Finite Group Databasebeta

← C2×#11749459 #14425107

Subgroups — C2×#11749459 #14425107

Order 1920.

1456 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1010C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic, complemented
3C2×#91375C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C2×C3×#3969C211yesmaximal, characteristic, complemented
6#11749459C218yesmaximal, direct product factor
7C2×#90979C211yesmaximal, characteristic, complemented
8C2×#90962C211yesmaximal, characteristic, complemented
9C2×#65534—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C22×D60C2211yescharacteristic
12C5×#1010—22no—
13C5×#1010—22no—
14C5×#1010—22no—
15C5×#1010C2214yescomplemented
16C2×C5×D3×Q8—21no—
17C2×C5×#237—21no—
18C2×C5×#237—22no—
19C2×C5×#235—21no—
20C2×C5×#235C2211yescharacteristic
21C22×C5×Dic6—21no—
22C22×C5×Dic6C2211yescharacteristic
23#91838—22no—
24#91838C2214yescomplemented
25C2×#6717—21no—
26C2×#6715—21no—
27C2×#6710C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×#681C2211yescharacteristic
30C2×#6667—22no—
31#91375—22no—
32#91375C2214yescomplemented
33C2×#6660—21no—
34#91305—22no—
35#91305C2214yescomplemented
36C2×#6654—21no—
37C3×#3969C2214yescomplemented
38#90979C2214yescomplemented
39#90962C2214yescomplemented
40C2×#4827—51nomaximal, Hall
41C2×C5×2−1+4—31no—
42C2×#4095—31no—
43C2×#4095—31no—
44C2×#4093—31no—
45#65534—38no—
46C2×#3969—31no—
47C2×#3969D311yescharacteristic, complemented
48C2×#3968—31no—
49C23×D15—21no—
50C3×C5×#41—21no—
51C3×C5×#41—21no—
52C3×C5×#41D412yes—
53C3×C5×#41C2312yes—
54C2×C3×C5×Q8D411yescharacteristic
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4D411yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×D60—21no—
60C2×D60—21no—
61C2×D60—21no—
62C2×D60—21no—
63C2×D60—21no—
64C2×D60C2312yes—
65C2×C5×#67—22no—
66C2×C5×#67—21no—
67C22×C5×Dic3—22no—
68C22×C5×Dic3D412yes—
69C5×D3×Q8—24no—
70C5×D3×Q8—24no—
71C5×#237—28no—
72C5×#237—24no—
73C5×#237—24no—
74C5×#237—28no—
75C5×#235—24no—
76C5×#235—21no—
77C5×#235—21no—
78C5×#235—24no—
79C5×#235D412yes—
80C5×#235C2312yes—
81C2×C5×D12D411yescharacteristic
82C2×C4×C5×D3—22no—
83C2×C4×C5×D3—21no—
84C2×C5×Dic6—22no—
85C2×C5×Dic6—24no—
86C2×C5×Dic6—21no—
87C2×C5×Dic6—21no—
88C2×C5×Dic6—21no—
89C2×C5×Dic6—21no—
90C2×C5×Dic6—24no—
91C2×C5×Dic6D412yes—
92C2×C5×Dic6D411yescharacteristic
93C2×C5×Dic6C2312yes—
94C22×C3×Dic5—21no—
95#6717—24no—
96#6715—24no—
97#6710—21no—
98#6710C2312yes—
99C2×C3⋊#168—21no—
100C3×C4×Dic5—21no—
101C3×C4×Dic5C2312yes—
102C3×#681—21no—
103C3×#681C2312yes—
104C2×C3×#168—21no—
105#6667—28no—
106#6660—24no—
107#6654—24no—
108C2×#1010D511yescharacteristic, complemented
109C2×#949—51no—
110C2×#908—51no—
111C2×#875—51no—
112C2×C3×#104—51no—
113C2×#824—51no—
114C2×#805—51no—
115#4827—58no—
116C5×2−1+4—34no—
117C5×2−1+4—62no—
118C5×2−1+4—62no—
119C5×2−1+4—62no—
120C2×C5×#41—31no—
121C2×C5×#41—61no—
122C2×C5×#41—62no—
123C2×C5×#41—61no—
124C2×C5×#41C2×D311yescharacteristic
125C22×C5×Q8—31no—
126C22×C5×Q8—61no—
127C22×C5×Q8—61no—
128C22×D20—31no—
129#4095—34no—
130#4095—34no—
131#4095—62no—
132#4095—62no—
133#4093—34no—
134#4093—62no—
135C2×#688—61no—
136C2×#688—61no—
137C2×#686—61no—
138C2×#686—61no—
139C2×#685—62no—
140C2×C4×Dic5C2×D311yescharacteristic
141C2×#681—31no—
142C2×#681C2×D311yescharacteristic
143#3969—34no—
144#3969C2×D314yescomplemented
145#3968—34no—
146C2×#454—151noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—22no—
150C22×D15—44no—
151C22×D15—41no—
152C22×D15—41no—
153C22×C5×D3—21no—
154C3×C5×Q8—21no—
155C3×C5×Q8C2×D412yes—
156C3×C5×D4—22no—
157C3×C5×D4—22no—
158C3×C5×D4—21no—
159C3×C5×D4C2×D412yes—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D411yescharacteristic
165C2×C3×C4×C5C2×D411yescharacteristic
166C2×C3×C4×C5C2×D411yescharacteristic
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2411yescharacteristic
169D60—22no—
170D60—22no—
171D60—41no—
172D60—41no—
173C5×#67—28no—
174C5×#67—22no—
175C5×#67—22no—
176C2×C5×Dic3—28no—
177C2×C5×Dic3—22no—
178C2×C5×Dic3—21no—
179C2×C5×Dic3—22no—
180C2×C5×Dic3C2×D414yes—
181C5×D12—21no—
182C5×D12C2×D412yes—
183C4×C5×D3—28no—
184C4×C5×D3—22no—
185C4×C5×D3—22no—
186C5×Dic6—28no—
187C5×Dic6—22no—
188C5×Dic6—21no—
189C5×Dic6—22no—
190C5×Dic6—22no—
191C5×Dic6—22no—
192C5×Dic6C2×D412yes—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—42no—
195C3⋊#168—22no—
196C3×#168—22no—
197C2×C3×#41C2×D511yescharacteristic
198#1010—22no—
199#1010—22no—
200#1010—22no—
201#1010C2×D514yescomplemented
202C2×D3×Q8—21no—
203C2×#237—21no—
204C2×#237—22no—
205C2×#235—21no—
206C2×#235C2×D511yescharacteristic
207C22×D12—51no—
208C22×Dic6—21no—
209C22×Dic6C2×D511yescharacteristic
210C2×C3×M16—51no—
211C2×C3×C42—51no—
212#949—54no—
213#949—102no—
214C2×#215—101no—
215C2×#213—101no—
216C2×(C2×D3)⋊C4—102no—
217C2×#208—51no—
218#908—54no—
219#908—102no—
220C2×D24—101no—
221C2×#204—101no—
222#875—54no—
223#875—102no—
224C3×#104—54no—
225#824—54no—
226#805—54no—
227C23×D5—61no—
228C5×#41—21no—
229C5×#41—21no—
230C5×#41—32no—
231C5×#41—32no—
232C5×#41—64no—
233C5×#41—64no—
234C5×#41—68no—
235C5×#41—68no—
236C5×#41—64no—
237C5×#41—64no—
238C5×#41—61no—
239C5×#41—61no—
240C5×#41D1212yes—
241C5×#41C22×D312yes—
242C2×C5×Q8—32no—
243C2×C5×Q8—32no—
244C2×C5×Q8—31no—
245C2×C5×Q8—64no—
246C2×C5×Q8—62no—
247C2×C5×Q8—64no—
248C2×C5×Q8—64no—
249C2×C5×Q8—64no—
250C2×C5×Q8—61no—
251C2×C5×Q8—61no—
252C2×C5×Q8—61no—
253C2×C5×Q8—61no—
254C2×C5×Q8D1211yescharacteristic
255C2×C5×D4—21no—
256C2×C5×D4—31no—
257C2×C5×D4—62no—
258C2×C5×D4—61no—
259C2×C5×D4D1211yescharacteristic
260C22×C4×C5—21no—
261C22×C4×C5—32no—
262C22×C4×C5—62no—
263C22×C4×C5—62no—
264C22×C4×C5—61no—
265C22×C4×C5C22×D311yescharacteristic
266C22×Dic5—21no—
267C2×D20—32no—
268C2×D20—61no—
269C2×D20—61no—
270C2×D20—61no—
271C2×D20—61no—
272C2×D20—61no—
273#688—64no—
274#688—64no—
275#686—64no—
276#686—64no—
277#685—68no—
278C4×Dic5—21no—
279C4×Dic5C22×D312yes—
280#681—21no—
281#681—32no—
282#681—61no—
283#681C22×D312yes—
284C2×#168—21no—
285C2×#168—61no—
286C2×2−1+4—31no—
287C2×AGL(1,ℤ/8)—151no—
288C2×AGL(1,ℤ/8)—151no—
289C2×#124—151no—
290#454—158no—
291C2×#104—51no—
292C2×#104—151no—
293C2×#101—151no—
294C22×C3×C5—22no—
295C22×C3×C5—22no—
296C22×C3×C5—42no—
297C22×C3×C5#12011yescharacteristic
298C22×C3×C5#12011yescharacteristic
299C22×C3×C5C22×D411yescharacteristic
300C2×D15—44no—
301C2×D15—42no—
302C2×D15—82no—
303C2×D15—82no—
304C2×C5×D3—22no—
305C2×C5×D3—42no—
306C3×C4×C5—22no—
307C3×C4×C5#12011yescharacteristic
308C3×C4×C5#12011yescharacteristic
309C3×C4×C5C22×D411yescharacteristic
310C3×C4×C5C22×D411yescharacteristic
311C3×Dic5—42no—
312C5×Dic3—24no—
313C5×Dic3—22no—
314C23×D3—101no—
315C3×#41—21no—
316C3×#41—21no—
317C3×#41C22⋊D512yes—
318C3×#41C22×D512yes—
319C2×C3×Q8C22⋊D511yescharacteristic
320C2×C3×D4—21no—
321C2×C3×D4C22⋊D511yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—101no—
324C22×C3×C4C22×D511yescharacteristic
325C2×#67—22no—
326C2×#67—21no—
327C22×Dic3—22no—
328C22×Dic3C22⋊D512yes—
329D3×Q8—24no—
330D3×Q8—24no—
331#237—28no—
332#237—24no—
333#237—24no—
334#237—28no—
335#235—24no—
336#235—21no—
337#235—21no—
338#235—24no—
339#235C22⋊D512yes—
340#235C22×D512yes—
341C2×D12—52no—
342C2×D12—101no—
343C2×D12—101no—
344C2×D12—101no—
345C2×D12—101no—
346C2×D12—101no—
347C2×D12C22⋊D511yescharacteristic
348C2×C4×D3—22no—
349C2×C4×D3—21no—
350C2×Dic6—22no—
351C2×Dic6—24no—
352C2×Dic6—21no—
353C2×Dic6—21no—
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—24no—
357C2×Dic6C22⋊D512yes—
358C2×Dic6C22⋊D511yescharacteristic
359C2×Dic6C22×D512yes—
360C3×M16—52no—
361C3×M16—101no—
362C2×C3×C8—101no—
363C3×C42—52no—
364C3×C42—101no—
365#215—104no—
366#213—104no—
367(C2×D3)⋊C4—108no—
368#208—52no—
369#208—101no—
370C2×C3⋊C8—101no—
371D24—104no—
372#204—104no—
373C23×C5—21no—
374C23×C5—61no—
375C23×C5D3×D411yescharacteristic
376C22×D5—62no—
377C22×D5—124no—
378C22×D5—121no—
379C22×D5—121no—
380C5×Q8—21no—
381C5×Q8—32no—
382C5×Q8—68no—
383C5×Q8—62no—
384C5×Q8—62no—
385C5×Q8—61no—
386C5×Q8—62no—
387C5×Q8—62no—
388C5×Q8C2×D1212yes—
389C5×D4—22no—
390C5×D4—22no—
391C5×D4—21no—
392C5×D4—32no—
393C5×D4—68no—
394C5×D4—62no—
395C5×D4—62no—
396C5×D4—61no—
397C5×D4C2×D1212yes—
398C2×C4×C5—21no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—34no—
402C2×C4×C5—68no—
403C2×C4×C5—68no—
404C2×C4×C5—62no—
405C2×C4×C5—62no—
406C2×C4×C5—61no—
407C2×C4×C5—62no—
408C2×C4×C5—62no—
409C2×C4×C5C2×D1211yescharacteristic
410C2×C4×C5C2×D1211yescharacteristic
411C2×C4×C5D3×D411yescharacteristic
412C2×C4×C5D3×D411yescharacteristic
413C2×C4×C5D3×D411yescharacteristic
414C2×C4×C5C23×D311yescharacteristic
415C2×Dic5—22no—
416C2×Dic5—42no—
417D20—62no—
418D20—62no—
419D20—121no—
420D20—121no—
421#168—22no—
422#168—62no—
4232−1+4—34no—
4242−1+4—62no—
4252−1+4—62no—
4262−1+4—62no—
427C2×#41—31no—
428C2×#41—61no—
429C2×#41—62no—
430C2×#41—61no—
431C2×#41D3×D511yescharacteristic
432C22×Q8—31no—
433C22×Q8—61no—
434C22×Q8—61no—
435C22×D4—151no—
436AGL(1,ℤ/8)—154no—
437AGL(1,ℤ/8)—154no—
438AGL(1,ℤ/8)—302no—
439AGL(1,ℤ/8)—302no—
440C2×SD16—301no—
441C2×SD16—301no—
442C2×D8—301no—
443C2×D8—301no—
444C2×M16—51no—
445C2×M16—151no—
446#124—154no—
447#124—302no—
448C2×C22⋊C4—302no—
449C2×C42—51no—
450#104—54no—
451#104—154no—
452#101—154no—
453C2×C3×C5—21no—
454C2×C3×C5—21no—
455C2×C3×C5—42no—
456C2×C3×C5#45412yescomplemented
457C2×C3×C5C2×#12011yescharacteristic
458D15—82no—
459C5×D3—42no—
460C23×C3—21no—
461C23×C3C2×C22⋊D511yescharacteristic
462C22×D3—21no—
463C22×D3—102no—
464C22×D3—204no—
465C22×D3—201no—
466C22×D3—201no—
467C3×Q8—21no—
468C3×Q8C2×C22⋊D512yes—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—21no—
472C3×D4C2×C22⋊D512yes—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—102no—
477C2×C3×C4—202no—
478C2×C3×C4C2×C22⋊D511yescharacteristic
479C2×C3×C4C2×C22⋊D511yescharacteristic
480C2×C3×C4C2×C22⋊D511yescharacteristic
481C2×C3×C4C2×C22⋊D511yescharacteristic
482C2×C3×C4C2×C22⋊D511yescharacteristic
483C2×C3×C4C23×D511yescharacteristic
484#67—28no—
485#67—22no—
486#67—22no—
487C2×Dic3—28no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3C2×C22⋊D514yes—
492D12—21no—
493D12—102no—
494D12—102no—
495D12—201no—
496D12—201no—
497D12C2×C22⋊D512yes—
498C4×D3—28no—
499C4×D3—22no—
500C4×D3—22no—
501Dic6—28no—
502Dic6—22no—
503Dic6—21no—
504Dic6—22no—
505Dic6—22no—
506Dic6—22no—
507Dic6C2×C22⋊D512yes—
508C3×C8—102no—
509C3⋊C8—102no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—42no—
513C22×C5—62no—
514C22×C5—122no—
515C22×C5#88211yescharacteristic
516C22×C5#88211yescharacteristic
517C22×C5C2×D3×D411yescharacteristic
518C2×D5—124no—
519C2×D5—122no—
520C2×D5—242no—
521C2×D5—242no—
522C4×C5—22no—
523C4×C5—64no—
524C4×C5—62no—
525C4×C5#88211yescharacteristic
526C4×C5#88211yescharacteristic
527C4×C5C22×D1211yescharacteristic
528C4×C5C2×D3×D411yescharacteristic
529Dic5—42no—
530C24—301no—
531#41—21no—
532#41—21no—
533#41—32no—
534#41—32no—
535#41—64no—
536#41—64no—
537#41—68no—
538#41—68no—
539#41—64no—
540#41—64no—
541#41—61no—
542#41—61no—
543#41#120312yes—
544#41C2×D3×D512yes—
545C2×Q8—32no—
546C2×Q8—32no—
547C2×Q8—31no—
548C2×Q8—64no—
549C2×Q8—62no—
550C2×Q8—64no—
551C2×Q8—64no—
552C2×Q8—64no—
553C2×Q8—61no—
554C2×Q8—61no—
555C2×Q8—61no—
556C2×Q8—61no—
557C2×Q8#120311yescharacteristic
558C2×D4—21no—
559C2×D4—31no—
560C2×D4—62no—
561C2×D4—61no—
562C2×D4—152no—
563C2×D4—301no—
564C2×D4—301no—
565C2×D4—301no—
566C2×D4—301no—
567C2×D4—301no—
568C2×D4#120311yescharacteristic
569C22×C4—21no—
570C22×C4—32no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—61no—
574C22×C4—101no—
575C22×C4C2×D3×D511yescharacteristic
576SD16—304no—
577SD16—304no—
578D8—304no—
579D8—304no—
580M16—52no—
581M16—101no—
582M16—152no—
583M16—301no—
584C2×C8—101no—
585C2×C8—301no—
586C22⋊C4—308no—
587C42—52no—
588C42—101no—
589C3×C5C2×#45411yescharacteristic, complemented, Hall
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—42no—
593C22×C3#409911yescharacteristic
594C22×C3#409911yescharacteristic
595C22×C3C22×C22⋊D511yescharacteristic
596C2×D3—22no—
597C2×D3—42no—
598C2×D3—204no—
599C2×D3—202no—
600C2×D3—402no—
601C2×D3—402no—
602C3×C4—22no—
603C3×C4—202no—
604C3×C4#409911yescharacteristic
605C3×C4#409911yescharacteristic
606C3×C4C22×C22⋊D511yescharacteristic
607C3×C4C22×C22⋊D511yescharacteristic
608Dic3—24no—
609Dic3—22no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—42no—
613C2×C5—122no—
614C2×C5#482712yescomplemented
615C2×C5C2×#88211yescharacteristic
616D5—242no—
617C23—21no—
618C23—61no—
619C23—302no—
620C23—604no—
621C23—601no—
622C23—601no—
623C23D3×C22⋊D511yescharacteristic
624Q8—21no—
625Q8—32no—
626Q8—68no—
627Q8—62no—
628Q8—62no—
629Q8—62no—
630Q8—62no—
631Q8—61no—
632Q8C2×#120312yes—
633D4—22no—
634D4—22no—
635D4—21no—
636D4—32no—
637D4—68no—
638D4—62no—
639D4—62no—
640D4—61no—
641D4—302no—
642D4—302no—
643D4—601no—
644D4—601no—
645D4C2×#120312yes—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—34no—
650C2×C4—68no—
651C2×C4—68no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—61no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—102no—
658C2×C4—202no—
659C2×C4C2×#120311yescharacteristic
660C2×C4C2×#120311yescharacteristic
661C2×C4D3×C22⋊D511yescharacteristic
662C2×C4D3×C22⋊D511yescharacteristic
663C2×C4D3×C22⋊D511yescharacteristic
664C2×C4C22×D3×D511yescharacteristic
665C8—102no—
666C8—302no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—42no—
670C2×C3#6553412yescomplemented
671C2×C3C2×#409911yescharacteristic
672D3—42no—
673D3—402no—
674C5C2×#482711yescharacteristic, complemented, Sylow
675C22—22no—
676C22—22no—
677C22—42no—
678C22—62no—
679C22—122no—
680C22—604no—
681C22—602no—
682C22—1202no—
683C22—1202no—
684C22#9157011yescharacteristic
685C22#9157011yescharacteristic
686C22C2×D3×C22⋊D511yescharacteristic
687C4—22no—
688C4—64no—
689C4—62no—
690C4—202no—
691C4#9157011yescharacteristic
692C4#9157011yescharacteristic
693C4C22×#120311yescharacteristic
694C4C2×D3×C22⋊D511yescharacteristic
695C3C2×#6553411yescharacteristic, complemented, Sylow
696C2—21no—
697C2—21no—
698C2—42no—
699C2—122no—
700C2—1202no—
701C2#1174945912yesdirect product factor
702C2C2×#9157011yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#454
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1010C2semidirect
2. C2×#91838C2semidirect
3. C2×#91375C2semidirect
4. C2×#91305C2semidirect
5. C2×C3×#3969C2semidirect
6. #11749459C2direct (N × H)
7. C2×#90979C2semidirect
8. C2×#90962C2semidirect
15. C5×#1010C22semidirect
24. #91838C22semidirect
32. #91375C22semidirect
35. #91305C22semidirect
37. C3×#3969C22semidirect
38. #90979C22semidirect
39. #90962C22semidirect
47. C2×#3969D3semidirect
108. C2×#1010D5semidirect
144. #3969C2×D3semidirect
201. #1010C2×D5semidirect
456. C2×C3×C5#454semidirect
589. C3×C5C2×#454semidirect
614. C2×C5#4827semidirect
670. C2×C3#65534semidirect
674. C5C2×#4827semidirect
695. C3C2×#65534semidirect
701. C2#11749459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#10102
C2×#918382
C2×#913752
C2×#913052
C2×C3×#39692
#117494592
C2×#909792
C2×#909622
C2×#655343
C2×#48275