Finite Group Databasebeta

← C2×#11747510 #14423463

Subgroups — C2×#11747510 #14423463

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×#6772C211yesmaximal, characteristic, complemented
2C2×C3×#4041C211yesmaximal, characteristic, complemented
3C22×#6657C211yesmaximal, characteristic, complemented
4C22×#6652C211yesmaximal, characteristic, complemented
5C2×#91094C211yesmaximal, characteristic, complemented
6C2×C5×#809C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747510C218yesmaximal, direct product factor
9C2×#65070—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C5×D12C2211yescharacteristic
12C22×C3×D20—21no—
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1201—21no—
16C22×D3×Dic5—21no—
17C2×#6772—24no—
18C2×#6772—24no—
19C2×#6772—22no—
20C2×#6772C2214yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C3×#685—21no—
25C3×#4041—22no—
26C3×#4041C2214yescomplemented
27C2×#6657—24no—
28C2×#6657C2214yescomplemented
29C2×#6652—24no—
30C2×#6652C2214yescomplemented
31#91094C2214yescomplemented
32C5×#809C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5037—51nomaximal, Hall
35C22×#711—31no—
36C22×#686—31no—
37C22×#677—31no—
38C2×#4041D311yescharacteristic, complemented
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65070—38no—
43C23×C5×D3—21no—
44C23×C3×D5—21no—
45C23×C3×D5D411yescharacteristic
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5C2311yescharacteristic
48C22×Dic15—21no—
49C2×Dic30—21no—
50C2×Dic30—22no—
51C2×Dic30D414yescomplemented
52C2×Dic30C2312yes—
53C2×C5×D12—21no—
54C2×C5×D12—22no—
55C2×C5×D12D414yescomplemented
56C2×C5×D12C2312yes—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×D20—22no—
59C2×C3×D20—22no—
60C2×C3×D20—24no—
61C2×C3×D20—21no—
62C2×C3×D20—44no—
63C2×C3×D20C2312yes—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5C2312yes—
68C2×#1201—28no—
69C2×#1201—24no—
70C2×D3×Dic5—28no—
71C2×D3×Dic5—24no—
72#6772—216no—
73#6772—28no—
74#6772—28no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77C2×C3⋊#168—22no—
78C2×C3⋊#168C2312yes—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—24no—
82#6657—28no—
83#6652—28no—
84C22×#235—51no—
85C2×C3×#121—51no—
86C22×#214—51no—
87C22×#213—51no—
88C2×#830—51no—
89#5037—58no—
90C2×#810—51no—
91C2×#809D511yescharacteristic, complemented
92C22×C5×D4—31no—
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—64no—
97C2×#711—64no—
98C2×#711—62no—
99C22×D20—21no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5C2×D311yescharacteristic
102C22×Dic10—31no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#686—34no—
106C2×#686—64no—
107C2×#685—21no—
108C22×#168—31no—
109C2×#677—34no—
110C2×#677—64no—
111#4041—22no—
112#4041C2×D314yescomplemented
113C5×#102—34no—
114#3952—34no—
115#3942—34no—
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C5×D3—24no—
119C22×C5×D3—22no—
120C22×C5×D3—42no—
121C22×C5×D3—42no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—42no—
127C22×C3×D5—42no—
128C22×C3×D5—42no—
129C22×C3×D5C2×D412yes—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—24no—
137C2×Dic15—22no—
138Dic30—24no—
139Dic30—22no—
140Dic30C2×D414yescomplemented
141C5×D12—24no—
142C5×D12—22no—
143C5×D12C2×D414yescomplemented
144C2×C3×Dic5—22no—
145C2×C3×Dic5C2×D412yes—
146C3×D20—22no—
147C3×D20—22no—
148C3×D20—48no—
149C3×D20—42no—
150C3×C4×D5—24no—
151C3×C4×D5—22no—
152C3×C4×D5—22no—
153#1201—216no—
154D3×Dic5—216no—
155C3⋊#168—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×C3×D4—101no—
159C23×C3×C4—51no—
160C22×#67—101no—
161C2×#235—54no—
162C2×#235—104no—
163C2×#235—102no—
164C2×#235—104no—
165C22×D12C2×D511yescharacteristic
166C22×C4×D3—101no—
167C22×Dic6—51no—
168C3×#121—54no—
169C3×#121—102no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C22⋊C4—101no—
172C2×#214—54no—
173C2×#214—104no—
174C2×#213—54no—
175C2×#213—104no—
176C22×C3⋊C8—51no—
177C22×C3⋊C8C2×D511yescharacteristic
178#830—54no—
179#810—54no—
180#809C2×D514yescomplemented
181C24×C5—61no—
182C23×D5—21no—
183C23×D5#6711yescharacteristic
184C2×C5×D4—34no—
185C2×C5×D4—32no—
186C2×C5×D4—62no—
187C2×C5×D4—61no—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—68no—
191C2×C22⋊D5—64no—
192C22×Dic5—68no—
193C22×Dic5—61no—
194C22×Dic5—64no—
195C22×Dic5#6711yescharacteristic
196#711—68no—
197#711—68no—
198#711—616no—
199C2×D20—22no—
200C2×D20—22no—
201C2×D20—24no—
202C2×D20—21no—
203C2×D20—44no—
204C2×D20C22×D312yes—
205C2×C4×D5—22no—
206C2×C4×D5—22no—
207C2×C4×D5#6712yes—
208C2×C4×D5C22×D312yes—
209C2×Dic10—34no—
210C2×Dic10—32no—
211C2×Dic10—62no—
212C2×Dic10—61no—
213C2×C5×C8—32no—
214C2×C5×C8—62no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217#686—68no—
218#685—24no—
219C2×#168—32no—
220C2×#168—62no—
221#677—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—51no—
226#449—158no—
227C2×#103—151no—
228C2×#102—31no—
229C2×C22⋊C8—151no—
230C22×C3×C5#12012yes—
231C22×C3×C5#13512yes—
232C22×C3×C5AGL(1,ℤ/8)12yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×C5×D3—24no—
235C2×C5×D3—42no—
236C2×C5×D3—42no—
237C2×C5×D3—48no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—22no—
241C2×C3×D5—44no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—84no—
246C3×C4×C5—42no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—24no—
251C3×Dic5—22no—
252C24×C3—51no—
253C24×C3—101no—
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—21no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—104no—
269C2×#67—108no—
270C22×Dic3—101no—
271#235—108no—
272#235—1016no—
273#235—108no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12D2014yescomplemented
277C2×D12C22×D512yes—
278C2×C4×D3—104no—
279C2×C4×D3—108no—
280C2×Dic6—54no—
281C2×Dic6—52no—
282C2×Dic6—102no—
283C2×Dic6—101no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C22×D512yes—
286C3×C22⋊C4—104no—
287#214—108no—
288#213—108no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—52no—
291C2×C3⋊C8—102no—
292C2×C3⋊C8C22×D512yes—
293C23×C5—64no—
294C23×C5—62no—
295C23×C5—122no—
296C23×C5—122no—
297C23×C5C2×#6711yescharacteristic
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—42no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5C2×#6712yes—
306C5×D4—34no—
307C5×D4—64no—
308C5×D4—62no—
309C2×C4×C5—22no—
310C2×C4×C5—42no—
311C2×C4×C5D3×D412yes—
312C2×C4×C5D3×D412yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—616no—
316C2×Dic5—22no—
317C2×Dic5—616no—
318C2×Dic5—64no—
319C2×Dic5—62no—
320C2×Dic5C2×#6712yes—
321D20—22no—
322D20—22no—
323D20—48no—
324D20—42no—
325C4×D5—24no—
326C4×D5—22no—
327C4×D5—22no—
328Dic10—34no—
329Dic10—64no—
330Dic10—62no—
331C5×C8—62no—
332#168—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—151no—
338C22×D4—31no—
339C22×D4—51no—
340C22×D4—101no—
341C22×D4—301no—
342C23×C4—51no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—151no—
350#121—54no—
351#121—102no—
352C2×C4⋊C4D3×D511yescharacteristic
353C2×C22⋊C4—101no—
354#103—154no—
355#102—34no—
356C22⋊C8—154no—
357C2×C3×C5#44914yescomplemented
358C2×C3×C5C2×#12011yescharacteristic
359C2×C3×C5C2×#13511yescharacteristic
360C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
361C3×D5—42no—
362C3×D5—82no—
363C5×D3—44no—
364C23×C3—52no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3—202no—
372C23×C3D4×D511yescharacteristic
373C22×D3—22no—
374C22×D3—24no—
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—42no—
383C2×C3×C4—52no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—104no—
388C2×C3×C4C2×D2012yes—
389C2×C3×C4D4×D512yes—
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—1016no—
393C2×Dic3—102no—
394C2×Dic3—104no—
395D12—22no—
396D12—24no—
397D12C2×D2014yescomplemented
398C4×D3—1016no—
399Dic6—54no—
400Dic6—102no—
401Dic6—104no—
402C3⋊C8—22no—
403C3⋊C8—102no—
404C22×C5—64no—
405C22×C5—122no—
406C22×C5—128no—
407C22×C5—122no—
408C22×C5#93212yes—
409C22×C5#93712yes—
410C22×C5#95012yes—
411C22×C5C22×#6711yescharacteristic
412C2×D5—22no—
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—44no—
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—42no—
419C2×D5—84no—
420C4×C5—42no—
421C4×C5#93712yes—
422C4×C5C2×D3×D411yescharacteristic
423C4×C5C2×D3×D411yescharacteristic
424Dic5—22no—
425Dic5—64no—
426C24—51no—
427C24—61no—
428C24—101no—
429#41—308no—
430#41—308no—
431#41—3016no—
432C2×Q8—154no—
433C2×Q8—152no—
434C2×Q8—302no—
435C2×Q8—301no—
436C2×D4—34no—
437C2×D4—32no—
438C2×D4—52no—
439C2×D4—62no—
440C2×D4—61no—
441C2×D4—104no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—101no—
445C2×D4—204no—
446C2×D4—304no—
447C2×D4—308no—
448C22×C4—21no—
449C22×C4—51no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—304no—
455C22×C4—308no—
456C22×C4—301no—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—32no—
461C2×C8—62no—
462C2×C8—152no—
463C2×C8—302no—
464C4⋊C4—21no—
465C4⋊C4C2×D3×D512yes—
466C22⋊C4—104no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3—102no—
469C22×C3—102no—
470C22×C3—102no—
471C22×C3—204no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—404no—
476C22×C3#402812yes—
477C22×C3#405712yes—
478C22×C3#406212yes—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—24no—
481C2×D3—42no—
482C2×D3—48no—
483C2×D3—42no—
484C3×C4—42no—
485C3×C4—102no—
486C3×C4#402812yes—
487C3×C4C22×D2011yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—104no—
490C2×C5—124no—
491C2×C5#503714yescomplemented
492C2×C5C2×#93211yescharacteristic
493C2×C5C2×#93711yescharacteristic
494C2×C5C2×#95011yescharacteristic
495D5—42no—
496D5—82no—
497C23—52no—
498C23—64no—
499C23—62no—
500C23—102no—
501C23—102no—
502C23—102no—
503C23—102no—
504C23—122no—
505C23—122no—
506C23—202no—
507C23—202no—
508C23—202no—
509C23D5×#6711yescharacteristic
510Q8—154no—
511Q8—304no—
512Q8—302no—
513D4—34no—
514D4—64no—
515D4—62no—
516D4—102no—
517D4—102no—
518D4—208no—
519D4—202no—
520D4—3016no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—52no—
524C2×C4—102no—
525C2×C4—104no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—3016no—
529C2×C4—304no—
530C2×C4—302no—
531C2×C4D3×D2012yes—
532C2×C4#677712yes—
533C2×C4D5×#6711yescharacteristic
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—302no—
537C2×C3—202no—
538C2×C3—402no—
539C2×C3#6507014yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#405711yescharacteristic
542C2×C3C2×#406211yescharacteristic
543D3—44no—
544C5C2×#503711yescharacteristic, complemented, Sylow
545C22—64no—
546C22—102no—
547C22—102no—
548C22—102no—
549C22—122no—
550C22—128no—
551C22—122no—
552C22—204no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—404no—
557C22#9147412yes—
558C22#9148912yes—
559C22#9151412yes—
560C22C2×D5×#6711yescharacteristic
561C4—42no—
562C4—102no—
563C4—304no—
564C4#9147412yes—
565C4C2×D3×D2011yescharacteristic
566C4C2×#677711yescharacteristic
567C3C2×#6507011yescharacteristic, complemented, Sylow
568C2—124no—
569C2—202no—
570C2—402no—
571C2#1174751014yesdirect product factor
572C2C2×#9147411yescharacteristic
573C2C2×#9148911yescharacteristic
574C2C2×#9151411yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6772C2semidirect
2. C2×C3×#4041C2semidirect
3. C22×#6657C2semidirect
4. C22×#6652C2semidirect
5. C2×#91094C2semidirect
6. C2×C5×#809C2semidirect
7. C2×#90955C2semidirect
8. #11747510C2direct (N × H)
20. C2×#6772C22semidirect
26. C3×#4041C22semidirect
28. C2×#6657C22semidirect
30. C2×#6652C22semidirect
31. #91094C22semidirect
32. C5×#809C22semidirect
33. #90955C22semidirect
38. C2×#4041D3semidirect
51. C2×Dic30D4semidirect
55. C2×C5×D12D4semidirect
91. C2×#809D5semidirect
112. #4041C2×D3semidirect
140. Dic30C2×D4semidirect
143. C5×D12C2×D4semidirect
180. #809C2×D5semidirect
276. C2×D12D20semidirect
357. C2×C3×C5#449semidirect
397. D12C2×D20semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5037semidirect
539. C2×C3#65070semidirect
544. C5C2×#5037semidirect
567. C3C2×#65070semidirect
571. C2#11747510direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67722
C2×C3×#40412
C22×#66572
C22×#66522
C2×#910942
C2×C5×#8092
C2×#909552
#117475102
C2×#650703
C2×#50375