×#41—64no—
95C2×C5×#41—62no—
96C22×C5×Q8—31no—
97C22×C5×D4—31no—
98C22×C5×D4—61no—
99C23×C4×C5—61no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—21no—
102C22×D20C2×D311yescharacteristic
103C2×#688—34no—
104C2×#688—64no—
105C2×#686—34no—
106C2×#686—64no—
107#4076—22no—
108#4076C2×D314yescomplemented
109C2×#685—21no—
110C2×C4⋊Dic5C2×D311yescharacteristic
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—22no—
119C23×C3×C5—22no—
120C23×C3×C5C2×D412yes—
121C23×C3×C5C2×D411yescharacteristic
122C22×C5×D3—24no—
123C22×C5×D3—22no—
124C22×C5×D3—42no—
125C22×C5×D3—42no—
126C22×C3×D5—22no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—24no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139C5×#67—216no—
140C2×C5×Dic3—24no—
141C2×C5×Dic3—22no—
142C5×D12—24no—
143C5×D12—22no—
144C5×D12C2×D414yescomplemented
145C4×C5×D3—216no—
146C5×Dic6—24no—
147C5×Dic6—22no—
148C5×Dic6C2×D414yescomplemented
149C3×C22⋊D5—48no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—42no—
152C3×D20—22no—
153C3×D20—22no—
154C3×D20—42no—
155C3⋊#168—22no—
156C3⋊#168—22no—
157C22×C3×D4—51no—
158C22×C3×D4—101no—
159C23×C3×C4C2×D511yescharacteristic
160C22×#67—21no—
161C2×#235—22no—
162C2×#235—24no—
163C2×#235—24no—
164C2×#235C2×D514yescomplemented
165C22×D12C2×D511yescharacteristic
166C22×C4×D3—21no—
167C22×Dic6C2×D511yescharacteristic
168C3×#121—54no—
169C3×#121—102no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C22⋊C4—101no—
172C2×#214—54no—
173C2×#214—104no—
174C2×#213—54no—
175C2×#213—104no—
176C22×C3⋊C8—51no—
177C22×C3⋊C8—51no—
178#830—54no—
179#810—54no—
180#809—54no—
181C24×C5—61no—
182C24×C5#6711yescharacteristic
183C23×D5—21no—
184C5×#41—68no—
185C5×#41—68no—
186C5×#41—616no—
187C2×C5×Q8—34no—
188C2×C5×Q8—32no—
189C2×C5×Q8—62no—
190C2×C5×Q8—61no—
191C2×C5×D4—34no—
192C2×C5×D4—32no—
193C2×C5×D4—68no—
194C2×C5×D4—64no—
195C2×C5×D4—62no—
196C2×C5×D4—61no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—68no—
200C22×C4×C5—61no—
201C22×C4×C5—64no—
202C22×C4×C5#6711yescharacteristic
203C22×C4×C5#6712yes—
204C22×C4×C5C22×D312yes—
205C22×C4×C5C22×D311yescharacteristic
206C2×C22⋊D5—24no—
207C2×C22⋊D5—44no—
208C22×Dic5—21no—
209C2×D20—22no—
210C2×D20—22no—
211C2×D20—21no—
212C2×D20C22×D312yes—
213#688—68no—
214#686—68no—
215#685—24no—
216C4⋊Dic5—21no—
217C4⋊Dic5C22×D312yes—
218C2×#168—32no—
219C2×#168—32no—
220C2×#168—62no—
221C2×#168—62no—
222C22×#41—31no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—51no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—44no—
234C22×C3×C5#12012yes—
235C22×C3×C5#13512yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×C5×D3—24no—
239C2×C5×D3—42no—
240C2×C5×D3—42no—
241C2×C5×D3—48no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5—22no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250C3×Dic5—42no—
251C5×Dic3—24no—
252C24×C3—101no—
253C24×C3C22⋊D511yescharacteristic
254C23×D3—21no—
255C2×C3×D4—52no—
256C2×C3×D4—104no—
257C2×C3×D4—102no—
258C2×C3×D4—102no—
259C2×C3×D4—101no—
260C2×C3×D4—204no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—101no—
264C22×C3×C4C22⋊D511yescharacteristic
265C22×C3×C4C22⋊D512yes—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—28no—
269C2×#67—24no—
270C22×Dic3—21no—
271#235—216no—
272#235—28no—
273#235—28no—
274C2×D12—21no—
275C2×D12—22no—
276C2×D12C22⋊D514yescomplemented
277C2×D12C22×D512yes—
278C2×C4×D3—28no—
279C2×C4×D3—24no—
280C2×Dic6—21no—
281C2×Dic6—22no—
282C2×Dic6C22⋊D514yescomplemented
283C2×Dic6C22×D512yes—
284C3×C4⋊C4—52no—
285C3×C4⋊C4—101no—
286C3×C22⋊C4—104no—
287#214—108no—
288#213—108no—
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—64no—
297C23×C5—62no—
298C23×C5—122no—
299C23×C5—122no—
300C23×C5C2×#6712yes—
301C23×C5C2×#6711yescharacteristic
302C22×D5—22no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C5×Q8—34no—
307C5×Q8—64no—
308C5×Q8—62no—
309C5×D4—34no—
310C5×D4—616no—
311C5×D4—64no—
312C5×D4—62no—
313C2×C4×C5—22no—
314C2×C4×C5—24no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—616no—
318C2×C4×C5—64no—
319C2×C4×C5—62no—
320C2×C4×C5D3×D412yes—
321C2×C4×C5D3×D412yes—
322C2×C4×C5C2×#6712yes—
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—48no—
326C2×Dic5—22no—
327C2×Dic5—42no—
328D20—22no—
329D20—22no—
330D20—42no—
331#168—62no—
332#168—62no—
333C2×#41—34no—
334C2×#41—64no—
335C2×#41—64no—
336C2×#41—62no—
337C22×Q8—31no—
338C22×D4—31no—
339C22×D4—51no—
340C22×D4—61no—
341C22×D4—101no—
342C23×C4—61no—
343C23×C4D3×D511yescharacteristic
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—151no—
349C22×C8—151no—
350#121—54no—
351#121—102no—
352C2×C4⋊C4—51no—
353C2×C22⋊C4—101no—
354#103—154no—
355#102—154no—
356C22⋊C8—154no—
357C2×C3×C5—42no—
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—44no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—102no—
368C23×C3—202no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3C2×C22⋊D512yes—
372C23×C3C2×C22⋊D511yescharacteristic
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—42no—
376C22×D3—42no—
377C3×D4—102no—
378C3×D4—102no—
379C3×D4—208no—
380C3×D4—202no—
381C2×C3×C4—22no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—102no—
386C2×C3×C4—202no—
387C2×C3×C4C2×C22⋊D512yes—
388C2×C3×C4C2×C22⋊D511yescharacteristic
389C2×C3×C4C2×C22⋊D512yes—
390C2×C3×C4C2×C22⋊D512yes—
391C2×C3×C4C23×D511yescharacteristic
392#67—216no—
393C2×Dic3—24no—
394C2×Dic3—22no—
395D12—24no—
396D12—22no—
397D12C2×C22⋊D514yescomplemented
398C4×D3—216no—
399Dic6—24no—
400Dic6—22no—
401Dic6C2×C22⋊D514yescomplemented
402C3⋊C8—102no—
403C3⋊C8—102no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—44no—
408C22×C5—64no—
409C22×C5—122no—
410C22×C5—128no—
411C22×C5—122no—
412C22×C5#93212yes—
413C22×C5#93712yes—
414C22×C5#95012yes—
415C22×C5C22×#6711yescharacteristic
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—84no—
420C4×C5—22no—
421C4×C5—64no—
422C4×C5#93712yes—
423C4×C5C2×D3×D411yescharacteristic
424C4×C5C2×D3×D411yescharacteristic
425Dic5—42no—
426C24—61no—
427C24—101no—
428C24#120111yescharacteristic
429#41—68no—
430#41—68no—
431#41—616no—
432C2×Q8—34no—
433C2×Q8—32no—
434C2×Q8—61no—
435C2×Q8—62no—
436C2×D4—34no—
437C2×D4—32no—
438C2×D4—52no—
439C2×D4—68no—
440C2×D4—64no—
441C2×D4—61no—
442C2×D4—62no—
443C2×D4—104no—
444C2×D4—101no—
445C2×D4—102no—
446C2×D4—102no—
447C2×D4—204no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—68no—
451C22×C4—61no—
452C22×C4—64no—
453C22×C4—101no—
454C22×C4#120112yes—
455C22×C4#120111yescharacteristic
456C22×C4C2×D3×D512yes—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—152no—
461C2×C8—152no—
462C2×C8—302no—
463C2×C8—302no—
464C4⋊C4—52no—
465C4⋊C4—101no—
466C22⋊C4—104no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—44no—
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—24no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—48no—
484C3×C4—22no—
485C3×C4—202no—
486C3×C4#409912yes—
487C3×C4C22×C22⋊D511yescharacteristic
488C3×C4C22×C22⋊D511yescharacteristic
489Dic3—24no—
490C2×C5—42no—
491C2×C5—124no—
492C2×C5#503714yescomplemented
493C2×C5C2×#93211yescharacteristic
494C2×C5C2×#93711yescharacteristic
495C2×C5C2×#95011yescharacteristic
496D5—82no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—62no—
501C23—64no—
502C23—102no—
503C23—122no—
504C23—122no—
505C23—202no—
506C23—202no—
507C23—202no—
508C23C2×#120112yes—
509C23C2×#120111yescharacteristic
510Q8—34no—
511Q8—62no—
512Q8—64no—
513D4—34no—
514D4—616no—
515D4—62no—
516D4—64no—
517D4—102no—
518D4—102no—
519D4—208no—
520D4—202no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—616no—
526C2×C4—62no—
527C2×C4—64no—
528C2×C4—102no—
529C2×C4—202no—
530C2×C4C2×#120112yes—
531C2×C4C2×#120111yescharacteristic
532C2×C4D3×C22⋊D512yes—
533C2×C4D3×C22⋊D512yes—
534C2×C4C22×D3×D511yescharacteristic
535C8—302no—
536C8—302no—
537C2×C3—42no—
538C2×C3—402no—
539C2×C3#6552714yescomplemented
540C2×C3C2×#409511yescharacteristic
541C2×C3C2×#409611yescharacteristic
542C2×C3C2×#409911yescharacteristic
543D3—44no—
544C5C2×#503711yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—44no—
549C22—64no—
550C22—122no—
551C22—122no—
552C22—128no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—404no—
557C22#9129712yes—
558C22#9129812yes—
559C22#9156812yes—
560C22C22×#120111yescharacteristic
561C4—22no—
562C4—64no—
563C4—202no—
564C4#9156812yes—
565C4C2×D3×C22⋊D511yescharacteristic
566C4C2×D3×C22⋊D511yescharacteristic
567C3C2×#6552711yescharacteristic, complemented, Sylow
568C2—42no—
569C2—124no—
570C2—402no—
571C2#1174851714yesdirect product factor
572C2C2×#9129711yescharacteristic
573C2C2×#9129811yescharacteristic
574C2C2×#9156811yescharacteristic
subgroupG/H
centerC23C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×#235C2semidirect
2. C2×C3×#4076C2semidirect
3. C22×#6655C2semidirect
4. C22×#6652C2semidirect
5. C2×#91114C2semidirect
6. #11748517C2direct (N × H)
7. C2×#90972C2semidirect
8. C2×#90966C2semidirect
15. C2×C5×#235C22semidirect
24. C3×#4076C22semidirect
28. C2×#6655C22semidirect
30. C2×#6652C22semidirect
31. #91114C22semidirect
32. #90972C22semidirect
33. #90966C22semidirect
38. C2×#4076D3semidirect
60. C2×C5×D12D4semidirect
66. C2×C5×Dic6D4semidirect
84. C22×#235D5semidirect
108. #4076C2×D3semidirect
144. C5×D12C2×D4semidirect
148. C5×Dic6C2×D4semidirect
164. C2×#235C2×D5semidirect
276. C2×D12C22⋊D5semidirect
282. C2×Dic6C22⋊D5semidirect
358. C2×C3×C5#449semidirect
397. D12C2×C22⋊D5semidirect
401. Dic6C2×C22⋊D5semidirect
467. C3×C5C2×#449semidirect
492. C2×C5#5037semidirect
539. C2×C3#65527semidirect
544. C5C2×#5037semidirect
567. C3C2×#65527semidirect
571. C2#11748517direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C2×C3×#40762
C22×#66552
C22×#66522
C2×#911142
#117485172
C2×#909722
C2×#909662
C2×#655273
C2×#50375