Finite Group Databasebeta

← C2×#11751340 #14423501

Subgroups — C2×#11751340 #14423501

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic
2C22×#6718C211yesmaximal, characteristic, complemented
3C22×#6716C211yesmaximal, characteristic, complemented
4C2×#91813C211yesmaximal, characteristic, complemented
5#11751340C218yesmaximal, direct product factor
6C2×#91119C211yesmaximal, characteristic, complemented
7C2×#91116C211yesmaximal, characteristic, complemented
8C2×#91114C211yesmaximal, characteristic, complemented
9C2×#65528—31nomaximal, Hall
10C2×C3×C5×#41—24no—
11C2×C3×C5×#41—24no—
12C2×C3×C5×#41—22no—
13C2×C3×C5×#41C2214yes—
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C3×C5×D4—21no—
16C22×C3×C5×D4C2211yescharacteristic
17C23×C3×C4×C5—21no—
18C23×C3×C4×C5C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C2×#6719—21no—
21C2×#6718—24no—
22C2×#6718C2214yescomplemented
23C2×#6716—24no—
24C2×#6716C2214yescomplemented
25C2×C4⋊Dic15C2211yescharacteristic
26#91813—22no—
27#91813C2214yescomplemented
28C2×#6712—21no—
29C22×C3⋊#168C2211yescharacteristic
30C22×C3⋊#168C2211yescharacteristic
31#91119C2214yescomplemented
32#91116C2214yescomplemented
33#91114C2214yescomplemented
34C2×#5239—51nomaximal, Hall
35C22×C5×#41D311yescharacteristic
36C22×#689—31no—
37C22×#687—31no—
38C2×#4070—31no—
39#65528—38no—
40C2×#3967—31no—
41C2×#3964—31no—
42C2×C22⋊#168—31no—
43C24×C3×C5—21no—
44C24×C3×C5D411yescharacteristic
45C3×C5×#41—216no—
46C3×C5×#41—28no—
47C3×C5×#41—28no—
48C2×C3×C5×Q8—22no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8D414yes—
51C2×C3×C5×Q8C2312yes—
52C2×C3×C5×D4—28no—
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4D414yes—
57C2×C3×C5×D4C2312yes—
58C22×C3×C4×C5—28no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5D411yescharacteristic
64C22×C3×C4×C5D412yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15—21no—
68C22×Dic15—21no—
69C2×Dic30—22no—
70C2×Dic30—22no—
71C2×Dic30—21no—
72C2×Dic30C2312yes—
73#6719—24no—
74#6718—28no—
75#6716—28no—
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78#6712—24no—
79C2×C3⋊#168—22no—
80C2×C3⋊#168—22no—
81C2×C3⋊#168C2312yes—
82C2×C3⋊#168C2312yes—
83C22×C3×#41D511yescharacteristic
84C22×#216—51no—
85C22×#214—51no—
86C2×#924—51no—
87#5239—58no—
88C2×#835—51no—
89C2×#832—51no—
90C2×#830—51no—
91C2×C5×#41—24no—
92C2×C5×#41—24no—
93C2×C5×#41—22no—
94C2×C5×#41C2×D314yes—
95C22×C5×Q8C2×D311yescharacteristic
96C22×C5×D4—21no—
97C22×C5×D4C2×D311yescharacteristic
98C23×C4×C5—21no—
99C23×C4×C5C2×D311yescharacteristic
100C22×Dic10—31no—
101C2×C22⋊Dic5—61no—
102C2×#689—34no—
103C2×#689—64no—
104C2×#687—34no—
105C2×#687—64no—
106C2×C4⋊Dic5—31no—
107#4070—34no—
108#4070—62no—
109C2×#683—61no—
110C22×#168—31no—
111C22×#168—31no—
112#3967—34no—
113#3964—34no—
114C22⋊#168—34no—
115C2×#452—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—24no—
118C23×C3×C5—22no—
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—42no—
122C23×C3×C5—42no—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D411yescharacteristic
125C3×C5×Q8—24no—
126C3×C5×Q8—22no—
127C3×C5×Q8C2×D414yes—
128C3×C5×D4—216no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C3×C5×D4C2×D414yes—
132C2×C3×C4×C5—216no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—24no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—24no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—42no—
147C2×Dic15—42no—
148Dic30—22no—
149Dic30—22no—
150Dic30—42no—
151C3⋊#168—22no—
152C3⋊#168—22no—
153C2×C3×#41—24no—
154C2×C3×#41—24no—
155C2×C3×#41—22no—
156C2×C3×#41C2×D514yes—
157C22×C3×Q8C2×D511yescharacteristic
158C22×C3×D4—21no—
159C22×C3×D4C2×D511yescharacteristic
160C23×C3×C4—21no—
161C23×C3×C4C2×D511yescharacteristic
162C22×Dic6—51no—
163C2×#217—101no—
164C2×#216—54no—
165C2×#216—104no—
166C2×#214—54no—
167C2×#214—104no—
168C2×C4⋊Dic3—51no—
169#924—54no—
170#924—102no—
171C2×Dic3⋊C4—101no—
172C22×C3⋊C8—51no—
173C22×C3⋊C8—51no—
174#835—54no—
175#832—54no—
176#830—54no—
177C24×C5—21no—
178C24×C5#6711yescharacteristic
179C5×#41—216no—
180C5×#41—28no—
181C5×#41—28no—
182C2×C5×Q8—22no—
183C2×C5×Q8—21no—
184C2×C5×Q8#6714yes—
185C2×C5×Q8C22×D312yes—
186C2×C5×D4—28no—
187C2×C5×D4—24no—
188C2×C5×D4—21no—
189C2×C5×D4—22no—
190C2×C5×D4#6714yes—
191C2×C5×D4C22×D312yes—
192C22×C4×C5—28no—
193C22×C4×C5—21no—
194C22×C4×C5—24no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5#6711yescharacteristic
198C22×C4×C5#6712yes—
199C22×C4×C5C22×D312yes—
200C22×C4×C5C22×D311yescharacteristic
201C22×Dic5—61no—
202C22×Dic5—61no—
203C2×Dic10—32no—
204C2×Dic10—62no—
205C2×Dic10—62no—
206C2×Dic10—61no—
207C22⋊Dic5—64no—
208#689—68no—
209#687—68no—
210C4⋊Dic5—32no—
211C4⋊Dic5—61no—
212#683—64no—
213C2×#168—32no—
214C2×#168—32no—
215C2×#168—62no—
216C2×#168—62no—
217C22×#41D1511yescharacteristic
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5—22no—
226C22×C3×C5—24no—
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5—44no—
232C22×C3×C5—48no—
233C22×C3×C5#12012yes—
234C22×C3×C5#13512yes—
235C22×C3×C5#13712yes—
236C22×C3×C5C22×D411yescharacteristic
237C3×C4×C5—22no—
238C3×C4×C5—24no—
239C3×C4×C5#12012yes—
240C3×C4×C5C22×D411yescharacteristic
241C3×C4×C5C22×D411yescharacteristic
242Dic15—42no—
243Dic15—42no—
244C24×C3—21no—
245C24×C3C22⋊D511yescharacteristic
246C3×#41—216no—
247C3×#41—28no—
248C3×#41—28no—
249C2×C3×Q8—22no—
250C2×C3×Q8—21no—
251C2×C3×Q8C22⋊D514yes—
252C2×C3×Q8C22×D512yes—
253C2×C3×D4—28no—
254C2×C3×D4—24no—
255C2×C3×D4—21no—
256C2×C3×D4—22no—
257C2×C3×D4C22⋊D514yes—
258C2×C3×D4C22×D512yes—
259C22×C3×C4—28no—
260C22×C3×C4—21no—
261C22×C3×C4—24no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4C22⋊D511yescharacteristic
265C22×C3×C4C22⋊D512yes—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—101no—
269C22×Dic3—101no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—102no—
273C2×Dic6—101no—
274#217—104no—
275#216—108no—
276#214—108no—
277C4⋊Dic3—52no—
278C4⋊Dic3—101no—
279Dic3⋊C4—104no—
280C2×C3⋊C8—52no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—102no—
283C2×C3⋊C8—102no—
284C23×C5—22no—
285C23×C5—22no—
286C23×C5—22no—
287C23×C5—24no—
288C23×C5—22no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5C2×#6712yes—
292C23×C5C2×#6711yescharacteristic
293C5×Q8—24no—
294C5×Q8—22no—
295C5×Q8C2×#6714yes—
296C5×D4—216no—
297C5×D4—24no—
298C5×D4—22no—
299C5×D4C2×#6714yes—
300C2×C4×C5—216no—
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—22no—
304C2×C4×C5—24no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5C2×#6712yes—
308C2×C4×C5C2×#6711yescharacteristic
309C2×C4×C5C2×#6712yes—
310C2×C4×C5C2×#6712yes—
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—62no—
313C2×Dic5—62no—
314C2×Dic5—122no—
315C2×Dic5—122no—
316Dic10—62no—
317Dic10—62no—
318Dic10—122no—
319#168—62no—
320#168—62no—
321C2×#41—24no—
322C2×#41—24no—
323C2×#41—22no—
324C2×#41C2×D1514yes—
325C22×Q8—151no—
326C22×Q8C2×D1511yescharacteristic
327C22×D4—21no—
328C22×D4C2×D1511yescharacteristic
329C23×C4—21no—
330C23×C4C2×D1511yescharacteristic
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—151no—
336C22×C8—151no—
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—151no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—154no—
343#102—154no—
344C22⋊C8—154no—
345C2×C3×C5—42no—
346C2×C3×C5—44no—
347C2×C3×C5#45214yescomplemented
348C2×C3×C5C2×#12011yescharacteristic
349C2×C3×C5C2×#13511yescharacteristic
350C2×C3×C5C2×#13711yescharacteristic
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3C2×C22⋊D512yes—
359C23×C3C2×C22⋊D511yescharacteristic
360C3×Q8—24no—
361C3×Q8—22no—
362C3×Q8C2×C22⋊D514yes—
363C3×D4—216no—
364C3×D4—24no—
365C3×D4—22no—
366C3×D4C2×C22⋊D514yes—
367C2×C3×C4—216no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4C2×C22⋊D512yes—
375C2×C3×C4C2×C22⋊D511yescharacteristic
376C2×C3×C4C2×C22⋊D512yes—
377C2×C3×C4C2×C22⋊D512yes—
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—202no—
382C2×Dic3—202no—
383Dic6—102no—
384Dic6—102no—
385Dic6—202no—
386C3⋊C8—102no—
387C3⋊C8—102no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—24no—
392C22×C5—44no—
393C22×C5—48no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5#95012yes—
397C22×C5#95112yes—
398C22×C5#95312yes—
399C22×C5C22×#6711yescharacteristic
400C4×C5—22no—
401C4×C5—24no—
402C4×C5#95312yes—
403C4×C5C22×#6711yescharacteristic
404C4×C5C22×#6711yescharacteristic
405Dic5—122no—
406Dic5—122no—
407C24—21no—
408C24#122011yescharacteristic
409#41—216no—
410#41—28no—
411#41—28no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—152no—
415C2×Q8—301no—
416C2×Q8—302no—
417C2×Q8—302no—
418C2×Q8#122014yes—
419C2×Q8C22×D1512yes—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4#122014yes—
425C2×D4C22×D1512yes—
426C22×C4—28no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—301no—
432C22×C4—301no—
433C22×C4#122012yes—
434C22×C4#122011yescharacteristic
435C22×C4C22×D1512yes—
436C22×C4C22×D1511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—152no—
440C2×C8—152no—
441C2×C8—302no—
442C2×C8—302no—
443C4⋊C4—152no—
444C4⋊C4—301no—
445C4⋊C4—304no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—24no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—44no—
455C22×C3—48no—
456C22×C3#409612yes—
457C22×C3#409712yes—
458C22×C3#409912yes—
459C22×C3C22×C22⋊D511yescharacteristic
460C3×C4—22no—
461C3×C4—24no—
462C3×C4#409912yes—
463C3×C4C22×C22⋊D511yescharacteristic
464C3×C4C22×C22⋊D511yescharacteristic
465Dic3—202no—
466Dic3—202no—
467C2×C5—42no—
468C2×C5—44no—
469C2×C5#523914yescomplemented
470C2×C5C2×#95011yescharacteristic
471C2×C5C2×#95111yescharacteristic
472C2×C5C2×#95311yescharacteristic
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23C2×#122012yes—
481C23C2×#122011yescharacteristic
482Q8—24no—
483Q8—22no—
484Q8—302no—
485Q8—302no—
486Q8—602no—
487Q8C2×#122014yes—
488D4—216no—
489D4—24no—
490D4—22no—
491D4C2×#122014yes—
492C2×C4—216no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—602no—
502C2×C4—602no—
503C2×C4C2×#122012yes—
504C2×C4C2×#122011yescharacteristic
505C2×C4C2×#122012yes—
506C2×C4C2×#122012yes—
507C2×C4C23×D1511yescharacteristic
508C8—302no—
509C8—302no—
510C2×C3—42no—
511C2×C3—44no—
512C2×C3#6552814yescomplemented
513C2×C3C2×#409611yescharacteristic
514C2×C3C2×#409711yescharacteristic
515C2×C3C2×#409911yescharacteristic
516C5C2×#523911yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—22no—
520C22—24no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—48no—
525C22#9183912yes—
526C22#9184012yes—
527C22#9184212yes—
528C22C22×#122011yescharacteristic
529C4—22no—
530C4—24no—
531C4—602no—
532C4—602no—
533C4#9184212yes—
534C4C22×#122011yescharacteristic
535C4C22×#122011yescharacteristic
536C3C2×#6552811yescharacteristic, complemented, Sylow
537C2—42no—
538C2—44no—
539C2#1175134014yesdirect product factor
540C2C2×#9183911yescharacteristic
541C2C2×#9184011yescharacteristic
542C2C2×#9184211yescharacteristic
subgroupG/H
centerC23C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC22×C3×C5×#41C2
socleC23×C3×C5C2×D4
hypercenterC22×#41D15
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C22×#6718C2semidirect
3. C22×#6716C2semidirect
4. C2×#91813C2semidirect
5. #11751340C2direct (N × H)
6. C2×#91119C2semidirect
7. C2×#91116C2semidirect
8. C2×#91114C2semidirect
22. C2×#6718C22semidirect
24. C2×#6716C22semidirect
27. #91813C22semidirect
31. #91119C22semidirect
32. #91116C22semidirect
33. #91114C22semidirect
347. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
469. C2×C5#5239semidirect
512. C2×C3#65528semidirect
516. C5C2×#5239semidirect
536. C3C2×#65528semidirect
539. C2#11751340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×#67182
C22×#67162
C2×#918132
#117513402
C2×#911192
C2×#911162
C2×#911142
C2×#655283
C2×#52395