Finite Group Databasebeta

← C2×#11750911 #14423423

Subgroups — C2×#11750911 #14423423

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×#6821C211yesmaximal, characteristic, complemented
2C22×#6717C211yesmaximal, characteristic, complemented
3C22×D120C211yesmaximal, characteristic, complemented
4C2×#91784C211yesmaximal, characteristic, complemented
5C2×C3×C5×#103C211yesmaximal, characteristic, complemented
6C2×#91104C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic, complemented
8#11750911C218yesmaximal, direct product factor
9C2×#65100—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6821—24no—
12C2×#6821—24no—
13C2×#6821—22no—
14C2×#6821C2214yescomplemented
15C22×D60—21no—
16C22×D60—21no—
17C22×D60C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C4×D15—21no—
20C22×C4×D15C2211yescharacteristic
21C22×C3×C5×C8C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×#6717—24no—
24C2×#6717C2214yescomplemented
25C2×#6714—21no—
26C22×C3⋊#168C2211yescharacteristic
27C2×D120—24no—
28C2×D120C2214yescomplemented
29#91784—22no—
30#91784C2214yescomplemented
31C3×C5×#103C2214yescomplemented
32#91104C2214yescomplemented
33#91093C2214yescomplemented
34C2×#4810—51nomaximal, Hall
35C22×#713—31no—
36C22×#688—31no—
37C22×D40—31no—
38C2×#4041—31no—
39C2×C5×#103D311yescharacteristic, complemented
40C2×#3952—31no—
41C2×#3941—31no—
42#65100—38no—
43C23×D15—21no—
44C23×D15—21no—
45C23×D15D411yescharacteristic
46C2×C3×C5×Q8—22no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8D414yescomplemented
49C2×C3×C5×Q8C2312yes—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15D411yescharacteristic
54#6821—216no—
55#6821—28no—
56#6821—28no—
57C2×D60—28no—
58C2×D60—24no—
59C2×D60—21no—
60C2×D60—22no—
61C2×D60—22no—
62C2×D60—22no—
63C2×D60—24no—
64C2×D60—21no—
65C2×D60—44no—
66C2×D60D414yescomplemented
67C2×D60C2312yes—
68C2×D60C2312yes—
69C2×C4×D15—28no—
70C2×C4×D15—22no—
71C2×C4×D15—22no—
72C2×C4×D15—24no—
73C2×C4×D15D412yes—
74C2×C4×D15C2312yes—
75C2×C3×C5×C8—22no—
76C2×C3×C5×C8C2312yes—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6717—28no—
80#6714—24no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83D120—28no—
84C22×#239—51no—
85C22×#215—51no—
86C22×D24—51no—
87C2×#895—51no—
88C2×C3×#103D511yescharacteristic, complemented
89C2×(C2×D3)⋊C8—51no—
90C2×#809—51no—
91#4810—58no—
92C22×C5×Q8C2×D311yescharacteristic
93C2×#713—34no—
94C2×#713—62no—
95C2×#713—64no—
96C2×#713—64no—
97C22×D20—31no—
98C22×D20—31no—
99C22×D20—61no—
100C22×D20—61no—
101C22×C4×D5—31no—
102C22×C4×D5—61no—
103C22×C5×C8C2×D311yescharacteristic
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#688—34no—
106C2×#688—64no—
107C2×#685—61no—
108C22×#168—31no—
109C2×D40—34no—
110C2×D40—64no—
111#4041—34no—
112#4041—62no—
113C5×#103C2×D314yescomplemented
114#3952—34no—
115#3941—34no—
116C2×#449—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—22no—
119C22×D15—24no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—42no—
125C22×D15—42no—
126C22×D15—42no—
127C22×D15—42no—
128C22×D15—42no—
129C22×D15C2×D412yes—
130C3×C5×Q8—24no—
131C3×C5×Q8—22no—
132C3×C5×Q8C2×D414yescomplemented
133C2×C3×C4×C5—24no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—42no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—22no—
142C2×Dic15C2×D412yes—
143D60—216no—
144D60—24no—
145D60—22no—
146D60—22no—
147D60—22no—
148D60—48no—
149D60—42no—
150D60C2×D414yescomplemented
151C4×D15—216no—
152C4×D15—24no—
153C4×D15—22no—
154C4×D15—22no—
155C3×C5×C8—22no—
156C3⋊#168—22no—
157C22×C3×Q8C2×D511yescharacteristic
158C2×#239—54no—
159C2×#239—102no—
160C2×#239—104no—
161C2×#239—104no—
162C22×D12—51no—
163C22×D12—51no—
164C22×D12—101no—
165C22×D12—101no—
166C22×C4×D3—51no—
167C22×C4×D3—101no—
168C22×C3×C8C2×D511yescharacteristic
169C2×C3×C4⋊C4C2×D511yescharacteristic
170C2×#215—54no—
171C2×#215—104no—
172C2×(C2×D3)⋊C4—101no—
173C22×C3⋊C8—51no—
174C2×D24—54no—
175C2×D24—104no—
176#895—54no—
177#895—102no—
178C3×#103C2×D514yescomplemented
179(C2×D3)⋊C8—54no—
180#809—54no—
181C23×D5—31no—
182C23×D5—61no—
183C23×D5—61no—
184C2×C5×Q8—22no—
185C2×C5×Q8—21no—
186C2×C5×Q8D1214yescomplemented
187C2×C5×Q8C22×D312yes—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5C22×D311yescharacteristic
191C22×Dic5—31no—
192#713—68no—
193#713—616no—
194#713—68no—
195C2×D20—34no—
196C2×D20—32no—
197C2×D20—32no—
198C2×D20—64no—
199C2×D20—68no—
200C2×D20—62no—
201C2×D20—61no—
202C2×D20—62no—
203C2×D20—62no—
204C2×D20—64no—
205C2×D20—61no—
206C2×D20—124no—
207C2×C4×D5—32no—
208C2×C4×D5—32no—
209C2×C4×D5—64no—
210C2×C4×D5—68no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C5×C8—22no—
214C2×C5×C8C22×D312yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217#688—68no—
218#685—64no—
219C2×#168—32no—
220C2×#168—62no—
221D40—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103D1511yescharacteristic, complemented
228C2×#102—151no—
229C2×C22⋊C8—151no—
230C22×C3×C5#12012yes—
231C22×C3×C5#13512yes—
232C22×C3×C5AGL(1,ℤ/8)12yes—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—22no—
235C2×D15—24no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—44no—
241C2×D15—48no—
242C2×D15—42no—
243C2×D15—42no—
244C2×D15—42no—
245C2×D15—84no—
246C3×C4×C5—24no—
247C3×C4×C5—42no—
248C3×C4×C5#12012yes—
249C3×C4×C5C22×D411yescharacteristic
250C3×C4×C5C22×D411yescharacteristic
251Dic15—22no—
252C23×D3—51no—
253C23×D3—101no—
254C23×D3—101no—
255C2×C3×Q8—21no—
256C2×C3×Q8—22no—
257C2×C3×Q8D2014yescomplemented
258C2×C3×Q8C22×D512yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—51no—
263#239—108no—
264#239—1016no—
265#239—108no—
266C2×D12—54no—
267C2×D12—52no—
268C2×D12—52no—
269C2×D12—104no—
270C2×D12—108no—
271C2×D12—102no—
272C2×D12—101no—
273C2×D12—102no—
274C2×D12—102no—
275C2×D12—104no—
276C2×D12—101no—
277C2×D12—204no—
278C2×C4×D3—52no—
279C2×C4×D3—52no—
280C2×C4×D3—104no—
281C2×C4×D3—108no—
282C2×C4×D3—102no—
283C2×C4×D3—102no—
284C2×C3×C8—22no—
285C2×C3×C8C22×D512yes—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C22×D512yes—
288#215—108no—
289(C2×D3)⋊C4—104no—
290C2×C3⋊C8—52no—
291C2×C3⋊C8—102no—
292D24—108no—
293C23×C5D3×D411yescharacteristic
294C22×D5—32no—
295C22×D5—64no—
296C22×D5—62no—
297C22×D5—62no—
298C22×D5—62no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—122no—
302C22×D5—122no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5—122no—
306C5×Q8—24no—
307C5×Q8—22no—
308C5×Q8C2×D1214yescomplemented
309C2×C4×C5—24no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—42no—
313C2×C4×C5C2×D1212yes—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D412yes—
316C2×C4×C5C23×D311yescharacteristic
317C2×Dic5—32no—
318C2×Dic5—62no—
319D20—34no—
320D20—616no—
321D20—64no—
322D20—62no—
323D20—62no—
324D20—62no—
325D20—128no—
326D20—122no—
327C4×D5—616no—
328C4×D5—64no—
329C4×D5—62no—
330C4×D5—62no—
331C5×C8—22no—
332#168—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8C2×D1511yescharacteristic
338C22×D4—151no—
339C22×D4—151no—
340C22×D4—301no—
341C22×D4—301no—
342C23×C4—151no—
343C23×C4—301no—
344C2×SD16—154no—
345C2×SD16—304no—
346C2×D8—154no—
347C2×D8—304no—
348C22×C8—151no—
349C22×C8C2×D1511yescharacteristic
350#121—154no—
351#121—302no—
352C2×C4⋊C4C2×D1511yescharacteristic
353C2×C22⋊C4—301no—
354#103C2×D1514yescomplemented
355#102—154no—
356C22⋊C8—154no—
357C2×C3×C5#44914yescomplemented
358C2×C3×C5C2×#12011yescharacteristic
359C2×C3×C5C2×#13511yescharacteristic
360C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
361D15—42no—
362D15—44no—
363D15—82no—
364C23×C3D4×D511yescharacteristic
365C22×D3—52no—
366C22×D3—102no—
367C22×D3—104no—
368C22×D3—102no—
369C22×D3—102no—
370C22×D3—102no—
371C22×D3—102no—
372C22×D3—202no—
373C22×D3—202no—
374C22×D3—202no—
375C22×D3—202no—
376C22×D3—202no—
377C3×Q8—22no—
378C3×Q8—24no—
379C3×Q8C2×D2014yescomplemented
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—22no—
383C2×C3×C4—42no—
384C2×C3×C4C2×D2012yes—
385C2×C3×C4D4×D512yes—
386C2×C3×C4D4×D511yescharacteristic
387C2×C3×C4C23×D511yescharacteristic
388C2×Dic3—52no—
389C2×Dic3—102no—
390D12—54no—
391D12—1016no—
392D12—102no—
393D12—102no—
394D12—102no—
395D12—104no—
396D12—208no—
397D12—202no—
398C4×D3—1016no—
399C4×D3—102no—
400C4×D3—102no—
401C4×D3—104no—
402C3×C8—22no—
403C3⋊C8—102no—
404C22×C5#88212yes—
405C22×C5#91412yes—
406C22×C5#91912yes—
407C22×C5C2×D3×D411yescharacteristic
408C2×D5—64no—
409C2×D5—62no—
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—124no—
415C2×D5—128no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—244no—
420C4×C5—24no—
421C4×C5—42no—
422C4×C5#88212yes—
423C4×C5C22×D1211yescharacteristic
424C4×C5C2×D3×D411yescharacteristic
425Dic5—62no—
426C24—151no—
427C24—301no—
428C24—301no—
429#41—308no—
430#41—3016no—
431#41—308no—
432C2×Q8—22no—
433C2×Q8—21no—
434C2×Q8D6014yescomplemented
435C2×Q8C22×D1512yes—
436C2×D4—154no—
437C2×D4—152no—
438C2×D4—152no—
439C2×D4—304no—
440C2×D4—308no—
441C2×D4—304no—
442C2×D4—302no—
443C2×D4—302no—
444C2×D4—301no—
445C2×D4—302no—
446C2×D4—301no—
447C2×D4—604no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—151no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—304no—
454C22×C4—308no—
455C22×C4—302no—
456C22×C4—302no—
457C22×C4C22×D1511yescharacteristic
458SD16—308no—
459D8—308no—
460C2×C8—22no—
461C2×C8—152no—
462C2×C8—302no—
463C2×C8C22×D1512yes—
464C4⋊C4—21no—
465C4⋊C4C22×D1512yes—
466C22⋊C4—304no—
467C3×C5C2×#44911yescharacteristic, complemented, Hall
468C22×C3#402812yes—
469C22×C3#406012yes—
470C22×C3#406512yes—
471C22×C3C2×D4×D511yescharacteristic
472C2×D3—104no—
473C2×D3—102no—
474C2×D3—102no—
475C2×D3—102no—
476C2×D3—202no—
477C2×D3—202no—
478C2×D3—204no—
479C2×D3—208no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—404no—
484C3×C4—24no—
485C3×C4—42no—
486C3×C4#402812yes—
487C3×C4C22×D2011yescharacteristic
488C3×C4C2×D4×D511yescharacteristic
489Dic3—102no—
490C2×C5#481014yescomplemented
491C2×C5C2×#88211yescharacteristic
492C2×C5C2×#91411yescharacteristic
493C2×C5C2×#91911yescharacteristic
494D5—122no—
495D5—124no—
496D5—242no—
497C23—152no—
498C23—304no—
499C23—302no—
500C23—302no—
501C23—302no—
502C23—302no—
503C23—302no—
504C23—602no—
505C23—602no—
506C23—602no—
507C23—602no—
508C23—602no—
509C23D4×D1511yescharacteristic
510Q8—24no—
511Q8—22no—
512Q8C2×D6014yescomplemented
513D4—154no—
514D4—3016no—
515D4—304no—
516D4—302no—
517D4—302no—
518D4—302no—
519D4—608no—
520D4—602no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—42no—
525C2×C4—152no—
526C2×C4—3016no—
527C2×C4—302no—
528C2×C4—304no—
529C2×C4—302no—
530C2×C4—302no—
531C2×C4C2×D6012yes—
532C2×C4D4×D1511yescharacteristic
533C2×C4D4×D1512yes—
534C2×C4C23×D1511yescharacteristic
535C8—22no—
536C8—302no—
537C2×C3#6510014yescomplemented
538C2×C3C2×#402811yescharacteristic
539C2×C3C2×#406011yescharacteristic
540C2×C3C2×#406511yescharacteristic
541D3—202no—
542D3—204no—
543D3—402no—
544C5C2×#481011yescharacteristic, complemented, Sylow
545C22—304no—
546C22—302no—
547C22—302no—
548C22—302no—
549C22—602no—
550C22—602no—
551C22—604no—
552C22—608no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—1204no—
557C22#9177112yes—
558C22#9180312yes—
559C22#9180812yes—
560C22C2×D4×D1511yescharacteristic
561C4—24no—
562C4—42no—
563C4—302no—
564C4#9177112yes—
565C4C22×D6011yescharacteristic
566C4C2×D4×D1511yescharacteristic
567C3C2×#6510011yescharacteristic, complemented, Sylow
568C2—602no—
569C2—604no—
570C2—1202no—
571C2#1175091114yesdirect product factor
572C2C2×#9177111yescharacteristic
573C2C2×#9180311yescharacteristic
574C2C2×#9180811yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#103C2
socleC23×C3×C5C2×D4
hypercenterC2×#103D15
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#6821C2semidirect
2. C22×#6717C2semidirect
3. C22×D120C2semidirect
4. C2×#91784C2semidirect
5. C2×C3×C5×#103C2semidirect
6. C2×#91104C2semidirect
7. C2×#91093C2semidirect
8. #11750911C2direct (N × H)
14. C2×#6821C22semidirect
24. C2×#6717C22semidirect
28. C2×D120C22semidirect
30. #91784C22semidirect
31. C3×C5×#103C22semidirect
32. #91104C22semidirect
33. #91093C22semidirect
39. C2×C5×#103D3semidirect
48. C2×C3×C5×Q8D4semidirect
66. C2×D60D4semidirect
88. C2×C3×#103D5semidirect
113. C5×#103C2×D3semidirect
132. C3×C5×Q8C2×D4semidirect
150. D60C2×D4semidirect
178. C3×#103C2×D5semidirect
186. C2×C5×Q8D12semidirect
227. C2×#103D15semidirect
257. C2×C3×Q8D20semidirect
308. C5×Q8C2×D12semidirect
354. #103C2×D15semidirect
357. C2×C3×C5#449semidirect
379. C3×Q8C2×D20semidirect
434. C2×Q8D60semidirect
467. C3×C5C2×#449semidirect
490. C2×C5#4810semidirect
512. Q8C2×D60semidirect
537. C2×C3#65100semidirect
544. C5C2×#4810semidirect
567. C3C2×#65100semidirect
571. C2#11750911direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68212
C22×#67172
C22×D1202
C2×#917842
C2×C3×C5×#1032
C2×#911042
C2×#910932
#117509112
C2×#651003
C2×#48105