Finite Group Databasebeta

← C2×#11749168 #14425101

Subgroups — C2×#11749168 #14425101

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×#92004C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic, complemented
3C2×C5×#932C211yesmaximal, characteristic, complemented
4C2×C3×#4082C211yesmaximal, characteristic, complemented
5#11749168C218yesmaximal, direct product factor
6C2×#90981C211yesmaximal, characteristic, complemented
7C2×#90979C211yesmaximal, characteristic, complemented
8C2×#90961C211yesmaximal, characteristic, complemented
9C2×#65490—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C2×#6817C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C3×Dic10C2211yescharacteristic
14C2×#6782—22no—
15C2×D15⋊Q8—21no—
16C2×#6769—21no—
17#92004—22no—
18#92004—22no—
19#92004—22no—
20#92004C2214yescomplemented
21C2×#6768—21no—
22C2×D3×Dic10—21no—
23C2×#6716—21no—
24#91821—22no—
25#91821C2214yescomplemented
26C2×#6715—21no—
27C2×#6710C2211yescharacteristic
28C2×C5×#214—21no—
29C5×#932—22no—
30C5×#932C2214yescomplemented
31C2×C5×#213—21no—
32C2×C5×#208C2211yescharacteristic
33C2×C3×C22⋊Dic5—22no—
34C3×#4082—22no—
35C3×#4082C2214yescomplemented
36C2×C3×C4×Dic5C2211yescharacteristic
37#90981C2214yescomplemented
38#90979C2214yescomplemented
39#90961C2214yescomplemented
40C2×#5062—51nomaximal, Hall
41C2×#4150—31no—
42C2×C5×AGL(1,ℤ/8)—31no—
43C2×#4082D311yescharacteristic, complemented
44C2×#4078—31no—
45C2×#3969—31no—
46#65490—38no—
47C2×#3957—31no—
48C2×#3956—31no—
49C24×C3×C5—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4—21no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—21no—
59#6817—21no—
60#6817D412yes—
61#6817C2312yes—
62C2×D60D411yescharacteristic
63C2×C4×D15—21no—
64C2×Dic30D411yescharacteristic
65C2×C5×#67—21no—
66C5×#235—21no—
67C5×#235—21no—
68C5×#235D412yes—
69C5×#235C2312yes—
70C2×C5×D12D411yescharacteristic
71C2×C4×C5×D3—21no—
72C2×C5×Dic6D411yescharacteristic
73C22×C3×Dic5—21no—
74C22×C3×Dic5D412yes—
75C2×C3×Dic10—21no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10—21no—
79C2×C3×Dic10D412yes—
80C2×C3×Dic10C2312yes—
81C2×#1204—22no—
82C2×#1203—22no—
83C2×#1200—22no—
84#6782—28no—
85#6782—28no—
86C2×D3×Dic5—22no—
87D15⋊Q8—24no—
88D15⋊Q8—24no—
89#6769—24no—
90#6769—24no—
91#6768—24no—
92#6768—24no—
93D3×Dic10—24no—
94D3×Dic10—24no—
95#6716—24no—
96#6715—24no—
97#6710—21no—
98#6710C2312yes—
99C2×C3⋊#168—21no—
100C5×#214—24no—
101C5×#213—24no—
102C5×#208—21no—
103C5×#208C2312yes—
104C2×C5×C3⋊C8—21no—
105C3×C22⋊Dic5—28no—
106C3×C4×Dic5—21no—
107C3×C4×Dic5C2312yes—
108C2×#1007—51no—
109C2×C3×#124—51no—
110C2×#932—51no—
111C2×#932D511yescharacteristic, complemented
112C2×#836—51no—
113#5062—58no—
114C2×#805—51no—
115C2×#805—51no—
116C2×C5×#41—31no—
117C22×C5×D4C2×D311yescharacteristic
118#4150—34no—
119#4150—62no—
120#4150—62no—
121#4150—62no—
122C2×Q8×D5—61no—
123C2×#711—61no—
124C2×#711—62no—
125C2×#709—31no—
126C2×#709—61no—
127C22×Dic10—61no—
128C22×Dic10C2×D311yescharacteristic
129C5×AGL(1,ℤ/8)—34no—
130C5×AGL(1,ℤ/8)—62no—
131C2×C5×SD16—61no—
132C2×C5×D8—61no—
133C2×C5×M16—31no—
134C2×C22⋊Dic5—22no—
135#4082—22no—
136#4082C2×D314yescomplemented
137C2×#687—61no—
138#4078—34no—
139#4078—62no—
140C2×#686—61no—
141C2×C4×Dic5C2×D311yescharacteristic
142C2×#681—31no—
143#3969—34no—
144#3957—34no—
145#3956—34no—
146C2×#454—151noSylow
147C23×C3×C5—22no—
148C23×C3×C5—44no—
149C23×C3×C5—41no—
150C23×C3×C5—41no—
151C23×C3×C5C2×D411yescharacteristic
152C22×D15—21no—
153C22×C5×D3—21no—
154C3×C5×D4—22no—
155C3×C5×D4—22no—
156C3×C5×D4—41no—
157C3×C5×D4—41no—
158C2×C3×C4×C5C2×D411yescharacteristic
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D411yescharacteristic
163C2×C3×C4×C5C2411yescharacteristic
164#1220—22no—
165#1220—22no—
166C2×Dic15—21no—
167D60—21no—
168D60C2×D412yes—
169C4×D15—22no—
170C4×D15—22no—
171Dic30—21no—
172Dic30C2×D412yes—
173C5×#67—22no—
174C5×#67—22no—
175C2×C5×Dic3—21no—
176C5×D12—21no—
177C5×D12C2×D412yes—
178C4×C5×D3—22no—
179C4×C5×D3—22no—
180C5×Dic6—21no—
181C5×Dic6C2×D412yes—
182C2×C3×Dic5—22no—
183C2×C3×Dic5—22no—
184C2×C3×Dic5—22no—
185C2×C3×Dic5—42no—
186C2×C3×Dic5C2×D414yes—
187C3×Dic10—22no—
188C3×Dic10—22no—
189C3×Dic10—22no—
190C3×Dic10—22no—
191#1204—28no—
192#1203—28no—
193#1200—28no—
194D3×Dic5—28no—
195C3⋊#168—22no—
196C5×C3⋊C8—22no—
197C22×C3×Q8—51no—
198C22×C3×D4C2×D511yescharacteristic
199#1007—54no—
200#1007—102no—
201#1007—102no—
202#1007—102no—
203C2×#239—101no—
204C2×#239—101no—
205C2×D3×Q8—101no—
206C2×D3×Q8—101no—
207C2×#235—51no—
208C2×#235—102no—
209C2×#235C2×D511yescharacteristic
210C3×#124—54no—
211C3×#124—102no—
212C2×C3×C22⋊C4—102no—
213C2×C3×C42—51no—
214C2×#214—21no—
215C2×#214—101no—
216#932—22no—
217#932—54no—
218#932—102no—
219#932C2×D514yescomplemented
220C2×#213—21no—
221C2×#213—101no—
222C2×#208—51no—
223C2×#208C2×D511yescharacteristic
224#836—54no—
225#805—54no—
226#805—54no—
227C24×C5—21no—
228C5×#41—32no—
229C5×#41—32no—
230C5×#41—61no—
231C5×#41—61no—
232C2×C5×Q8—31no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—21no—
236C2×C5×D4—21no—
237C2×C5×D4—21no—
238C2×C5×D4—31no—
239C2×C5×D4—61no—
240C2×C5×D4C22×D312yes—
241C22×C4×C5—61no—
242C22×C4×C5C22×D311yescharacteristic
243C2×C22⋊D5—62no—
244C2×C22⋊D5—61no—
245C22×Dic5—21no—
246C22×Dic5—62no—
247C22×Dic5#6712yes—
248Q8×D5—64no—
249Q8×D5—64no—
250#711—64no—
251#711—64no—
252#711—68no—
253#711—68no—
254#709—32no—
255#709—32no—
256#709—64no—
257#709—64no—
258#709—61no—
259#709—61no—
260C2×D20—31no—
261C2×C4×D5—62no—
262C2×C4×D5—61no—
263C2×Dic10—21no—
264C2×Dic10—21no—
265C2×Dic10—21no—
266C2×Dic10—21no—
267C2×Dic10—31no—
268C2×Dic10—64no—
269C2×Dic10—64no—
270C2×Dic10—62no—
271C2×Dic10#6712yes—
272C2×Dic10C22×D312yes—
273C5×SD16—64no—
274C5×D8—64no—
275C5×M16—32no—
276C5×M16—61no—
277C2×C5×C8—61no—
278C22⋊Dic5—28no—
279#687—64no—
280#686—64no—
281C4×Dic5—21no—
282C4×Dic5C22×D312yes—
283#681—32no—
284#681—61no—
285C2×#168—61no—
286C2×2−1+4—151no—
287C2×AGL(1,ℤ/8)—31no—
288C2×AGL(1,ℤ/8)—151no—
289C2×#124—51no—
290#454—158no—
291C2×#104—151no—
292C2×#104—151no—
293C2×#101—151no—
294C22×C3×C5—22no—
295C22×C3×C5—44no—
296C22×C3×C5—42no—
297C22×C3×C5—82no—
298C22×C3×C5—82no—
299C22×C3×C5#12011yescharacteristic
300C22×C3×C5#12011yescharacteristic
301C22×C3×C5C22×D411yescharacteristic
302C2×D15—22no—
303C2×D15—42no—
304C2×C5×D3—22no—
305C2×C5×D3—42no—
306C3×C4×C5#12011yescharacteristic
307C3×C4×C5#12011yescharacteristic
308C3×C4×C5C22×D411yescharacteristic
309C3×C4×C5C22×D411yescharacteristic
310Dic15—22no—
311C3×Dic5—24no—
312C3×Dic5—42no—
313C5×Dic3—22no—
314C24×C3—21no—
315C2×C3×Q8—52no—
316C2×C3×Q8—52no—
317C2×C3×Q8—101no—
318C2×C3×Q8—101no—
319C2×C3×Q8—101no—
320C2×C3×Q8—101no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4C22×D512yes—
327C22×C3×C4—52no—
328C22×C3×C4—101no—
329C22×C3×C4C22×D511yescharacteristic
330C2×#67—21no—
331C2×#67—101no—
332#239—104no—
333#239—104no—
334#239—104no—
335#239—104no—
336D3×Q8—104no—
337D3×Q8—104no—
338D3×Q8—104no—
339D3×Q8—104no—
340#235—21no—
341#235—21no—
342#235—52no—
343#235—52no—
344#235—108no—
345#235—108no—
346#235—101no—
347#235—101no—
348#235C22⋊D512yes—
349#235C22×D512yes—
350C2×D12—51no—
351C2×D12—102no—
352C2×D12C22⋊D511yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—102no—
355C2×C4×D3—102no—
356C2×C4×D3—101no—
357C2×Dic6—51no—
358C2×Dic6—102no—
359C2×Dic6C22⋊D511yescharacteristic
360C3×C22⋊C4—108no—
361C3×C42—52no—
362C3×C42—101no—
363#214—24no—
364#214—104no—
365#213—24no—
366#213—104no—
367#208—21no—
368#208—52no—
369#208—101no—
370#208C22×D512yes—
371C2×C3⋊C8—21no—
372C2×C3⋊C8—101no—
373C23×C5—22no—
374C23×C5—44no—
375C23×C5—41no—
376C23×C5—41no—
377C23×C5—61no—
378C23×C5C2×#6711yescharacteristic
379C22×D5—61no—
380C5×Q8—32no—
381C5×Q8—61no—
382C5×D4—22no—
383C5×D4—22no—
384C5×D4—32no—
385C5×D4—41no—
386C5×D4—41no—
387C5×D4—62no—
388C5×D4—62no—
389C5×D4—61no—
390C2×C4×C5—61no—
391C2×C4×C5—62no—
392C2×C4×C5—62no—
393C2×C4×C5D3×D411yescharacteristic
394C2×C4×C5D3×D411yescharacteristic
395C2×C4×C5D3×D411yescharacteristic
396C2×C4×C5D3×D411yescharacteristic
397C2×C4×C5C2×#6711yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—68no—
400C22⋊D5—62no—
401C22⋊D5—62no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—42no—
406C2×Dic5—68no—
407C2×Dic5—61no—
408C2×Dic5C2×#6714yes—
409D20—32no—
410D20—61no—
411C4×D5—68no—
412C4×D5—62no—
413C4×D5—62no—
414Dic10—22no—
415Dic10—22no—
416Dic10—22no—
417Dic10—22no—
418Dic10—32no—
419Dic10—68no—
420Dic10—61no—
421C5×C8—62no—
422#168—62no—
4232−1+4—154no—
4242−1+4—302no—
4252−1+4—302no—
4262−1+4—302no—
427C2×#41—31no—
428C2×#41—151no—
429C2×#41—302no—
430C2×#41—301no—
431C2×#41—301no—
432C22×Q8—51no—
433C22×Q8—301no—
434C22×Q8—301no—
435C22×D4D3×D511yescharacteristic
436AGL(1,ℤ/8)—34no—
437AGL(1,ℤ/8)—62no—
438AGL(1,ℤ/8)—154no—
439AGL(1,ℤ/8)—302no—
440C2×SD16—61no—
441C2×SD16—301no—
442C2×D8—61no—
443C2×D8—301no—
444C2×M16—31no—
445C2×M16—151no—
446#124—54no—
447#124—102no—
448C2×C22⋊C4—102no—
449C2×C42—51no—
450#104—154no—
451#104—154no—
452#101—154no—
453C2×C3×C5—21no—
454C2×C3×C5—21no—
455C2×C3×C5—82no—
456C2×C3×C5#45412yescomplemented
457C2×C3×C5C2×#12011yescharacteristic
458D15—42no—
459C5×D3—42no—
460C23×C3—22no—
461C23×C3—44no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3D4×D511yescharacteristic
465C22×D3—21no—
466C22×D3—101no—
467C3×Q8—102no—
468C3×Q8—102no—
469C3×Q8—102no—
470C3×Q8—102no—
471C3×D4—22no—
472C3×D4—22no—
473C3×D4—41no—
474C3×D4—41no—
475C2×C3×C4—54no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—202no—
480C2×C3×C4D4×D511yescharacteristic
481C2×C3×C4D4×D511yescharacteristic
482C2×C3×C4D4×D511yescharacteristic
483C2×C3×C4C2×C22⋊D511yescharacteristic
484C2×C3×C4C2×C22⋊D511yescharacteristic
485C2×C3×C4C23×D511yescharacteristic
486#67—22no—
487#67—22no—
488#67—102no—
489#67—102no—
490C2×Dic3—21no—
491C2×Dic3—101no—
492D12—21no—
493D12—52no—
494D12—108no—
495D12—101no—
496D12C2×C22⋊D512yes—
497C4×D3—22no—
498C4×D3—22no—
499C4×D3—108no—
500C4×D3—108no—
501C4×D3—102no—
502C4×D3—102no—
503Dic6—21no—
504Dic6—52no—
505Dic6—108no—
506Dic6—101no—
507Dic6C2×C22⋊D512yes—
508C3⋊C8—22no—
509C3⋊C8—102no—
510C22×C5—22no—
511C22×C5—44no—
512C22×C5—42no—
513C22×C5—62no—
514C22×C5—82no—
515C22×C5—82no—
516C22×C5—122no—
517C22×C5#93711yescharacteristic
518C22×C5#93711yescharacteristic
519C22×C5C22×#6711yescharacteristic
520C2×D5—62no—
521C2×D5—122no—
522C4×C5—62no—
523C4×C5#93711yescharacteristic
524C4×C5#93711yescharacteristic
525C4×C5C2×D3×D411yescharacteristic
526C4×C5C2×D3×D411yescharacteristic
527Dic5—24no—
528Dic5—42no—
529Dic5—62no—
530C24—21no—
531#41—32no—
532#41—32no—
533#41—61no—
534#41—61no—
535#41—152no—
536#41—152no—
537#41—308no—
538#41—304no—
539#41—304no—
540#41—308no—
541#41—304no—
542#41—304no—
543#41—301no—
544#41—301no—
545C2×Q8—31no—
546C2×Q8—52no—
547C2×Q8—52no—
548C2×Q8—101no—
549C2×Q8—101no—
550C2×Q8—101no—
551C2×Q8—101no—
552C2×Q8—151no—
553C2×Q8—302no—
554C2×Q8—304no—
555C2×Q8—304no—
556C2×Q8—304no—
557C2×Q8—304no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—31no—
564C2×D4—61no—
565C2×D4—151no—
566C2×D4—302no—
567C2×D4—301no—
568C2×D4C2×D3×D512yes—
569C22×C4—52no—
570C22×C4—61no—
571C22×C4—101no—
572C22×C4—302no—
573C22×C4—302no—
574C22×C4—301no—
575C22×C4C2×D3×D511yescharacteristic
576SD16—64no—
577SD16—304no—
578D8—64no—
579D8—304no—
580M16—32no—
581M16—61no—
582M16—152no—
583M16—301no—
584C2×C8—61no—
585C2×C8—301no—
586C22⋊C4—108no—
587C42—52no—
588C42—101no—
589C3×C5C2×#45411yescharacteristic, complemented, Hall
590C22×C3—22no—
591C22×C3—44no—
592C22×C3—42no—
593C22×C3—82no—
594C22×C3—82no—
595C22×C3#408311yescharacteristic
596C22×C3#408311yescharacteristic
597C22×C3C2×D4×D511yescharacteristic
598C2×D3—22no—
599C2×D3—42no—
600C2×D3—102no—
601C2×D3—202no—
602C3×C4—104no—
603C3×C4—202no—
604C3×C4#408311yescharacteristic
605C3×C4#408311yescharacteristic
606C3×C4C2×D4×D511yescharacteristic
607C3×C4C22×C22⋊D511yescharacteristic
608Dic3—22no—
609Dic3—102no—
610C2×C5—21no—
611C2×C5—21no—
612C2×C5—82no—
613C2×C5—122no—
614C2×C5#506212yescomplemented
615C2×C5C2×#93711yescharacteristic
616D5—122no—
617C23—22no—
618C23—44no—
619C23—41no—
620C23—41no—
621C23—61no—
622C23—301no—
623C23D5×#6711yescharacteristic
624Q8—32no—
625Q8—61no—
626Q8—102no—
627Q8—102no—
628Q8—102no—
629Q8—102no—
630Q8—152no—
631Q8—308no—
632Q8—301no—
633D4—22no—
634D4—22no—
635D4—32no—
636D4—41no—
637D4—41no—
638D4—62no—
639D4—62no—
640D4—61no—
641D4—152no—
642D4—308no—
643D4—302no—
644D4—302no—
645D4—301no—
646C2×C4—54no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—102no—
653C2×C4—202no—
654C2×C4—308no—
655C2×C4—308no—
656C2×C4—301no—
657C2×C4—302no—
658C2×C4—302no—
659C2×C4D5×#6711yescharacteristic
660C2×C4D3×C22⋊D511yescharacteristic
661C2×C4D3×C22⋊D511yescharacteristic
662C2×C4#679011yescharacteristic
663C2×C4#679011yescharacteristic
664C2×C4C22×D3×D511yescharacteristic
665C8—62no—
666C8—302no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—82no—
670C2×C3#6549012yescomplemented
671C2×C3C2×#408311yescharacteristic
672D3—42no—
673D3—202no—
674C5C2×#506211yescharacteristic, complemented, Sylow
675C22—22no—
676C22—44no—
677C22—42no—
678C22—62no—
679C22—82no—
680C22—82no—
681C22—122no—
682C22—302no—
683C22—602no—
684C22#9157711yescharacteristic
685C22#9157711yescharacteristic
686C22C2×D5×#6711yescharacteristic
687C4—62no—
688C4—104no—
689C4—202no—
690C4—302no—
691C4#9157711yescharacteristic
692C4#9157711yescharacteristic
693C4C2×D3×C22⋊D511yescharacteristic
694C4C2×#679011yescharacteristic
695C3C2×#6549011yescharacteristic, complemented, Sylow
696C2—21no—
697C2—21no—
698C2—82no—
699C2—122no—
700C2—602no—
701C2#1174916812yesdirect product factor
702C2C2×#9157711yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#120
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#454
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#92004C2semidirect
2. C2×#91821C2semidirect
3. C2×C5×#932C2semidirect
4. C2×C3×#4082C2semidirect
5. #11749168C2direct (N × H)
6. C2×#90981C2semidirect
7. C2×#90979C2semidirect
8. C2×#90961C2semidirect
20. #92004C22semidirect
25. #91821C22semidirect
30. C5×#932C22semidirect
35. C3×#4082C22semidirect
37. #90981C22semidirect
38. #90979C22semidirect
39. #90961C22semidirect
43. C2×#4082D3semidirect
111. C2×#932D5semidirect
136. #4082C2×D3semidirect
219. #932C2×D5semidirect
456. C2×C3×C5#454semidirect
589. C3×C5C2×#454semidirect
614. C2×C5#5062semidirect
670. C2×C3#65490semidirect
674. C5C2×#5062semidirect
695. C3C2×#65490semidirect
701. C2#11749168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920042
C2×#918212
C2×C5×#9322
C2×C3×#40822
#117491682
C2×#909812
C2×#909792
C2×#909612
C2×#654903
C2×#50625