Finite Group Databasebeta

← C2×#11748538 #14423540

Subgroups — C2×#11748538 #14423540

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×C5×#235C211yesmaximal, characteristic
2C2×C3×#4070C211yesmaximal, characteristic, complemented
3C22×#6661C211yesmaximal, characteristic, complemented
4C22×#6656C211yesmaximal, characteristic, complemented
5C2×#91114C211yesmaximal, characteristic, complemented
6#11748538C218yesmaximal, direct product factor
7C2×#90972C211yesmaximal, characteristic, complemented
8C2×#90966C211yesmaximal, characteristic, complemented
9C2×#65528—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C5×#67—21no—
12C2×C5×#235—22no—
13C2×C5×#235—24no—
14C2×C5×#235—24no—
15C2×C5×#235C2214yes—
16C22×C5×D12C2211yescharacteristic
17C22×C4×C5×D3—21no—
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C3×C22⋊Dic5—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C3×#4070—22no—
25C3×#4070C2214yescomplemented
26C2×C3×#683—21no—
27C2×#6661—24no—
28C2×#6661C2214yescomplemented
29C2×#6656—24no—
30C2×#6656C2214yescomplemented
31#91114C2214yescomplemented
32#90972C2214yescomplemented
33#90966C2214yescomplemented
34C2×#5047—51nomaximal, Hall
35C22×C5×#41—31no—
36C22×#689—31no—
37C22×#687—31no—
38C2×#4070D311yescharacteristic, complemented
39#65528—38no—
40C2×#3967—31no—
41C2×#3964—31no—
42C2×C22⋊#168—31no—
43C24×C3×C5D411yescharacteristic
44C23×C5×D3—21no—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5D412yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C5×#67—28no—
52C2×C5×#67—24no—
53C22×C5×Dic3—21no—
54C5×#235—216no—
55C5×#235—28no—
56C5×#235—28no—
57C2×C5×D12—21no—
58C2×C5×D12—22no—
59C2×C5×D12D414yes—
60C2×C5×D12C2312yes—
61C2×C4×C5×D3—28no—
62C2×C4×C5×D3—24no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6D414yes—
66C2×C5×Dic6C2312yes—
67C22×C3×Dic5—21no—
68C22×C3×Dic5—21no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10—22no—
71C2×C3×Dic10—21no—
72C2×C3×Dic10C2312yes—
73C2×C3⋊#168—22no—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C2×C3⋊#168C2312yes—
77C3×C22⋊Dic5—24no—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C3×#683—24no—
81#6661—28no—
82#6656—28no—
83C22×#235D511yescharacteristic
84C2×C3×C22⋊Q8—51no—
85C22×#216—51no—
86C22×#215—51no—
87C2×#830—51no—
88#5047—58no—
89C2×#810—51no—
90C2×#809—51no—
91C2×C5×#41—34no—
92C2×C5×#41—64no—
93C2×C5×#41—64no—
94C2×C5×#41—62no—
95C22×C5×Q8—31no—
96C22×C5×D4—31no—
97C22×C5×D4—61no—
98C23×C4×C5—61no—
99C23×C4×C5C2×D311yescharacteristic
100C22×Dic10C2×D311yescharacteristic
101C2×C22⋊Dic5—21no—
102C2×#689—34no—
103C2×#689—64no—
104C2×#687—34no—
105C2×#687—64no—
106C2×C4⋊Dic5C2×D311yescharacteristic
107#4070—22no—
108#4070C2×D314yescomplemented
109C2×#683—21no—
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—22no—
118C23×C3×C5—22no—
119C23×C3×C5C2×D412yes—
120C23×C3×C5C2×D411yescharacteristic
121C22×C5×D3—24no—
122C22×C5×D3—22no—
123C22×C5×D3—42no—
124C22×C5×D3—42no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—24no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D412yes—
133C2×C3×C4×C5C2411yescharacteristic
134C5×#67—216no—
135C2×C5×Dic3—24no—
136C2×C5×Dic3—22no—
137C5×D12—24no—
138C5×D12—22no—
139C5×D12C2×D414yes—
140C4×C5×D3—216no—
141C5×Dic6—24no—
142C5×Dic6—22no—
143C5×Dic6C2×D414yes—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—42no—
147C2×C3×Dic5—42no—
148C3×Dic10—22no—
149C3×Dic10—22no—
150C3×Dic10—42no—
151C3⋊#168—22no—
152C3⋊#168—22no—
153C22×C3×Q8—51no—
154C23×C3×C4C2×D511yescharacteristic
155C22×#67—21no—
156C2×#235—22no—
157C2×#235—24no—
158C2×#235—24no—
159C2×#235C2×D514yes—
160C22×D12C2×D511yescharacteristic
161C22×C4×D3—21no—
162C22×Dic6C2×D511yescharacteristic
163C3×C22⋊Q8—54no—
164C3×C22⋊Q8—102no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4—101no—
167C2×C3×C22⋊C4—101no—
168C2×#216—54no—
169C2×#216—104no—
170C2×#215—54no—
171C2×#215—104no—
172C22×C3⋊C8—51no—
173C22×C3⋊C8—51no—
174#830—54no—
175#810—54no—
176#809—54no—
177C24×C5—61no—
178C24×C5#6711yescharacteristic
179C5×#41—68no—
180C5×#41—68no—
181C5×#41—616no—
182C2×C5×Q8—34no—
183C2×C5×Q8—32no—
184C2×C5×Q8—62no—
185C2×C5×Q8—61no—
186C2×C5×D4—34no—
187C2×C5×D4—32no—
188C2×C5×D4—68no—
189C2×C5×D4—64no—
190C2×C5×D4—62no—
191C2×C5×D4—61no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—68no—
195C22×C4×C5—61no—
196C22×C4×C5—64no—
197C22×C4×C5#6711yescharacteristic
198C22×C4×C5#6712yes—
199C22×C4×C5C22×D312yes—
200C22×C4×C5C22×D311yescharacteristic
201C22×Dic5—21no—
202C22×Dic5—21no—
203C2×Dic10—22no—
204C2×Dic10—22no—
205C2×Dic10—21no—
206C2×Dic10C22×D312yes—
207C22⋊Dic5—24no—
208#689—68no—
209#687—68no—
210C4⋊Dic5—21no—
211C4⋊Dic5C22×D312yes—
212#683—24no—
213C2×#168—32no—
214C2×#168—32no—
215C2×#168—62no—
216C2×#168—62no—
217C22×#41—31no—
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—51no—
221#452—158no—
222C2×#103—151no—
223C2×#102—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—44no—
229C22×C3×C5#12012yes—
230C22×C3×C5#13512yes—
231C22×C3×C5#13712yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—24no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—48no—
237C3×C4×C5—22no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241C3×Dic5—42no—
242C3×Dic5—42no—
243C5×Dic3—24no—
244C24×C3C22⋊D511yescharacteristic
245C23×D3—21no—
246C2×C3×Q8—52no—
247C2×C3×Q8—101no—
248C2×C3×Q8—102no—
249C2×C3×Q8—102no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—101no—
253C22×C3×C4—101no—
254C22×C3×C4C22⋊D511yescharacteristic
255C22×C3×C4C22⋊D512yes—
256C22×C3×C4C22×D512yes—
257C22×C3×C4C22×D511yescharacteristic
258C2×#67—28no—
259C2×#67—24no—
260C22×Dic3—21no—
261#235—216no—
262#235—28no—
263#235—28no—
264C2×D12—21no—
265C2×D12—22no—
266C2×D12C22⋊D514yes—
267C2×D12C22×D512yes—
268C2×C4×D3—28no—
269C2×C4×D3—24no—
270C2×Dic6—21no—
271C2×Dic6—22no—
272C2×Dic6C22⋊D514yes—
273C2×Dic6C22×D512yes—
274C3×C4⋊C4—52no—
275C3×C4⋊C4—104no—
276C3×C4⋊C4—101no—
277C3×C22⋊C4—104no—
278#216—108no—
279#215—108no—
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—64no—
288C23×C5—62no—
289C23×C5—122no—
290C23×C5—122no—
291C23×C5C2×#6712yes—
292C23×C5C2×#6711yescharacteristic
293C5×Q8—34no—
294C5×Q8—64no—
295C5×Q8—62no—
296C5×D4—34no—
297C5×D4—616no—
298C5×D4—64no—
299C5×D4—62no—
300C2×C4×C5—22no—
301C2×C4×C5—24no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—616no—
305C2×C4×C5—64no—
306C2×C4×C5—62no—
307C2×C4×C5D3×D412yes—
308C2×C4×C5D3×D412yes—
309C2×C4×C5C2×#6712yes—
310C2×C4×C5C2×#6711yescharacteristic
311C2×C4×C5C23×D311yescharacteristic
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316Dic10—22no—
317Dic10—22no—
318Dic10—42no—
319#168—62no—
320#168—62no—
321C2×#41—34no—
322C2×#41—64no—
323C2×#41—64no—
324C2×#41—62no—
325C22×Q8—31no—
326C22×Q8—51no—
327C22×D4—31no—
328C22×D4—61no—
329C23×C4—61no—
330C23×C4D3×D511yescharacteristic
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—151no—
336C22×C8—151no—
337C22⋊Q8—54no—
338C22⋊Q8—102no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—101no—
341C2×C22⋊C4—101no—
342#103—154no—
343#102—154no—
344C22⋊C8—154no—
345C2×C3×C5—42no—
346C2×C3×C5#45214yescomplemented
347C2×C3×C5C2×#12011yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C5×D3—44no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3C2×C22⋊D512yes—
355C23×C3C2×C22⋊D511yescharacteristic
356C22×D3—24no—
357C22×D3—22no—
358C22×D3—42no—
359C22×D3—42no—
360C3×Q8—102no—
361C3×Q8—102no—
362C3×Q8—202no—
363C2×C3×C4—22no—
364C2×C3×C4—24no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—202no—
370C2×C3×C4—202no—
371C2×C3×C4C2×C22⋊D512yes—
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×C3×C4C2×C22⋊D512yes—
374C2×C3×C4C2×C22⋊D512yes—
375C2×C3×C4C23×D511yescharacteristic
376#67—216no—
377C2×Dic3—24no—
378C2×Dic3—22no—
379D12—24no—
380D12—22no—
381D12C2×C22⋊D514yes—
382C4×D3—216no—
383Dic6—24no—
384Dic6—22no—
385Dic6C2×C22⋊D514yes—
386C3⋊C8—102no—
387C3⋊C8—102no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—44no—
392C22×C5—64no—
393C22×C5—122no—
394C22×C5—128no—
395C22×C5—122no—
396C22×C5#93712yes—
397C22×C5#94212yes—
398C22×C5#95012yes—
399C22×C5C22×#6711yescharacteristic
400C4×C5—22no—
401C4×C5—64no—
402C4×C5#93712yes—
403C4×C5C2×D3×D411yescharacteristic
404C4×C5C2×D3×D411yescharacteristic
405Dic5—42no—
406Dic5—42no—
407C24—61no—
408C24#120111yescharacteristic
409#41—68no—
410#41—68no—
411#41—616no—
412C2×Q8—34no—
413C2×Q8—32no—
414C2×Q8—52no—
415C2×Q8—61no—
416C2×Q8—62no—
417C2×Q8—101no—
418C2×Q8—102no—
419C2×Q8—102no—
420C2×D4—34no—
421C2×D4—32no—
422C2×D4—68no—
423C2×D4—64no—
424C2×D4—61no—
425C2×D4—62no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—68no—
429C22×C4—61no—
430C22×C4—64no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4#120112yes—
434C22×C4#120111yescharacteristic
435C22×C4C2×D3×D512yes—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—152no—
440C2×C8—152no—
441C2×C8—302no—
442C2×C8—302no—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—104no—
446C22⋊C4—104no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—44no—
452C22×C3#409612yes—
453C22×C3#409712yes—
454C22×C3#409912yes—
455C22×C3C22×C22⋊D511yescharacteristic
456C2×D3—24no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—48no—
460C3×C4—22no—
461C3×C4—202no—
462C3×C4—202no—
463C3×C4#409912yes—
464C3×C4C22×C22⋊D511yescharacteristic
465C3×C4C22×C22⋊D511yescharacteristic
466Dic3—24no—
467C2×C5—42no—
468C2×C5—124no—
469C2×C5#504714yescomplemented
470C2×C5C2×#93711yescharacteristic
471C2×C5C2×#94211yescharacteristic
472C2×C5C2×#95011yescharacteristic
473C23—22no—
474C23—22no—
475C23—22no—
476C23—62no—
477C23—64no—
478C23—122no—
479C23—122no—
480C23C2×#120112yes—
481C23C2×#120111yescharacteristic
482Q8—34no—
483Q8—62no—
484Q8—64no—
485Q8—102no—
486Q8—102no—
487Q8—202no—
488D4—34no—
489D4—616no—
490D4—62no—
491D4—64no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—616no—
497C2×C4—62no—
498C2×C4—64no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—202no—
502C2×C4—202no—
503C2×C4C2×#120112yes—
504C2×C4C2×#120111yescharacteristic
505C2×C4D3×C22⋊D512yes—
506C2×C4D3×C22⋊D512yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—302no—
509C8—302no—
510C2×C3—42no—
511C2×C3#6552814yescomplemented
512C2×C3C2×#409611yescharacteristic
513C2×C3C2×#409711yescharacteristic
514C2×C3C2×#409911yescharacteristic
515D3—44no—
516C5C2×#504711yescharacteristic, complemented, Sylow
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—64no—
522C22—122no—
523C22—122no—
524C22—128no—
525C22#9129712yes—
526C22#9130912yes—
527C22#9156812yes—
528C22C22×#120111yescharacteristic
529C4—22no—
530C4—64no—
531C4—202no—
532C4—202no—
533C4#9156812yes—
534C4C2×D3×C22⋊D511yescharacteristic
535C4C2×D3×C22⋊D511yescharacteristic
536C3C2×#6552811yescharacteristic, complemented, Sylow
537C2—42no—
538C2—124no—
539C2#1174853814yesdirect product factor
540C2C2×#9129711yescharacteristic
541C2C2×#9130911yescharacteristic
542C2C2×#9156811yescharacteristic
subgroupG/H
centerC23C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×#235C2
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#452
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
2. C2×C3×#4070C2semidirect
3. C22×#6661C2semidirect
4. C22×#6656C2semidirect
5. C2×#91114C2semidirect
6. #11748538C2direct (N × H)
7. C2×#90972C2semidirect
8. C2×#90966C2semidirect
25. C3×#4070C22semidirect
28. C2×#6661C22semidirect
30. C2×#6656C22semidirect
31. #91114C22semidirect
32. #90972C22semidirect
33. #90966C22semidirect
38. C2×#4070D3semidirect
108. #4070C2×D3semidirect
346. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
469. C2×C5#5047semidirect
511. C2×C3#65528semidirect
516. C5C2×#5047semidirect
536. C3C2×#65528semidirect
539. C2#11748538direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C2×C3×#40702
C22×#66612
C22×#66562
C2×#911142
#117485382
C2×#909722
C2×#909662
C2×#655283
C2×#50475