Finite Group Databasebeta

← C2×#11750926 #14425025

Subgroups — C2×#11750926 #14425025

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92100C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91798C211yesmaximal, characteristic, complemented
4C2×#91764C211yesmaximal, characteristic, complemented
5C2×C3×C5×#104C211yesmaximal, characteristic, complemented
6C2×#91107C211yesmaximal, characteristic, complemented
7C2×#91089C211yesmaximal, characteristic, complemented
8#11750926C218yesmaximal, direct product factor
9C2×#65114—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11#92100—22no—
12#92100—22no—
13#92100—22no—
14#92100C2214yes—
15C2×#6821—21no—
16C2×D4×D15—22no—
17C2×D4×D15—21no—
18C2×#6817—21no—
19C2×#6817C2211yescharacteristic
20C22×D60—21no—
21C22×D60C2211yescharacteristic
22C22×Dic30C2211yescharacteristic, complemented
23C2×C3×C5×M16C2211yescharacteristic, complemented
24C2×C3×C42×C5C2211yescharacteristic, complemented
25#91840—22no—
26#91840C2214yescomplemented
27C2×#6718—21no—
28C2×#6716—21no—
29C2×#6714—22no—
30C2×#6710C2211yescharacteristic, complemented
31#91798—22no—
32#91798C2214yescomplemented
33C2×Dic60—21no—
34C2×#6706—21no—
35#91764—22no—
36#91764C2214yescomplemented
37C3×C5×#104C2214yescomplemented
38#91107C2214yescomplemented
39#91089C2214yescomplemented
40C2×#4825—51nomaximal, Hall
41C2×#4149—31no—
42C2×#4097—31no—
43C2×#4055—31no—
44C2×#4021—31no—
45C2×C5×#104D311yescharacteristic, complemented
46C2×#3955—31no—
47C2×#3937—31no—
48#65114—38no—
49C23×D15—22no—
50C23×D15D412yes—
51C3×C5×#41—21no—
52C3×C5×#41—21no—
53C3×C5×#41D412yes—
54C3×C5×#41C2312yes—
55C2×C3×C5×Q8D411yescharacteristic
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4D411yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5C2311yescharacteristic
61C2×#1220—22no—
62C2×#1220—21no—
63C22×Dic15—21no—
64#6821—24no—
65#6821—24no—
66D4×D15—28no—
67D4×D15—24no—
68D4×D15—28no—
69D4×D15—24no—
70#6817—24no—
71#6817—21no—
72#6817—21no—
73#6817—24no—
74#6817D412yes—
75#6817C2312yes—
76C2×D60—22no—
77C2×D60—24no—
78C2×D60—21no—
79C2×D60—21no—
80C2×D60—21no—
81C2×D60—21no—
82C2×D60—24no—
83C2×D60D412yes—
84C2×D60D411yescharacteristic
85C2×D60C2312yes—
86C2×C4×D15—22no—
87C2×C4×D15—21no—
88C2×Dic30—21no—
89C2×Dic30—21no—
90C2×Dic30—21no—
91C2×Dic30—21no—
92C2×Dic30—21no—
93C2×Dic30D411yescharacteristic
94C2×Dic30C2312yescomplemented
95C3×C5×M16—21no—
96C3×C5×M16C2312yescomplemented
97C2×C3×C5×C8—21no—
98C3×C42×C5—21no—
99C3×C42×C5C2312yescomplemented
100#6718—24no—
101#6716—24no—
102#6714—28no—
103#6710—21no—
104#6710C2312yescomplemented
105C2×C3⋊#168—21no—
106Dic60—24no—
107#6706—24no—
108C2×#1009—51no—
109C2×#951—51no—
110C2×#909—51no—
111C2×#875—51no—
112C2×C3×#104D511yescharacteristic, complemented
113C2×#823—51no—
114C2×#805—51no—
115#4825—58no—
116C2×C5×#41C2×D311yescharacteristic
117#4149—34no—
118#4149—62no—
119#4149—62no—
120#4149—62no—
121C2×#713—61no—
122C2×D4×D5—62no—
123C2×D4×D5—61no—
124C2×#709—31no—
125C2×#709—61no—
126C22×D20—31no—
127C22×D20—61no—
128C22×Dic10—31no—
129C2×C5×M16C2×D311yescharacteristic, complemented
130C2×C42×C5C2×D311yescharacteristic, complemented
131#4097—34no—
132#4097—62no—
133C2×#689—61no—
134C2×#687—61no—
135C2×#685—62no—
136C2×#681—31no—
137#4055—34no—
138#4055—62no—
139C2×Dic20—61no—
140C2×#677—61no—
141#4021—34no—
142#4021—62no—
143C5×#104C2×D314yescomplemented
144#3955—34no—
145#3937—34no—
146C2×#455—151noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—22no—
150C22×D15—21no—
151C22×D15—28no—
152C22×D15—22no—
153C22×D15—44no—
154C22×D15—84no—
155C22×D15C2×D414yes—
156C3×C5×Q8—21no—
157C3×C5×Q8C2×D412yes—
158C3×C5×D4—22no—
159C3×C5×D4—22no—
160C3×C5×D4—21no—
161C3×C5×D4C2×D412yes—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—42no—
167C2×C3×C4×C5C2×D411yescharacteristic
168C2×C3×C4×C5C2×D411yescharacteristic
169C2×C3×C4×C5C2×D411yescharacteristic
170C2×C3×C4×C5C2×D411yescharacteristic
171C2×C3×C4×C5C2×D411yescharacteristic
172C2×C3×C4×C5C2411yescharacteristic
173#1220—28no—
174#1220—22no—
175#1220—22no—
176C2×Dic15—21no—
177C2×Dic15—22no—
178C2×Dic15—41no—
179C2×Dic15—41no—
180D60—28no—
181D60—22no—
182D60—21no—
183D60—22no—
184D60—22no—
185D60—22no—
186D60C2×D412yes—
187C4×D15—28no—
188C4×D15—22no—
189C4×D15—22no—
190Dic30—21no—
191Dic30—22no—
192Dic30—22no—
193Dic30—41no—
194Dic30—41no—
195Dic30C2×D412yes—
196C3×C5×C8—22no—
197C3⋊#168—22no—
198C2×C3×#41C2×D511yescharacteristic
199#1009—54no—
200#1009—102no—
201#1009—102no—
202#1009—102no—
203C2×#239—101no—
204C2×D3×D4—102no—
205C2×D3×D4—101no—
206C2×#235—51no—
207C2×#235—101no—
208C22×D12—51no—
209C22×D12—101no—
210C22×Dic6—51no—
211C2×C3×M16C2×D511yescharacteristic, complemented
212C2×C3×C42C2×D511yescharacteristic, complemented
213#951—54no—
214#951—102no—
215C2×#216—101no—
216C2×#214—101no—
217C2×(C2×D3)⋊C4—102no—
218C2×#208—51no—
219#909—54no—
220#909—102no—
221C2×Dic12—101no—
222C2×#204—101no—
223#875—54no—
224#875—102no—
225C3×#104C2×D514yescomplemented
226#823—54no—
227#805—54no—
228C23×D5—32no—
229C23×D5—62no—
230C5×#41—21no—
231C5×#41—21no—
232C5×#41D1212yes—
233C5×#41C22×D312yes—
234C2×C5×Q8D1211yescharacteristic
235C2×C5×D4—21no—
236C2×C5×D4D1211yescharacteristic
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5C22×D311yescharacteristic
240C2×C22⋊D5—62no—
241C2×C22⋊D5—61no—
242C22×Dic5—61no—
243#713—64no—
244#713—64no—
245D4×D5—68no—
246D4×D5—68no—
247D4×D5—64no—
248D4×D5—64no—
249#709—32no—
250#709—32no—
251#709—64no—
252#709—64no—
253#709—61no—
254#709—61no—
255C2×D20—31no—
256C2×D20—32no—
257C2×D20—32no—
258C2×D20—64no—
259C2×D20—62no—
260C2×D20—64no—
261C2×D20—61no—
262C2×D20—61no—
263C2×D20—61no—
264C2×D20—61no—
265C2×C4×D5—62no—
266C2×C4×D5—61no—
267C2×Dic10—31no—
268C2×Dic10—32no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×Dic10—61no—
272C2×Dic10—61no—
273C2×Dic10—61no—
274C5×M16—21no—
275C5×M16C22×D312yescomplemented
276C2×C5×C8—21no—
277C42×C5—21no—
278C42×C5C22×D312yescomplemented
279#689—64no—
280#687—64no—
281#685—68no—
282#681—32no—
283#681—61no—
284C2×#168—61no—
285Dic20—64no—
286#677—64no—
287C2×H(5,𝔽2)—151no—
288C2×#137—151no—
289C2×#137—151no—
290C2×#124—151no—
291#455—158no—
292C2×#104—151no—
293C2×#104D1511yescharacteristic, complemented
294C2×#100—151no—
295C22×C3×C5—22no—
296C22×C3×C5—22no—
297C22×C3×C5—42no—
298C22×C3×C5#12011yescharacteristic
299C22×C3×C5#12011yescharacteristic
300C22×C3×C5C22×D411yescharacteristic
301C2×D15—24no—
302C2×D15—22no—
303C2×D15—44no—
304C2×D15—42no—
305C2×D15—44no—
306C2×D15—82no—
307C2×D15—88no—
308C3×C4×C5—22no—
309C3×C4×C5—42no—
310C3×C4×C5#12011yescharacteristic
311C3×C4×C5#12011yescharacteristic
312C3×C4×C5C22×D411yescharacteristic
313C3×C4×C5C22×D411yescharacteristic
314Dic15—22no—
315Dic15—42no—
316C23×D3—52no—
317C23×D3—102no—
318C3×#41—21no—
319C3×#41—21no—
320C3×#41D2012yes—
321C3×#41C22×D512yes—
322C2×C3×Q8D2011yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4D2011yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4C22×D511yescharacteristic
328C2×#67—102no—
329C2×#67—101no—
330C22×Dic3—101no—
331#239—104no—
332#239—104no—
333D3×D4—108no—
334D3×D4—108no—
335D3×D4—104no—
336D3×D4—104no—
337#235—52no—
338#235—52no—
339#235—104no—
340#235—104no—
341#235—101no—
342#235—101no—
343C2×D12—51no—
344C2×D12—52no—
345C2×D12—52no—
346C2×D12—104no—
347C2×D12—102no—
348C2×D12—104no—
349C2×D12—101no—
350C2×D12—101no—
351C2×D12—101no—
352C2×D12—101no—
353C2×C4×D3—102no—
354C2×C4×D3—101no—
355C2×Dic6—51no—
356C2×Dic6—52no—
357C2×Dic6—101no—
358C2×Dic6—101no—
359C2×Dic6—101no—
360C2×Dic6—101no—
361C2×Dic6—101no—
362C3×M16—21no—
363C3×M16C22×D512yescomplemented
364C2×C3×C8—21no—
365C3×C42—21no—
366C3×C42C22×D512yescomplemented
367#216—104no—
368#214—104no—
369(C2×D3)⋊C4—108no—
370#208—52no—
371#208—101no—
372C2×C3⋊C8—101no—
373Dic12—104no—
374#204—104no—
375C23×C5—21no—
376C23×C5D3×D411yescharacteristic
377C22×D5—34no—
378C22×D5—61no—
379C22×D5—62no—
380C22×D5—68no—
381C22×D5—62no—
382C22×D5—124no—
383C22×D5—244no—
384C5×Q8—21no—
385C5×Q8C2×D1212yes—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—21no—
389C5×D4C2×D1212yes—
390C2×C4×C5—21no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—42no—
395C2×C4×C5C2×D1211yescharacteristic
396C2×C4×C5C2×D1211yescharacteristic
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5D3×D411yescharacteristic
399C2×C4×C5D3×D411yescharacteristic
400C2×C4×C5C23×D311yescharacteristic
401C22⋊D5—68no—
402C22⋊D5—62no—
403C22⋊D5—62no—
404C2×Dic5—61no—
405C2×Dic5—62no—
406C2×Dic5—121no—
407C2×Dic5—121no—
408D20—32no—
409D20—68no—
410D20—61no—
411D20—62no—
412D20—62no—
413D20—62no—
414D20—62no—
415C4×D5—68no—
416C4×D5—62no—
417C4×D5—62no—
418Dic10—32no—
419Dic10—61no—
420Dic10—62no—
421Dic10—62no—
422Dic10—121no—
423Dic10—121no—
424C5×C8—22no—
425#168—62no—
426H(5,𝔽2)—154no—
427H(5,𝔽2)—302no—
428H(5,𝔽2)—302no—
429H(5,𝔽2)—302no—
430C2×#41—151no—
431C2×#41—301no—
432C2×#41—301no—
433C2×#41C2×D1511yescharacteristic
434C22×Q8—151no—
435C22×D4—151no—
436C22×D4—301no—
437C22×D4—302no—
438C22×D4—301no—
439#137—154no—
440#137—154no—
441#137—302no—
442#137—302no—
443C2×Q16—301no—
444C2×Q16—301no—
445C2×SD16—301no—
446C2×SD16—301no—
447C2×M16—151no—
448C2×M16C2×D1511yescharacteristic, complemented
449#124—154no—
450#124—302no—
451C2×C22⋊C4—302no—
452C2×C42C2×D1511yescharacteristic, complemented
453#104—154no—
454#104C2×D1514yescomplemented
455#100—154no—
456C2×C3×C5—21no—
457C2×C3×C5—21no—
458C2×C3×C5—42no—
459C2×C3×C5#45512yescomplemented
460C2×C3×C5C2×#12011yescharacteristic
461D15—44no—
462D15—42no—
463C23×C3—21no—
464C23×C3D4×D511yescharacteristic
465C22×D3—54no—
466C22×D3—101no—
467C22×D3—102no—
468C22×D3—108no—
469C22×D3—102no—
470C22×D3—204no—
471C22×D3—404no—
472C3×Q8—21no—
473C3×Q8C2×D2012yes—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—21no—
477C3×D4C2×D2012yes—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—42no—
483C2×C3×C4C2×D2011yescharacteristic
484C2×C3×C4C2×D2011yescharacteristic
485C2×C3×C4D4×D511yescharacteristic
486C2×C3×C4D4×D511yescharacteristic
487C2×C3×C4D4×D511yescharacteristic
488C2×C3×C4C23×D511yescharacteristic
489#67—108no—
490#67—102no—
491#67—102no—
492C2×Dic3—101no—
493C2×Dic3—102no—
494C2×Dic3—201no—
495C2×Dic3—201no—
496D12—52no—
497D12—108no—
498D12—102no—
499D12—102no—
500D12—101no—
501D12—102no—
502D12—102no—
503C4×D3—108no—
504C4×D3—102no—
505C4×D3—102no—
506Dic6—52no—
507Dic6—101no—
508Dic6—102no—
509Dic6—102no—
510Dic6—201no—
511Dic6—201no—
512C3×C8—22no—
513C3⋊C8—102no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—42no—
517C22×C5#88211yescharacteristic
518C22×C5#88211yescharacteristic
519C22×C5C2×D3×D411yescharacteristic
520C2×D5—62no—
521C2×D5—64no—
522C2×D5—124no—
523C2×D5—122no—
524C2×D5—124no—
525C2×D5—242no—
526C2×D5—248no—
527C4×C5—22no—
528C4×C5—42no—
529C4×C5#88211yescharacteristic
530C4×C5#88211yescharacteristic
531C4×C5C22×D1211yescharacteristic
532C4×C5C2×D3×D411yescharacteristic
533Dic5—62no—
534Dic5—122no—
535C24—152no—
536C24—302no—
537#41—21no—
538#41—21no—
539#41—152no—
540#41—152no—
541#41—304no—
542#41—304no—
543#41—304no—
544#41—304no—
545#41—301no—
546#41—301no—
547#41D6012yes—
548#41C22×D1512yes—
549C2×Q8—151no—
550C2×Q8—152no—
551C2×Q8—301no—
552C2×Q8—301no—
553C2×Q8—301no—
554C2×Q8—301no—
555C2×Q8—301no—
556C2×Q8D6011yescharacteristic
557C2×D4—21no—
558C2×D4—151no—
559C2×D4—152no—
560C2×D4—152no—
561C2×D4—304no—
562C2×D4—302no—
563C2×D4—304no—
564C2×D4—308no—
565C2×D4—308no—
566C2×D4—304no—
567C2×D4—302no—
568C2×D4—301no—
569C2×D4—304no—
570C2×D4—301no—
571C2×D4—301no—
572C2×D4—301no—
573C2×D4—301no—
574C2×D4D6011yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—302no—
578C22×C4—301no—
579C22×C4—301no—
580C22×C4C22×D1511yescharacteristic
581Q16—304no—
582Q16—304no—
583SD16—304no—
584SD16—304no—
585M16—21no—
586M16—152no—
587M16—301no—
588M16C22×D1512yescomplemented
589C2×C8—21no—
590C2×C8—301no—
591C22⋊C4—308no—
592C42—21no—
593C42C22×D1512yescomplemented
594C3×C5C2×#45511yescharacteristic, complemented, Hall
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—42no—
598C22×C3#402811yescharacteristic
599C22×C3#402811yescharacteristic
600C22×C3C2×D4×D511yescharacteristic
601C2×D3—102no—
602C2×D3—104no—
603C2×D3—204no—
604C2×D3—202no—
605C2×D3—204no—
606C2×D3—402no—
607C2×D3—408no—
608C3×C4—22no—
609C3×C4—42no—
610C3×C4#402811yescharacteristic
611C3×C4#402811yescharacteristic
612C3×C4C22×D2011yescharacteristic
613C3×C4C2×D4×D511yescharacteristic
614Dic3—102no—
615Dic3—202no—
616C2×C5—21no—
617C2×C5—21no—
618C2×C5—42no—
619C2×C5#482512yescomplemented
620C2×C5C2×#88211yescharacteristic
621D5—124no—
622D5—122no—
623C23—21no—
624C23—154no—
625C23—308no—
626C23—301no—
627C23—302no—
628C23—302no—
629C23—604no—
630C23—1204no—
631C23D4×D1511yescharacteristic
632Q8—21no—
633Q8—152no—
634Q8—301no—
635Q8—302no—
636Q8—302no—
637Q8—601no—
638Q8—601no—
639Q8C2×D6012yes—
640D4—22no—
641D4—22no—
642D4—21no—
643D4—152no—
644D4—308no—
645D4—308no—
646D4—302no—
647D4—302no—
648D4—301no—
649D4—302no—
650D4—302no—
651D4—302no—
652D4—302no—
653D4C2×D6012yes—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—308no—
660C2×C4—301no—
661C2×C4—302no—
662C2×C4—302no—
663C2×C4—302no—
664C2×C4—601no—
665C2×C4—601no—
666C2×C4C2×D6011yescharacteristic
667C2×C4C2×D6011yescharacteristic
668C2×C4D4×D1511yescharacteristic
669C2×C4D4×D1511yescharacteristic
670C2×C4D4×D1511yescharacteristic
671C2×C4C23×D1511yescharacteristic
672C8—22no—
673C8—302no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—42no—
677C2×C3#6511412yescomplemented
678C2×C3C2×#402811yescharacteristic
679D3—204no—
680D3—202no—
681C5C2×#482511yescharacteristic, complemented, Sylow
682C22—22no—
683C22—22no—
684C22—42no—
685C22—302no—
686C22—304no—
687C22—604no—
688C22—604no—
689C22—602no—
690C22—1202no—
691C22—1208no—
692C22#9177111yescharacteristic
693C22#9177111yescharacteristic
694C22C2×D4×D1511yescharacteristic
695C4—22no—
696C4—42no—
697C4—302no—
698C4—602no—
699C4#9177111yescharacteristic
700C4#9177111yescharacteristic
701C4C22×D6011yescharacteristic
702C4C2×D4×D1511yescharacteristic
703C3C2×#6511411yescharacteristic, complemented, Sylow
704C2—21no—
705C2—21no—
706C2—42no—
707C2—604no—
708C2—602no—
709C2#1175092612yesdirect product factor
710C2C2×#9177111yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×#92100C2
hypercenterC2×#104D15
hypocenterC3×C5C2×#455
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C2×#91798C2semidirect
4. C2×#91764C2semidirect
5. C2×C3×C5×#104C2semidirect
6. C2×#91107C2semidirect
7. C2×#91089C2semidirect
8. #11750926C2direct (N × H)
22. C22×Dic30C22semidirect
23. C2×C3×C5×M16C22semidirect
24. C2×C3×C42×C5C22semidirect
26. #91840C22semidirect
30. C2×#6710C22semidirect
32. #91798C22semidirect
36. #91764C22semidirect
37. C3×C5×#104C22semidirect
38. #91107C22semidirect
39. #91089C22semidirect
45. C2×C5×#104D3semidirect
94. C2×Dic30C23semidirect
96. C3×C5×M16C23semidirect
99. C3×C42×C5C23semidirect
104. #6710C23semidirect
112. C2×C3×#104D5semidirect
129. C2×C5×M16C2×D3semidirect
130. C2×C42×C5C2×D3semidirect
143. C5×#104C2×D3semidirect
211. C2×C3×M16C2×D5semidirect
212. C2×C3×C42C2×D5semidirect
225. C3×#104C2×D5semidirect
275. C5×M16C22×D3semidirect
278. C42×C5C22×D3semidirect
293. C2×#104D15semidirect
363. C3×M16C22×D5semidirect
366. C3×C42C22×D5semidirect
448. C2×M16C2×D15semidirect
452. C2×C42C2×D15semidirect
454. #104C2×D15semidirect
459. C2×C3×C5#455semidirect
588. M16C22×D15semidirect
593. C42C22×D15semidirect
594. C3×C5C2×#455semidirect
619. C2×C5#4825semidirect
677. C2×C3#65114semidirect
681. C5C2×#4825semidirect
703. C3C2×#65114semidirect
709. C2#11750926direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921002
C2×#918402
C2×#917982
C2×#917642
C2×C3×C5×#1042
C2×#911072
C2×#910892
#117509262
C2×#651143
C2×#48255