Finite Group Databasebeta

← C2×#11748550 #14423455

Subgroups — C2×#11748550 #14423455

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×#6817C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic, complemented
3C22×#6657C211yesmaximal, characteristic, complemented
4C22×#6653C211yesmaximal, characteristic, complemented
5C2×C5×#830C211yesmaximal, characteristic, complemented
6#11748550C218yesmaximal, direct product factor
7C2×#90974C211yesmaximal, characteristic, complemented
8C2×#90968C211yesmaximal, characteristic, complemented
9C2×#65023—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×#1220—21no—
12C2×#6817—22no—
13C2×#6817—24no—
14C2×#6817—24no—
15C2×#6817C2214yescomplemented
16C22×D60C2211yescharacteristic
17C22×C4×D15—21no—
18C22×Dic30C2211yescharacteristic
19C22×C3×C22⋊D5—21no—
20C22×C3×D20C2211yescharacteristic
21C22×C5×C3⋊C8C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4076—22no—
24C3×#4076C2214yescomplemented
25C2×C3×#685—21no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×#6657—24no—
28C2×#6657C2214yescomplemented
29C2×#6653—24no—
30C2×#6653C2214yescomplemented
31C5×#830C2214yescomplemented
32#90974C2214yescomplemented
33#90968C2214yescomplemented
34C2×#5037—51nomaximal, Hall
35C22×#709—31no—
36C2×#4076D311yescharacteristic, complemented
37C22×D40—31no—
38C22×#677—31no—
39C2×C5×C22⋊C8—31no—
40C2×#3953—31no—
41C2×#3948—31no—
42#65023—38no—
43C24×C3×C5D411yescharacteristic
44C23×D15—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×#1220—28no—
53C2×#1220—24no—
54C22×Dic15—21no—
55#6817—216no—
56#6817—28no—
57#6817—28no—
58C2×D60—21no—
59C2×D60—22no—
60C2×D60D414yescomplemented
61C2×D60C2312yes—
62C2×C4×D15—28no—
63C2×C4×D15—24no—
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×Dic30D414yescomplemented
67C2×Dic30C2312yes—
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×C5×C3⋊C8—22no—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2312yes—
78C2×C5×C3⋊C8C2312yes—
79C3×#685—24no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82#6657—28no—
83#6653—28no—
84C22×#235—51no—
85C2×C3×#121—51no—
86C22×#214—51no—
87C22×#213—51no—
88C2×#830D511yescharacteristic, complemented
89#5037—58no—
90C2×#810—51no—
91C2×#809—51no—
92C23×C4×C5C2×D311yescharacteristic
93C22×C22⋊D5—21no—
94C22×C22⋊D5—61no—
95C2×#709—34no—
96C2×#709—64no—
97C2×#709—64no—
98C2×#709—62no—
99C22×D20—31no—
100C22×D20C2×D311yescharacteristic
101C22×C4×D5—61no—
102C22×Dic10—31no—
103C22×C5×C8—31no—
104C22×C5×C8—31no—
105#4076—22no—
106#4076C2×D314yescomplemented
107C2×#685—21no—
108C2×C4⋊Dic5C2×D311yescharacteristic
109C2×D40—34no—
110C2×D40—64no—
111C2×#677—34no—
112C2×#677—64no—
113C5×C22⋊C8—34no—
114#3953—34no—
115#3948—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×D15—24no—
123C22×D15—22no—
124C22×D15—42no—
125C22×D15—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
139#1220—216no—
140C2×Dic15—24no—
141C2×Dic15—22no—
142D60—24no—
143D60—22no—
144D60C2×D414yescomplemented
145C4×D15—216no—
146Dic30—24no—
147Dic30—22no—
148Dic30C2×D414yescomplemented
149C3×C22⋊D5—48no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—42no—
152C3×D20—22no—
153C3×D20—22no—
154C3×D20—42no—
155C5×C3⋊C8—22no—
156C5×C3⋊C8—22no—
157C22×C3×D4—51no—
158C22×C3×D4—101no—
159C23×C3×C4C2×D511yescharacteristic
160C22×#67—101no—
161C2×#235—54no—
162C2×#235—104no—
163C2×#235—104no—
164C2×#235—102no—
165C22×D12—51no—
166C22×C4×D3—101no—
167C22×Dic6—51no—
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⋊C8C2×D511yescharacteristic
177C22×C3⋊C8C2×D511yescharacteristic
178#830C2×D514yescomplemented
179#810—54no—
180#809—54no—
181C24×C5#6711yescharacteristic
182C23×D5—21no—
183C23×D5—61no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5#6711yescharacteristic
187C22×C4×C5#6712yes—
188C22×C4×C5C22×D312yes—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—24no—
191C2×C22⋊D5—44no—
192C2×C22⋊D5—68no—
193C2×C22⋊D5—64no—
194C22×Dic5—21no—
195C22×Dic5—61no—
196#709—68no—
197#709—68no—
198#709—616no—
199C2×D20—22no—
200C2×D20—22no—
201C2×D20—21no—
202C2×D20—34no—
203C2×D20—32no—
204C2×D20—62no—
205C2×D20—61no—
206C2×D20C22×D312yes—
207C2×C4×D5—68no—
208C2×C4×D5—64no—
209C2×Dic10—34no—
210C2×Dic10—32no—
211C2×Dic10—62no—
212C2×Dic10—61no—
213C2×C5×C8—32no—
214C2×C5×C8—32no—
215C2×C5×C8—62no—
216C2×C5×C8—62no—
217#685—24no—
218C4⋊Dic5—21no—
219C4⋊Dic5C22×D312yes—
220D40—68no—
221#677—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—51no—
226#449—158no—
227C2×#103—151no—
228C2×#102—151no—
229C2×C22⋊C8—31no—
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×D15—24no—
239C2×D15—42no—
240C2×D15—42no—
241C2×D15—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
250Dic15—24no—
251C3×Dic5—42no—
252C24×C3—101no—
253C24×C3D2011yescharacteristic
254C23×D3—101no—
255C2×C3×D4—52no—
256C2×C3×D4—104no—
257C2×C3×D4—101no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C2×C3×D4—204no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—101no—
264C22×C3×C4D2011yescharacteristic
265C22×C3×C4D2012yes—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—108no—
269C2×#67—104no—
270C22×Dic3—101no—
271#235—108no—
272#235—108no—
273#235—1016no—
274C2×D12—54no—
275C2×D12—52no—
276C2×D12—101no—
277C2×D12—102no—
278C2×C4×D3—108no—
279C2×C4×D3—104no—
280C2×Dic6—54no—
281C2×Dic6—52no—
282C2×Dic6—101no—
283C2×Dic6—102no—
284C3×C4⋊C4—52no—
285C3×C4⋊C4—101no—
286C3×C22⋊C4—104no—
287#214—108no—
288#213—108no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C22×D512yes—
292C2×C3⋊C8C22×D512yes—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5C2×#6712yes—
297C23×C5C2×#6711yescharacteristic
298C22×D5—22no—
299C22×D5—42no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—64no—
303C22×D5—62no—
304C22×D5—122no—
305C22×D5—122no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5D3×D412yes—
311C2×C4×C5D3×D412yes—
312C2×C4×C5C2×#6712yes—
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—48no—
316C22⋊D5—616no—
317C2×Dic5—22no—
318C2×Dic5—42no—
319C2×Dic5—64no—
320C2×Dic5—62no—
321D20—22no—
322D20—22no—
323D20—34no—
324D20—42no—
325D20—64no—
326D20—62no—
327C4×D5—616no—
328Dic10—34no—
329Dic10—64no—
330Dic10—62no—
331C5×C8—62no—
332C5×C8—62no—
333C2×#41—154no—
334C2×#41—304no—
335C2×#41—304no—
336C2×#41—302no—
337C22×Q8—151no—
338C22×D4—51no—
339C22×D4—101no—
340C22×D4—151no—
341C22×D4—301no—
342C23×C4—301no—
343C23×C4D3×D511yescharacteristic
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—31no—
349C22×C8—31no—
350#121—54no—
351#121—102no—
352C2×C4⋊C4—51no—
353C2×C22⋊C4—101no—
354#103—154no—
355#102—154no—
356C22⋊C8—34no—
357C2×C3×C5—42no—
358C2×C3×C5#44914yescomplemented
359C2×C3×C5C2×#12011yescharacteristic
360C2×C3×C5C2×#13511yescharacteristic
361C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
362D15—44no—
363C3×D5—82no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—22no—
367C23×C3—102no—
368C23×C3—202no—
369C23×C3—202no—
370C23×C3—202no—
371C23×C3C2×D2012yes—
372C23×C3C2×D2011yescharacteristic
373C22×D3—102no—
374C22×D3—104no—
375C22×D3—202no—
376C22×D3—202no—
377C3×D4—102no—
378C3×D4—102no—
379C3×D4—208no—
380C3×D4—202no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—102no—
386C2×C3×C4—202no—
387C2×C3×C4C2×D2012yes—
388C2×C3×C4C2×D2011yescharacteristic
389C2×C3×C4D4×D512yes—
390C2×C3×C4D4×D512yes—
391C2×C3×C4C23×D511yescharacteristic
392#67—1016no—
393C2×Dic3—102no—
394C2×Dic3—104no—
395D12—54no—
396D12—102no—
397D12—104no—
398C4×D3—1016no—
399Dic6—54no—
400Dic6—102no—
401Dic6—104no—
402C3⋊C8—22no—
403C3⋊C8—22no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—44no—
408C22×C5#93212yes—
409C22×C5#93712yes—
410C22×C5#95012yes—
411C22×C5C22×#6711yescharacteristic
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—64no—
416C2×D5—84no—
417C2×D5—122no—
418C2×D5—128no—
419C2×D5—122no—
420C4×C5—22no—
421C4×C5#93712yes—
422C4×C5C2×D3×D411yescharacteristic
423C4×C5C2×D3×D411yescharacteristic
424Dic5—42no—
425Dic5—64no—
426C24—101no—
427C24—301no—
428C24#120211yescharacteristic
429#41—308no—
430#41—308no—
431#41—3016no—
432C2×Q8—154no—
433C2×Q8—152no—
434C2×Q8—301no—
435C2×Q8—302no—
436C2×D4—52no—
437C2×D4—104no—
438C2×D4—101no—
439C2×D4—102no—
440C2×D4—102no—
441C2×D4—154no—
442C2×D4—152no—
443C2×D4—204no—
444C2×D4—308no—
445C2×D4—304no—
446C2×D4—301no—
447C2×D4—302no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—101no—
451C22×C4—308no—
452C22×C4—301no—
453C22×C4—304no—
454C22×C4#120212yes—
455C22×C4#120211yescharacteristic
456C22×C4C2×D3×D512yes—
457C22×C4C2×D3×D511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—32no—
461C2×C8—32no—
462C2×C8—62no—
463C2×C8—62no—
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#402812yes—
477C22×C3#405012yes—
478C22×C3#405412yes—
479C22×C3C22×D2011yescharacteristic
480C2×D3—104no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—208no—
484C3×C4—22no—
485C3×C4—202no—
486C3×C4#402812yes—
487C3×C4C2×D4×D511yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—104no—
490C2×C5—42no—
491C2×C5#503714yescomplemented
492C2×C5C2×#93211yescharacteristic
493C2×C5C2×#93711yescharacteristic
494C2×C5C2×#95011yescharacteristic
495D5—82no—
496D5—124no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—102no—
501C23—202no—
502C23—202no—
503C23—202no—
504C23—302no—
505C23—304no—
506C23—602no—
507C23—602no—
508C23C2×#120212yes—
509C23C2×#120211yescharacteristic
510Q8—154no—
511Q8—302no—
512Q8—304no—
513D4—102no—
514D4—102no—
515D4—154no—
516D4—208no—
517D4—202no—
518D4—3016no—
519D4—302no—
520D4—304no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—102no—
526C2×C4—202no—
527C2×C4—3016no—
528C2×C4—302no—
529C2×C4—304no—
530C2×C4C2×#120212yes—
531C2×C4C2×#120211yescharacteristic
532C2×C4#679012yes—
533C2×C4#679012yes—
534C2×C4C22×D3×D511yescharacteristic
535C8—62no—
536C8—62no—
537C2×C3—42no—
538C2×C3—402no—
539C2×C3#6502314yescomplemented
540C2×C3C2×#402811yescharacteristic
541C2×C3C2×#405011yescharacteristic
542C2×C3C2×#405411yescharacteristic
543D3—204no—
544C5C2×#503711yescharacteristic, complemented, Sylow
545C22—22no—
546C22—22no—
547C22—22no—
548C22—44no—
549C22—202no—
550C22—202no—
551C22—202no—
552C22—304no—
553C22—404no—
554C22—602no—
555C22—602no—
556C22—608no—
557C22#9131112yes—
558C22#9131212yes—
559C22#9157212yes—
560C22C22×#120211yescharacteristic
561C4—22no—
562C4—202no—
563C4—304no—
564C4#9157212yes—
565C4C2×#679011yescharacteristic
566C4C2×#679011yescharacteristic
567C3C2×#6502311yescharacteristic, complemented, Sylow
568C2—42no—
569C2—402no—
570C2—604no—
571C2#1174855014yesdirect product factor
572C2C2×#9131111yescharacteristic
573C2C2×#9131211yescharacteristic
574C2C2×#9157211yescharacteristic
subgroupG/H
centerC23C2×#1202
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×#6817C2semidirect
2. C2×C3×#4076C2semidirect
3. C22×#6657C2semidirect
4. C22×#6653C2semidirect
5. C2×C5×#830C2semidirect
6. #11748550C2direct (N × H)
7. C2×#90974C2semidirect
8. C2×#90968C2semidirect
15. C2×#6817C22semidirect
24. C3×#4076C22semidirect
28. C2×#6657C22semidirect
30. C2×#6653C22semidirect
31. C5×#830C22semidirect
32. #90974C22semidirect
33. #90968C22semidirect
36. C2×#4076D3semidirect
60. C2×D60D4semidirect
66. C2×Dic30D4semidirect
88. C2×#830D5semidirect
106. #4076C2×D3semidirect
144. D60C2×D4semidirect
148. Dic30C2×D4semidirect
178. #830C2×D5semidirect
358. C2×C3×C5#449semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#5037semidirect
539. C2×C3#65023semidirect
544. C5C2×#5037semidirect
567. C3C2×#65023semidirect
571. C2#11748550direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68172
C2×C3×#40762
C22×#66572
C22×#66532
C2×C5×#8302
#117485502
C2×#909742
C2×#909682
C2×#650233
C2×#50375