Finite Group Databasebeta

← C2×#11750927 #14425139

Subgroups — C2×#11750927 #14425139

Order 1920.

1416 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic
2C2×#91840C211yesmaximal, characteristic, complemented
3C2×#91798C211yesmaximal, characteristic, complemented
4C2×#91758C211yesmaximal, characteristic, complemented
5C2×C3×C5×#104C211yesmaximal, characteristic, complemented
6C2×#91108C211yesmaximal, characteristic, complemented
7C2×#91089C211yesmaximal, characteristic, complemented
8#11750927C218yesmaximal, direct product factor
9C2×#65115—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11#92101—22no—
12#92101—22no—
13#92101—22no—
14#92101C2214yes—
15C2×Q8×D15—21no—
16C2×#6819—21no—
17C2×#6819—22no—
18C2×#6817—21no—
19C2×#6817C2211yescharacteristic
20C22×Dic30—21no—
21C22×Dic30C2211yescharacteristic
22C22×Dic30C2211yescharacteristic
23C2×C3×C5×M16C2211yescharacteristic
24C2×C3×C42×C5C2211yescharacteristic
25#91840—22no—
26#91840C2214yescomplemented
27C2×#6718—21no—
28C2×#6716—21no—
29C2×C4⋊Dic15—22no—
30C2×#6710C2211yescharacteristic
31#91798—22no—
32#91798C2214yescomplemented
33C2×Dic60—21no—
34C2×#6706—21no—
35#91758—22no—
36#91758C2214yescomplemented
37C3×C5×#104C2214yescomplemented
38#91108C2214yescomplemented
39#91089C2214yescomplemented
40C2×#4826—51nomaximal, Hall
41C2×#4150—31no—
42C2×#4097—31no—
43C2×#4055—31no—
44C2×#4015—31no—
45C2×C5×#104D311yescharacteristic, complemented
46C2×#3956—31no—
47C2×#3937—31no—
48#65115—38no—
49C3×C5×#41—21no—
50C3×C5×#41—21no—
51C3×C5×#41D412yes—
52C3×C5×#41C2312yes—
53C2×C3×C5×Q8D411yescharacteristic
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4D411yescharacteristic
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—22no—
60C2×#1220—21no—
61C22×Dic15—22no—
62C22×Dic15—21no—
63C22×Dic15D412yes—
64Q8×D15—24no—
65Q8×D15—24no—
66#6819—28no—
67#6819—24no—
68#6819—24no—
69#6819—28no—
70#6817—24no—
71#6817—21no—
72#6817—21no—
73#6817—24no—
74#6817D412yes—
75#6817C2312yes—
76C2×D60D411yescharacteristic
77C2×C4×D15—22no—
78C2×C4×D15—21no—
79C2×Dic30—22no—
80C2×Dic30—24no—
81C2×Dic30—21no—
82C2×Dic30—21no—
83C2×Dic30—21no—
84C2×Dic30—21no—
85C2×Dic30—24no—
86C2×Dic30—21no—
87C2×Dic30—21no—
88C2×Dic30—21no—
89C2×Dic30—21no—
90C2×Dic30—21no—
91C2×Dic30D412yes—
92C2×Dic30D411yescharacteristic
93C2×Dic30C2312yes—
94C2×Dic30C2312yes—
95C3×C5×M16—21no—
96C3×C5×M16C2312yes—
97C2×C3×C5×C8—21no—
98C3×C42×C5—21no—
99C3×C42×C5C2312yes—
100#6718—24no—
101#6716—24no—
102C4⋊Dic15—28no—
103#6710—21no—
104#6710C2312yes—
105C2×C3⋊#168—21no—
106Dic60—24no—
107#6706—24no—
108C2×#1010—51no—
109C2×#951—51no—
110C2×#909—51no—
111C2×#869—51no—
112C2×C3×#104D511yescharacteristic, complemented
113C2×#824—51no—
114C2×#805—51no—
115#4826—58no—
116C2×C5×#41C2×D311yescharacteristic
117#4150—34no—
118#4150—62no—
119#4150—62no—
120#4150—62no—
121C2×Q8×D5—61no—
122C2×#711—62no—
123C2×#711—61no—
124C2×#709—31no—
125C2×#709—61no—
126C22×Dic10—31no—
127C22×Dic10—31no—
128C22×Dic10—61no—
129C2×C5×M16C2×D311yescharacteristic
130C2×C42×C5C2×D311yescharacteristic
131#4097—34no—
132#4097—62no—
133C2×#689—61no—
134C2×#687—61no—
135C2×C4⋊Dic5—62no—
136C2×#681—31no—
137#4055—34no—
138#4055—62no—
139C2×Dic20—61no—
140C2×#677—61no—
141#4015—34no—
142#4015—62no—
143C5×#104C2×D314yescomplemented
144#3956—34no—
145#3937—34no—
146C2×#456—151noSylow
147C23×C3×C5—21no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8C2×D412yes—
152C3×C5×D4—22no—
153C3×C5×D4—22no—
154C3×C5×D4—21no—
155C3×C5×D4C2×D412yes—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D411yescharacteristic
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D411yescharacteristic
165C2×C3×C4×C5C2×D411yescharacteristic
166C2×C3×C4×C5C2411yescharacteristic
167#1220—28no—
168#1220—22no—
169#1220—22no—
170C2×Dic15—28no—
171C2×Dic15—22no—
172C2×Dic15—21no—
173C2×Dic15—22no—
174C2×Dic15—22no—
175C2×Dic15—41no—
176C2×Dic15—41no—
177C2×Dic15C2×D414yes—
178D60—21no—
179D60C2×D412yes—
180C4×D15—28no—
181C4×D15—22no—
182C4×D15—22no—
183Dic30—28no—
184Dic30—22no—
185Dic30—21no—
186Dic30—22no—
187Dic30—22no—
188Dic30—22no—
189Dic30—22no—
190Dic30—22no—
191Dic30—41no—
192Dic30—41no—
193Dic30C2×D412yes—
194C3×C5×C8—22no—
195C3⋊#168—22no—
196C2×C3×#41C2×D511yescharacteristic
197#1010—54no—
198#1010—102no—
199#1010—102no—
200#1010—102no—
201C2×D3×Q8—101no—
202C2×#237—102no—
203C2×#237—101no—
204C2×#235—51no—
205C2×#235—101no—
206C22×Dic6—51no—
207C22×Dic6—51no—
208C22×Dic6—101no—
209C2×C3×M16C2×D511yescharacteristic
210C2×C3×C42C2×D511yescharacteristic
211#951—54no—
212#951—102no—
213C2×#216—101no—
214C2×#214—101no—
215C2×C4⋊Dic3—102no—
216C2×#208—51no—
217#909—54no—
218#909—102no—
219C2×Dic12—101no—
220C2×#204—101no—
221#869—54no—
222#869—102no—
223C3×#104C2×D514yescomplemented
224#824—54no—
225#805—54no—
226C5×#41—21no—
227C5×#41—21no—
228C5×#41D1212yes—
229C5×#41C22×D312yes—
230C2×C5×Q8D1211yescharacteristic
231C2×C5×D4—21no—
232C2×C5×D4D1211yescharacteristic
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5C22×D311yescharacteristic
236C2×C22⋊D5—62no—
237C2×C22⋊D5—61no—
238C22×Dic5—32no—
239C22×Dic5—62no—
240C22×Dic5—61no—
241Q8×D5—64no—
242Q8×D5—64no—
243#711—68no—
244#711—68no—
245#711—64no—
246#711—64no—
247#709—32no—
248#709—32no—
249#709—64no—
250#709—64no—
251#709—61no—
252#709—61no—
253C2×D20—31no—
254C2×C4×D5—62no—
255C2×C4×D5—61no—
256C2×Dic10—31no—
257C2×Dic10—32no—
258C2×Dic10—32no—
259C2×Dic10—32no—
260C2×Dic10—64no—
261C2×Dic10—62no—
262C2×Dic10—64no—
263C2×Dic10—61no—
264C2×Dic10—61no—
265C2×Dic10—61no—
266C2×Dic10—61no—
267C2×Dic10—61no—
268C2×Dic10—61no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×Dic10—61no—
272C5×M16—21no—
273C5×M16C22×D312yes—
274C2×C5×C8—21no—
275C42×C5—21no—
276C42×C5C22×D312yes—
277#689—64no—
278#687—64no—
279C4⋊Dic5—68no—
280#681—32no—
281#681—61no—
282C2×#168—61no—
283Dic20—64no—
284#677—64no—
285C2×2−1+4—151no—
286C2×#137—151no—
287C2×#137—151no—
288C2×C4⋊Q8—151no—
289#456—158no—
290C2×#104—151no—
291C2×#104D1511yescharacteristic, complemented
292C2×#101—151no—
293C22×C3×C5—22no—
294C22×C3×C5—22no—
295C22×C3×C5—42no—
296C22×C3×C5#12011yescharacteristic
297C22×C3×C5#12011yescharacteristic
298C22×C3×C5C22×D411yescharacteristic
299C2×D15—22no—
300C2×D15—42no—
301C3×C4×C5—24no—
302C3×C4×C5—22no—
303C3×C4×C5#12011yescharacteristic
304C3×C4×C5#12011yescharacteristic
305C3×C4×C5C22×D411yescharacteristic
306C3×C4×C5C22×D411yescharacteristic
307Dic15—24no—
308Dic15—22no—
309Dic15—42no—
310C3×#41—21no—
311C3×#41—21no—
312C3×#41D2012yes—
313C3×#41C22×D512yes—
314C2×C3×Q8D2011yescharacteristic
315C2×C3×D4—21no—
316C2×C3×D4D2011yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4C22×D511yescharacteristic
320C2×#67—102no—
321C2×#67—101no—
322C22×Dic3—52no—
323C22×Dic3—102no—
324C22×Dic3—101no—
325D3×Q8—104no—
326D3×Q8—104no—
327#237—108no—
328#237—108no—
329#237—104no—
330#237—104no—
331#235—52no—
332#235—52no—
333#235—104no—
334#235—104no—
335#235—101no—
336#235—101no—
337C2×D12—51no—
338C2×C4×D3—102no—
339C2×C4×D3—101no—
340C2×Dic6—51no—
341C2×Dic6—52no—
342C2×Dic6—52no—
343C2×Dic6—52no—
344C2×Dic6—104no—
345C2×Dic6—102no—
346C2×Dic6—104no—
347C2×Dic6—101no—
348C2×Dic6—101no—
349C2×Dic6—101no—
350C2×Dic6—101no—
351C2×Dic6—101no—
352C2×Dic6—101no—
353C2×Dic6—101no—
354C2×Dic6—101no—
355C2×Dic6—101no—
356C3×M16—21no—
357C3×M16C22×D512yes—
358C2×C3×C8—21no—
359C3×C42—21no—
360C3×C42C22×D512yes—
361#216—104no—
362#214—104no—
363C4⋊Dic3—108no—
364#208—52no—
365#208—101no—
366C2×C3⋊C8—101no—
367Dic12—104no—
368#204—104no—
369C23×C5—21no—
370C23×C5D3×D411yescharacteristic
371C22×D5—61no—
372C5×Q8—21no—
373C5×Q8C2×D1212yes—
374C5×D4—22no—
375C5×D4—22no—
376C5×D4—21no—
377C5×D4C2×D1212yes—
378C2×C4×C5—24no—
379C2×C4×C5—21no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5C2×D1211yescharacteristic
384C2×C4×C5C2×D1211yescharacteristic
385C2×C4×C5D3×D411yescharacteristic
386C2×C4×C5D3×D411yescharacteristic
387C2×C4×C5D3×D411yescharacteristic
388C2×C4×C5C23×D311yescharacteristic
389C22⋊D5—68no—
390C22⋊D5—62no—
391C22⋊D5—62no—
392C2×Dic5—34no—
393C2×Dic5—68no—
394C2×Dic5—61no—
395C2×Dic5—62no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5—121no—
399C2×Dic5—121no—
400D20—32no—
401D20—61no—
402C4×D5—68no—
403C4×D5—62no—
404C4×D5—62no—
405Dic10—32no—
406Dic10—68no—
407Dic10—61no—
408Dic10—62no—
409Dic10—62no—
410Dic10—62no—
411Dic10—62no—
412Dic10—62no—
413Dic10—62no—
414Dic10—121no—
415Dic10—121no—
416C5×C8—22no—
417#168—62no—
4182−1+4—154no—
4192−1+4—302no—
4202−1+4—302no—
4212−1+4—302no—
422C2×#41—151no—
423C2×#41—301no—
424C2×#41—302no—
425C2×#41—301no—
426C2×#41C2×D1511yescharacteristic
427C22×Q8—151no—
428C22×Q8—151no—
429C22×Q8—301no—
430C22×Q8—301no—
431#137—154no—
432#137—154no—
433#137—302no—
434#137—302no—
435C2×Q16—301no—
436C2×Q16—301no—
437C2×SD16—301no—
438C2×SD16—301no—
439C2×M16—151no—
440C2×M16C2×D1511yescharacteristic
441C4⋊Q8—154no—
442C4⋊Q8—302no—
443C2×C4⋊C4—302no—
444C2×C42C2×D1511yescharacteristic
445#104—154no—
446#104C2×D1514yescomplemented
447#101—154no—
448C2×C3×C5—21no—
449C2×C3×C5—21no—
450C2×C3×C5—42no—
451C2×C3×C5#45612yescomplemented
452C2×C3×C5C2×#12011yescharacteristic
453D15—42no—
454C23×C3—21no—
455C23×C3D4×D511yescharacteristic
456C22×D3—101no—
457C3×Q8—21no—
458C3×Q8C2×D2012yes—
459C3×D4—22no—
460C3×D4—22no—
461C3×D4—21no—
462C3×D4C2×D2012yes—
463C2×C3×C4—24no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4C2×D2011yescharacteristic
469C2×C3×C4C2×D2011yescharacteristic
470C2×C3×C4D4×D511yescharacteristic
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4D4×D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474#67—108no—
475#67—102no—
476#67—102no—
477C2×Dic3—54no—
478C2×Dic3—108no—
479C2×Dic3—101no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—201no—
484C2×Dic3—201no—
485D12—52no—
486D12—101no—
487C4×D3—108no—
488C4×D3—102no—
489C4×D3—102no—
490Dic6—52no—
491Dic6—108no—
492Dic6—102no—
493Dic6—102no—
494Dic6—101no—
495Dic6—102no—
496Dic6—102no—
497Dic6—102no—
498Dic6—102no—
499Dic6—201no—
500Dic6—201no—
501C3×C8—22no—
502C3⋊C8—102no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—42no—
506C22×C5#88211yescharacteristic
507C22×C5#88211yescharacteristic
508C22×C5C2×D3×D411yescharacteristic
509C2×D5—62no—
510C2×D5—122no—
511C4×C5—24no—
512C4×C5—22no—
513C4×C5#88211yescharacteristic
514C4×C5#88211yescharacteristic
515C4×C5C22×D1211yescharacteristic
516C4×C5C2×D3×D411yescharacteristic
517Dic5—62no—
518Dic5—64no—
519Dic5—122no—
520#41—21no—
521#41—21no—
522#41—152no—
523#41—152no—
524#41—304no—
525#41—304no—
526#41—308no—
527#41—308no—
528#41—304no—
529#41—304no—
530#41—301no—
531#41—301no—
532#41D6012yes—
533#41C22×D1512yes—
534C2×Q8—152no—
535C2×Q8—152no—
536C2×Q8—151no—
537C2×Q8—152no—
538C2×Q8—304no—
539C2×Q8—302no—
540C2×Q8—304no—
541C2×Q8—304no—
542C2×Q8—304no—
543C2×Q8—301no—
544C2×Q8—301no—
545C2×Q8—301no—
546C2×Q8—301no—
547C2×Q8—301no—
548C2×Q8—301no—
549C2×Q8—301no—
550C2×Q8—301no—
551C2×Q8—301no—
552C2×Q8D6011yescharacteristic
553C2×D4—21no—
554C2×D4—151no—
555C2×D4—302no—
556C2×D4—301no—
557C2×D4D6011yescharacteristic
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—152no—
561C22×C4—302no—
562C22×C4—302no—
563C22×C4—301no—
564C22×C4—301no—
565C22×C4C22×D1511yescharacteristic
566Q16—304no—
567Q16—304no—
568SD16—304no—
569SD16—304no—
570M16—21no—
571M16—152no—
572M16—301no—
573M16C22×D1512yes—
574C2×C8—21no—
575C2×C8—301no—
576C4⋊C4—308no—
577C42—21no—
578C42C22×D1512yes—
579C3×C5C2×#45611yescharacteristic, complemented, Hall
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—42no—
583C22×C3#402811yescharacteristic
584C22×C3#402811yescharacteristic
585C22×C3C2×D4×D511yescharacteristic
586C2×D3—102no—
587C2×D3—202no—
588C3×C4—24no—
589C3×C4—22no—
590C3×C4#402811yescharacteristic
591C3×C4#402811yescharacteristic
592C3×C4C22×D2011yescharacteristic
593C3×C4C2×D4×D511yescharacteristic
594Dic3—102no—
595Dic3—104no—
596Dic3—202no—
597C2×C5—21no—
598C2×C5—21no—
599C2×C5—42no—
600C2×C5#482612yescomplemented
601C2×C5C2×#88211yescharacteristic
602D5—122no—
603C23—21no—
604C23—301no—
605C23D4×D1511yescharacteristic
606Q8—21no—
607Q8—152no—
608Q8—308no—
609Q8—302no—
610Q8—302no—
611Q8—301no—
612Q8—302no—
613Q8—302no—
614Q8—302no—
615Q8—302no—
616Q8—601no—
617Q8—601no—
618Q8C2×D6012yes—
619D4—22no—
620D4—22no—
621D4—21no—
622D4—152no—
623D4—308no—
624D4—302no—
625D4—302no—
626D4—301no—
627D4C2×D6012yes—
628C2×C4—24no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—154no—
634C2×C4—308no—
635C2×C4—308no—
636C2×C4—302no—
637C2×C4—302no—
638C2×C4—301no—
639C2×C4—302no—
640C2×C4—302no—
641C2×C4—302no—
642C2×C4—601no—
643C2×C4—601no—
644C2×C4C2×D6011yescharacteristic
645C2×C4C2×D6011yescharacteristic
646C2×C4D4×D1511yescharacteristic
647C2×C4D4×D1511yescharacteristic
648C2×C4D4×D1511yescharacteristic
649C2×C4C23×D1511yescharacteristic
650C8—22no—
651C8—302no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—42no—
655C2×C3#6511512yescomplemented
656C2×C3C2×#402811yescharacteristic
657D3—202no—
658C5C2×#482611yescharacteristic, complemented, Sylow
659C22—22no—
660C22—22no—
661C22—42no—
662C22—302no—
663C22—602no—
664C22#9177111yescharacteristic
665C22#9177111yescharacteristic
666C22C2×D4×D1511yescharacteristic
667C4—24no—
668C4—22no—
669C4—304no—
670C4—302no—
671C4—602no—
672C4#9177111yescharacteristic
673C4#9177111yescharacteristic
674C4C22×D6011yescharacteristic
675C4C2×D4×D1511yescharacteristic
676C3C2×#6511511yescharacteristic, complemented, Sylow
677C2—21no—
678C2—21no—
679C2—42no—
680C2—602no—
681C2#1175092712yesdirect product factor
682C2C2×#9177111yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×#92101C2
hypercenterC2×#104D15
hypocenterC3×C5C2×#456
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×#91758C2semidirect
5. C2×C3×C5×#104C2semidirect
6. C2×#91108C2semidirect
7. C2×#91089C2semidirect
8. #11750927C2direct (N × H)
26. #91840C22semidirect
32. #91798C22semidirect
36. #91758C22semidirect
37. C3×C5×#104C22semidirect
38. #91108C22semidirect
39. #91089C22semidirect
45. C2×C5×#104D3semidirect
112. C2×C3×#104D5semidirect
143. C5×#104C2×D3semidirect
223. C3×#104C2×D5semidirect
291. C2×#104D15semidirect
446. #104C2×D15semidirect
451. C2×C3×C5#456semidirect
579. C3×C5C2×#456semidirect
600. C2×C5#4826semidirect
655. C2×C3#65115semidirect
658. C5C2×#4826semidirect
676. C3C2×#65115semidirect
681. C2#11750927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921012
C2×#918402
C2×#917982
C2×#917582
C2×C3×C5×#1042
C2×#911082
C2×#910892
#117509272
C2×#651153
C2×#48265