Finite Group Databasebeta

← C2×#11750882 #14423417

Subgroups — C2×#11750882 #14423417

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×#6819C211yesmaximal, characteristic, complemented
2C22×#6715C211yesmaximal, characteristic, complemented
3C22×#6706C211yesmaximal, characteristic, complemented
4C2×#91784C211yesmaximal, characteristic, complemented
5C2×C3×C5×#102C211yesmaximal, characteristic, complemented
6C2×#91104C211yesmaximal, characteristic, complemented
7C2×#91094C211yesmaximal, characteristic, complemented
8#11750882C218yesmaximal, direct product factor
9C2×#65070—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×#1220—21no—
12C23×Dic15—21no—
13C2×#6819—24no—
14C2×#6819—22no—
15C2×#6819—24no—
16C2×#6819C2214yescomplemented
17C22×D60—21no—
18C22×D60C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×Dic30C2211yescharacteristic
21C22×C3×C5×C8C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×#6715—24no—
24C2×#6715C2214yescomplemented
25C2×#6714—21no—
26C22×C3⋊#168C2211yescharacteristic
27C2×#6706—24no—
28C2×#6706C2214yescomplemented
29#91784—22no—
30#91784C2214yescomplemented
31C3×C5×#102C2214yescomplemented
32#91104C2214yescomplemented
33#91094C2214yescomplemented
34C2×#4781—51nomaximal, Hall
35C22×#711—31no—
36C22×#686—31no—
37C22×#677—31no—
38C2×#4041—31no—
39C2×C5×#102D311yescharacteristic, complemented
40C2×#3952—31no—
41C2×#3942—31no—
42#65070—38no—
43C24×C3×C5—21no—
44C23×D15—21no—
45C23×D15D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D414yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2311yescharacteristic
52C2×#1220—28no—
53C2×#1220—24no—
54C22×Dic15—28no—
55C22×Dic15—21no—
56C22×Dic15—24no—
57C22×Dic15D411yescharacteristic
58#6819—216no—
59#6819—28no—
60#6819—28no—
61C2×D60—22no—
62C2×D60—22no—
63C2×D60—24no—
64C2×D60—21no—
65C2×D60—44no—
66C2×D60C2312yes—
67C2×C4×D15—22no—
68C2×C4×D15—22no—
69C2×C4×D15D412yes—
70C2×C4×D15C2312yes—
71C2×Dic30—21no—
72C2×Dic30—22no—
73C2×Dic30D414yescomplemented
74C2×Dic30C2312yes—
75C2×C3×C5×C8—22no—
76C2×C3×C5×C8C2312yes—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6715—28no—
80#6714—24no—
81C2×C3⋊#168—22no—
82C2×C3⋊#168C2312yes—
83#6706—28no—
84C22×#237—51no—
85C22×#213—51no—
86C22×#204—51no—
87C2×#895—51no—
88C2×C3×#102D511yescharacteristic, complemented
89C2×(C2×D3)⋊C8—51no—
90C2×#810—51no—
91#4781—58no—
92C22×C5×D4C2×D311yescharacteristic
93C22×C22⋊D5—61no—
94C23×Dic5—61no—
95C2×#711—34no—
96C2×#711—64no—
97C2×#711—62no—
98C2×#711—64no—
99C22×D20—31no—
100C22×D20—61no—
101C22×C4×D5—31no—
102C22×Dic10—31no—
103C22×C5×C8C2×D311yescharacteristic
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#686—34no—
106C2×#686—64no—
107C2×#685—61no—
108C22×#168—31no—
109C2×#677—34no—
110C2×#677—64no—
111#4041—34no—
112#4041—62no—
113C5×#102C2×D314yescomplemented
114#3952—34no—
115#3942—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×D15—22no—
123C22×D15—22no—
124C22×D15—22no—
125C22×D15—22no—
126C22×D15—42no—
127C22×D15—42no—
128C22×D15—42no—
129C22×D15C2×D412yes—
130C3×C5×D4—24no—
131C3×C5×D4—22no—
132C3×C5×D4C2×D414yescomplemented
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—42no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139#1220—216no—
140C2×Dic15—216no—
141C2×Dic15—24no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15C2×D412yes—
145D60—22no—
146D60—22no—
147D60—48no—
148D60—42no—
149C4×D15—24no—
150C4×D15—22no—
151C4×D15—22no—
152Dic30—24no—
153Dic30—22no—
154Dic30C2×D414yescomplemented
155C3×C5×C8—22no—
156C3⋊#168—22no—
157C22×C3×D4C2×D511yescharacteristic
158C22×#67—101no—
159C23×Dic3—101no—
160C2×#237—54no—
161C2×#237—104no—
162C2×#237—102no—
163C2×#237—104no—
164C22×D12—51no—
165C22×D12—101no—
166C22×C4×D3—51no—
167C22×Dic6—51no—
168C22×C3×C8C2×D511yescharacteristic
169C2×C3×C4⋊C4C2×D511yescharacteristic
170C2×#213—54no—
171C2×#213—104no—
172C2×(C2×D3)⋊C4—101no—
173C22×C3⋊C8—51no—
174C2×#204—54no—
175C2×#204—104no—
176#895—54no—
177#895—102no—
178C3×#102C2×D514yescomplemented
179(C2×D3)⋊C8—54no—
180#810—54no—
181C24×C5—21no—
182C23×D5—31no—
183C23×D5—61no—
184C2×C5×D4—21no—
185C2×C5×D4—22no—
186C2×C5×D4D1214yescomplemented
187C2×C5×D4C22×D312yes—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—64no—
191C2×C22⋊D5—68no—
192C22×Dic5—31no—
193C22×Dic5—64no—
194C22×Dic5—68no—
195C22×Dic5—61no—
196#711—68no—
197#711—616no—
198#711—68no—
199C2×D20—32no—
200C2×D20—62no—
201C2×D20—62no—
202C2×D20—64no—
203C2×D20—61no—
204C2×D20—124no—
205C2×C4×D5—32no—
206C2×C4×D5—32no—
207C2×C4×D5—62no—
208C2×C4×D5—62no—
209C2×Dic10—34no—
210C2×Dic10—32no—
211C2×Dic10—62no—
212C2×Dic10—61no—
213C2×C5×C8—22no—
214C2×C5×C8C22×D312yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217#686—68no—
218#685—64no—
219C2×#168—32no—
220C2×#168—62no—
221#677—68no—
222C22×#41—151no—
223C22×SD16—151no—
224C22×D8—151no—
225C2×#121—151no—
226#449—158no—
227C2×#103—151no—
228C2×#102D1511yescharacteristic, complemented
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×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C2×D15—44no—
242C2×D15—42no—
243C2×D15—42no—
244C2×D15—42no—
245C2×D15—84no—
246C3×C4×C5—42no—
247C3×C4×C5#12012yes—
248C3×C4×C5C22×D411yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15—24no—
251Dic15—22no—
252C24×C3—21no—
253C23×D3—51no—
254C23×D3—101no—
255C2×C3×D4—22no—
256C2×C3×D4—21no—
257C2×C3×D4D2014yescomplemented
258C2×C3×D4C22×D512yes—
259C22×C3×C4—21no—
260C22×C3×C4C22×D511yescharacteristic
261C2×#67—104no—
262C2×#67—108no—
263C22×Dic3—51no—
264C22×Dic3—104no—
265C22×Dic3—108no—
266C22×Dic3—101no—
267#237—108no—
268#237—1016no—
269#237—108no—
270C2×D12—52no—
271C2×D12—102no—
272C2×D12—102no—
273C2×D12—104no—
274C2×D12—101no—
275C2×D12—204no—
276C2×C4×D3—52no—
277C2×C4×D3—52no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×Dic6—54no—
281C2×Dic6—52no—
282C2×Dic6—102no—
283C2×Dic6—101no—
284C2×C3×C8—22no—
285C2×C3×C8C22×D512yes—
286C3×C4⋊C4—21no—
287C3×C4⋊C4C22×D512yes—
288#213—108no—
289(C2×D3)⋊C4—104no—
290C2×C3⋊C8—52no—
291C2×C3⋊C8—102no—
292#204—108no—
293C23×C5—24no—
294C23×C5—22no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5D3×D411yescharacteristic
298C22×D5—32no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—122no—
304C22×D5—122no—
305C22×D5—122no—
306C5×D4—24no—
307C5×D4—22no—
308C5×D4C2×D1214yescomplemented
309C2×C4×C5—22no—
310C2×C4×C5—42no—
311C2×C4×C5C2×D1212yes—
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D412yes—
314C2×C4×C5C23×D311yescharacteristic
315C22⋊D5—616no—
316C2×Dic5—32no—
317C2×Dic5—616no—
318C2×Dic5—64no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321D20—62no—
322D20—62no—
323D20—128no—
324D20—122no—
325C4×D5—64no—
326C4×D5—62no—
327C4×D5—62no—
328Dic10—34no—
329Dic10—64no—
330Dic10—62no—
331C5×C8—22no—
332#168—62no—
333C2×#41—154no—
334C2×#41—302no—
335C2×#41—304no—
336C2×#41—304no—
337C22×Q8—151no—
338C22×D4—151no—
339C22×D4—301no—
340C22×D4—301no—
341C22×D4C2×D1511yescharacteristic
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#103—154no—
355#102C2×D1514yescomplemented
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
362D15—42no—
363D15—82no—
364C23×C3—22no—
365C23×C3—24no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3D4×D511yescharacteristic
369C22×D3—52no—
370C22×D3—102no—
371C22×D3—102no—
372C22×D3—102no—
373C22×D3—102no—
374C22×D3—202no—
375C22×D3—202no—
376C22×D3—202no—
377C3×D4—22no—
378C3×D4—24no—
379C3×D4C2×D2014yescomplemented
380C2×C3×C4—22no—
381C2×C3×C4—42no—
382C2×C3×C4C2×D2012yes—
383C2×C3×C4D4×D512yes—
384C2×C3×C4D4×D511yescharacteristic
385C2×C3×C4C23×D511yescharacteristic
386#67—1016no—
387C2×Dic3—52no—
388C2×Dic3—1016no—
389C2×Dic3—102no—
390C2×Dic3—104no—
391C2×Dic3—102no—
392D12—102no—
393D12—102no—
394D12—208no—
395D12—202no—
396C4×D3—102no—
397C4×D3—102no—
398C4×D3—104no—
399Dic6—54no—
400Dic6—102no—
401Dic6—104no—
402C3×C8—22no—
403C3⋊C8—102no—
404C22×C5—24no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—48no—
408C22×C5#88212yes—
409C22×C5#91112yes—
410C22×C5#91612yes—
411C22×C5C2×D3×D411yescharacteristic
412C2×D5—62no—
413C2×D5—62no—
414C2×D5—62no—
415C2×D5—124no—
416C2×D5—122no—
417C2×D5—122no—
418C2×D5—122no—
419C2×D5—244no—
420C4×C5—42no—
421C4×C5#88212yes—
422C4×C5C22×D1211yescharacteristic
423C4×C5C2×D3×D411yescharacteristic
424Dic5—64no—
425Dic5—62no—
426C24—21no—
427C24—151no—
428C24—301no—
429#41—308no—
430#41—3016no—
431#41—308no—
432C2×Q8—154no—
433C2×Q8—152no—
434C2×Q8—302no—
435C2×Q8—301no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—152no—
439C2×D4—304no—
440C2×D4—304no—
441C2×D4—308no—
442C2×D4—302no—
443C2×D4—302no—
444C2×D4—301no—
445C2×D4—604no—
446C2×D4D6014yescomplemented
447C2×D4C22×D1512yes—
448C22×C4—21no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—152no—
452C22×C4—304no—
453C22×C4—308no—
454C22×C4—301no—
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—24no—
469C22×C3—42no—
470C22×C3—48no—
471C22×C3—42no—
472C22×C3#402812yes—
473C22×C3#405712yes—
474C22×C3#406212yes—
475C22×C3C2×D4×D511yescharacteristic
476C2×D3—102no—
477C2×D3—102no—
478C2×D3—102no—
479C2×D3—204no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3—404no—
484C3×C4—42no—
485C3×C4#402812yes—
486C3×C4C22×D2011yescharacteristic
487C3×C4C2×D4×D511yescharacteristic
488Dic3—104no—
489Dic3—102no—
490C2×C5—44no—
491C2×C5#478114yescomplemented
492C2×C5C2×#88211yescharacteristic
493C2×C5C2×#91111yescharacteristic
494C2×C5C2×#91611yescharacteristic
495D5—122no—
496D5—242no—
497C23—24no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—152no—
502C23—302no—
503C23—302no—
504C23—302no—
505C23—302no—
506C23—602no—
507C23—602no—
508C23—602no—
509C23D4×D1511yescharacteristic
510Q8—154no—
511Q8—304no—
512Q8—302no—
513D4—24no—
514D4—22no—
515D4—3016no—
516D4—302no—
517D4—302no—
518D4—608no—
519D4—602no—
520D4C2×D6014yescomplemented
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—152no—
524C2×C4—3016no—
525C2×C4—302no—
526C2×C4—304no—
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—44no—
538C2×C3#6507014yescomplemented
539C2×C3C2×#402811yescharacteristic
540C2×C3C2×#405711yescharacteristic
541C2×C3C2×#406211yescharacteristic
542D3—202no—
543D3—402no—
544C5C2×#478111yescharacteristic, complemented, Sylow
545C22—24no—
546C22—48no—
547C22—42no—
548C22—42no—
549C22—302no—
550C22—302no—
551C22—302no—
552C22—604no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—1204no—
557C22#9177112yes—
558C22#9180012yes—
559C22#9180512yes—
560C22C2×D4×D1511yescharacteristic
561C4—42no—
562C4—302no—
563C4—304no—
564C4#9177112yes—
565C4C22×D6011yescharacteristic
566C4C2×D4×D1511yescharacteristic
567C3C2×#6507011yescharacteristic, complemented, Sylow
568C2—44no—
569C2—602no—
570C2—1202no—
571C2#1175088214yesdirect product factor
572C2C2×#9177111yescharacteristic
573C2C2×#9180011yescharacteristic
574C2C2×#9180511yescharacteristic
subgroupG/H
centerC23D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
hypercenterC2×#102D15
hypocenterC3×C5C2×#449
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#6819C2semidirect
2. C22×#6715C2semidirect
3. C22×#6706C2semidirect
4. C2×#91784C2semidirect
5. C2×C3×C5×#102C2semidirect
6. C2×#91104C2semidirect
7. C2×#91094C2semidirect
8. #11750882C2direct (N × H)
16. C2×#6819C22semidirect
24. C2×#6715C22semidirect
28. C2×#6706C22semidirect
30. #91784C22semidirect
31. C3×C5×#102C22semidirect
32. #91104C22semidirect
33. #91094C22semidirect
39. C2×C5×#102D3semidirect
48. C2×C3×C5×D4D4semidirect
73. C2×Dic30D4semidirect
88. C2×C3×#102D5semidirect
113. C5×#102C2×D3semidirect
132. C3×C5×D4C2×D4semidirect
154. Dic30C2×D4semidirect
178. C3×#102C2×D5semidirect
186. C2×C5×D4D12semidirect
228. C2×#102D15semidirect
257. C2×C3×D4D20semidirect
308. C5×D4C2×D12semidirect
355. #102C2×D15semidirect
358. C2×C3×C5#449semidirect
379. C3×D4C2×D20semidirect
446. C2×D4D60semidirect
467. C3×C5C2×#449semidirect
491. C2×C5#4781semidirect
520. D4C2×D60semidirect
538. C2×C3#65070semidirect
544. C5C2×#4781semidirect
567. C3C2×#65070semidirect
571. C2#11750882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C22×#67152
C22×#67062
C2×#917842
C2×C3×C5×#1022
C2×#911042
C2×#910942
#117508822
C2×#650703
C2×#47815