Finite Group Databasebeta

← C2×#11751863 #14411956

Subgroups — C2×#11751863 #14411956

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6766C211yesmaximal, characteristic
2C2×#91923C212yesmaximal, complemented
3C2×#91228C211yesmaximal, characteristic, complemented
4C2×C3×#3999C211yesmaximal, characteristic, complemented
5C2×#91173C212yesmaximal, complemented
6#11751863C218yesmaximal, direct product factor
7C2×#65785—31nomaximal, Hall
8C22×C4×D15C411yescharacteristic, complemented
9C22×C5×Dic6C411yescharacteristic, complemented
10C22×C3×D20C2211yescharacteristic
11C22×#1202C411yescharacteristic, complemented
12C22×#1202C2211yescharacteristic
13C22×D5×Dic3C411yescharacteristic, complemented
14C22×D5×Dic3C2211yescharacteristic
15C2×#6766—22no—
16C2×#6766—24no—
17C2×#6766—22no—
18C2×#6766C414yescomplemented
19C2×#6766C2214yes—
20C2×#6763C2212yes—
21C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)—22no—
23#91923—24no—
24#91923C2218yescomplemented
25C2×Dic3×AGL(1,𝔽5)—22no—
26#91228C2214yescomplemented
27C3×#3999C2214yescomplemented
28#91173C2218yescomplemented
29C2×#4740—51nomaximal, Hall
30C22×#713—31no—
31C2×#4130—32no—
32#65785—38no—
33C2×#3999—31no—
34C2×#3999—32no—
35C2×#3999D311yescharacteristic, complemented
36C23×D15C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C23×C3×D5C2311yescharacteristic
39C22×ΓL(1,𝔽16)—22no—
40C22×C3×AGL(1,𝔽5)—22no—
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×Dic15C2×C411yescharacteristic
43C2×C4×D15—22no—
44C2×C4×D15—21no—
45C2×C4×D15—21no—
46C2×C4×D15C2×C414yescomplemented
47C22×C5×Dic3C2×C411yescharacteristic
48C22×C5×Dic3C2×C411yescharacteristic
49C2×C5×Dic6—22no—
50C2×C5×Dic6—22no—
51C2×C5×Dic6C2×C414yescomplemented
52C2×C3×D20—22no—
53C2×C3×D20—22no—
54C2×C3×D20C2×C412yes—
55C2×C3×D20C2312yes—
56C2×#1202—22no—
57C2×#1202—22no—
58C2×#1202—22no—
59C2×#1202—22no—
60C2×#1202C2×C412yes—
61C2×#1202C2×C414yescomplemented
62C2×#1202C2312yes—
63C2×D5×Dic3—22no—
64C2×D5×Dic3—21no—
65C2×D5×Dic3—21no—
66C2×D5×Dic3C2×C412yes—
67C2×D5×Dic3C2×C414yescomplemented
68C2×D5×Dic3D412yes—
69C2×D5×Dic3D414yes—
70C2×D5×Dic3D412yes—
71C2×D5×Dic3C2312yes—
72#6766—28no—
73#6766—28no—
74#6766—28no—
75#6766—28no—
76#6763—22no—
77#6763C2314yes—
78C3×C22⋊AGL(1,𝔽5)—22no—
79C3×C22⋊AGL(1,𝔽5)C2314yes—
80Dic3⋊AGL(1,𝔽5)—28no—
81Dic3×AGL(1,𝔽5)—28no—
82C22×#237—51no—
83C2×#877—52no—
84C2×C3×#99—51no—
85C2×#834—51no—
86C2×#806—52no—
87#4740—58no—
88C22×C5×Q8—31no—
89C2×#713—34no—
90C2×#713—34no—
91C2×#713—62no—
92C2×#713—62no—
93C2×#713—64no—
94C22×D20—31no—
95C22×D20—31no—
96C22×D20C2×D311yescharacteristic
97C22×C4×D5—31no—
98C22×C4×D5—31no—
99C22×C4×D5—31no—
100C2×C22⋊AGL(1,𝔽5)—32no—
101C2×C22⋊AGL(1,𝔽5)C2×D312yes—
102#4130—38no—
103#4130—64no—
104C2×C4⋊AGL(1,𝔽5)—62no—
105C2×C4×AGL(1,𝔽5)—62no—
106#3999—34no—
107#3999—38no—
108#3999C2×D314yescomplemented
109C2×#410—151noSylow
110C23×C3×C5C22×C411yescharacteristic
111C22×D15—21no—
112C22×D15—21no—
113C22×D15—42no—
114C22×D15C22×C412yes—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—42no—
118C22×C3×D5—42no—
119C22×C3×D5C22×C412yes—
120C22×C3×D5C22×C411yescharacteristic
121C22×C3×D5C2×D412yes—
122C22×C3×D5C2×D412yes—
123C22×C3×D5C2411yescharacteristic
124C2×ΓL(1,𝔽16)—24no—
125C2×ΓL(1,𝔽16)—44no—
126C2×C3×AGL(1,𝔽5)—24no—
127C2×C3×AGL(1,𝔽5)—44no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15C22⋊C412yes—
132C2×Dic15C22⋊C411yescharacteristic
133C2×Dic15C22⋊C411yescharacteristic
134C2×Dic15C22×C412yes—
135C4×D15—24no—
136C4×D15—24no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3C22⋊C412yes—
140C2×C5×Dic3C22⋊C412yes—
141C2×C5×Dic3C22×C412yes—
142C2×C5×Dic3C22×C412yes—
143C5×Dic6—28no—
144C3×D20—24no—
145C3×D20—24no—
146#1202—24no—
147#1202—24no—
148#1202—28no—
149D5×Dic3—24no—
150D5×Dic3—24no—
151D5×Dic3C22⋊C414yes—
152D5×Dic3C22⋊C414yes—
153D5×Dic3C2×D414yes—
154D5×Dic3C2×D414yes—
155C22×C3×D4—51no—
156C22×#67—51no—
157C22×#67—51no—
158C23×Dic3—51no—
159C23×Dic3—51no—
160C2×#237—54no—
161C2×#237—54no—
162C2×#237—104no—
163C2×#237—102no—
164C2×#237—102no—
165C22×C4×D3—51no—
166C22×Dic6AGL(1,𝔽5)11yescharacteristic, complemented
167C2×C3×C22⋊C4—52no—
168C2×#217—52no—
169C2×Dic3⋊C4—102no—
170C2×C4×Dic3—102no—
171#877—58no—
172#877—104no—
173C3×#99—54no—
174#834—54no—
175#806—58no—
176C23×D5—31no—
177C23×D5C4×D311yescharacteristic
178C23×D5C22×D311yescharacteristic
179C22×AGL(1,𝔽5)—22no—
180C22×AGL(1,𝔽5)—62no—
181C2×C5×Q8—34no—
182C2×C5×Q8—62no—
183C2×C5×Q8—62no—
184C22×C4×C5—31no—
185C22×C4×C5—31no—
186C22×C4×C5C4×D311yescharacteristic
187C22×Dic5—31no—
188#713—68no—
189#713—68no—
190#713—68no—
191#713—68no—
192C2×D20—22no—
193C2×D20—22no—
194C2×D20—32no—
195C2×D20—34no—
196C2×D20—32no—
197C2×D20—62no—
198C2×D20—62no—
199C2×D20—62no—
200C2×D20—62no—
201C2×D20C4×D312yes—
202C2×D20C22×D312yes—
203C2×C4×D5—32no—
204C2×C4×D5—32no—
205C2×C4×D5—32no—
206C2×C4×D5—34no—
207C2×C4×D5—32no—
208C2×C4×D5—34no—
209C2×C4×D5—34no—
210C2×C4×D5—62no—
211C2×C4×D5—61no—
212C2×C4×D5—61no—
213C2×C4×D5—62no—
214C2×C4×D5—61no—
215C2×C4×D5—61no—
216C22⋊AGL(1,𝔽5)—22no—
217C22⋊AGL(1,𝔽5)—34no—
218C22⋊AGL(1,𝔽5)—62no—
219C22⋊AGL(1,𝔽5)C22×D314yes—
220C4⋊AGL(1,𝔽5)—68no—
221C4×AGL(1,𝔽5)—68no—
222C22×#41—151no—
223C2×#117—152no—
224#410—158no—
225C2×#99—51no—
226C2×#99—152no—
227C2×#99—151no—
228C22×C3×C5—22no—
229C22×C3×C5C2×C22⋊C411yescharacteristic
230C22×C3×C5C2×C22⋊C411yescharacteristic
231C22×C3×C5C23×C411yescharacteristic
232C2×D15—22no—
233C2×D15—42no—
234C2×D15—42no—
235C2×D15—42no—
236C2×C3×D5—24no—
237C2×C3×D5—22no—
238C2×C3×D5—41no—
239C2×C3×D5—42no—
240C2×C3×D5—41no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5C2×C22⋊C412yes—
245C2×C3×D5C22×D412yes—
246ΓL(1,𝔽16)—44no—
247C3×AGL(1,𝔽5)—44no—
248C3×C4×C5—22no—
249Dic15C2×C22⋊C412yes—
250Dic15C2×C22⋊C412yes—
251C5×Dic3—22no—
252C5×Dic3C2×C22⋊C414yes—
253C24×C3—51no—
254C24×C3—51no—
255C23×D3—51no—
256C2×C3×D4—52no—
257C2×C3×D4—52no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C22×C3×C4—102no—
261C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
262C2×#67—52no—
263C2×#67—52no—
264C2×#67—54no—
265C2×#67—102no—
266C2×#67—102no—
267C2×#67—102no—
268C2×#67—102no—
269C22×Dic3—51no—
270C22×Dic3—54no—
271C22×Dic3—52no—
272C22×Dic3—52no—
273C22×Dic3—52no—
274C22×Dic3—52no—
275C22×Dic3—54no—
276C22×Dic3—102no—
277C22×Dic3—101no—
278C22×Dic3—101no—
279C22×Dic3—102no—
280C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
281C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
282#237—108no—
283#237—108no—
284#237—108no—
285#237—108no—
286C2×C4×D3—54no—
287C2×C4×D3—102no—
288C2×C4×D3—101no—
289C2×C4×D3—101no—
290C2×Dic6—22no—
291C2×Dic6—22no—
292C2×Dic6C2×AGL(1,𝔽5)14yescomplemented
293C3×C22⋊C4—54no—
294C3×C22⋊C4—102no—
295#217—54no—
296#217—102no—
297Dic3⋊C4—108no—
298C4×Dic3—108no—
299C23×C5C2×C4×D311yescharacteristic
300C22×D5—21no—
301C22×D5—21no—
302C22×D5—32no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—61no—
306C22×D5—61no—
307C22×D5—122no—
308C22×D5C2×C4×D312yes—
309C22×D5C2×C4×D311yescharacteristic
310C22×D5D3×D412yes—
311C22×D5D3×D412yes—
312C22×D5C23×D311yescharacteristic
313C2×AGL(1,𝔽5)—24no—
314C2×AGL(1,𝔽5)—44no—
315C2×AGL(1,𝔽5)—64no—
316C2×AGL(1,𝔽5)—124no—
317C5×Q8—68no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—32no—
321C2×C4×C5—32no—
322C2×C4×C5—32no—
323C2×C4×C5—32no—
324C2×C4×C5—61no—
325C2×C4×C5—61no—
326C2×C4×C5C2×C4×D312yes—
327C2×Dic5—32no—
328C2×Dic5—31no—
329C2×Dic5—31no—
330C2×Dic5—32no—
331D20—24no—
332D20—24no—
333D20—68no—
334D20—64no—
335D20—64no—
336C4×D5—34no—
337C4×D5—34no—
338C4×D5—34no—
339C4×D5—34no—
340C4×D5—64no—
341C4×D5—64no—
342C4×D5—64no—
343C4×D5—64no—
344C2×#41—154no—
345C2×#41—154no—
346C2×#41—302no—
347C2×#41—302no—
348C2×#41—304no—
349C22×Q8—31no—
350C22×D4—51no—
351C22×D4—151no—
352C22×D4—151no—
353C23×C4—151no—
354C23×C4—151no—
355C23×C4—151no—
356#117—158no—
357#117—304no—
358C2×C4⋊C4—302no—
359C2×C22⋊C4—52no—
360C2×C22⋊C4—152no—
361C2×C42—302no—
362#99—54no—
363#99—158no—
364#99—154no—
365C2×C3×C5—21no—
366C2×C3×C5—21no—
367C2×C3×C5#41012yescomplemented
368C2×C3×C5C22×C22⋊C411yescharacteristic
369D15—42no—
370C3×D5—22no—
371C3×D5—22no—
372C3×D5—42no—
373C23×C3—52no—
374C23×C3—52no—
375C23×C3—51no—
376C23×C3—51no—
377C23×C3—52no—
378C23×C3—101no—
379C23×C3—101no—
380C23×C3—202no—
381C23×C3—202no—
382C23×C3C22×AGL(1,𝔽5)11yescharacteristic
383C22×D3—52no—
384C22×D3—101no—
385C22×D3—101no—
386C22×D3—202no—
387C3×D4—104no—
388C3×D4—104no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—104no—
392C2×C3×C4—204no—
393C2×C3×C4C22×AGL(1,𝔽5)12yes—
394#67—104no—
395#67—104no—
396#67—108no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—52no—
400C2×Dic3—51no—
401C2×Dic3—51no—
402C2×Dic3—52no—
403C2×Dic3—54no—
404C2×Dic3—54no—
405C2×Dic3—54no—
406C2×Dic3—54no—
407C2×Dic3—104no—
408C2×Dic3—104no—
409C2×Dic3—104no—
410C2×Dic3—204no—
411C2×Dic3C22⋊AGL(1,𝔽5)12yes—
412C2×Dic3C22⋊AGL(1,𝔽5)12yes—
413C2×Dic3C22×AGL(1,𝔽5)12yes—
414C2×Dic3C22×AGL(1,𝔽5)12yes—
415C4×D3—104no—
416C4×D3—104no—
417Dic6—28no—
418C22×C5—22no—
419C22×C5D3×C22⋊C411yescharacteristic
420C22×C5D3×C22⋊C411yescharacteristic
421C22×C5C22×C4×D311yescharacteristic
422C2×D5—24no—
423C2×D5—22no—
424C2×D5—41no—
425C2×D5—42no—
426C2×D5—41no—
427C2×D5—42no—
428C2×D5—42no—
429C2×D5—42no—
430C2×D5—62no—
431C2×D5—122no—
432C2×D5—122no—
433C2×D5—122no—
434C2×D5D3×C22⋊C412yes—
435C2×D5C2×D3×D412yes—
436AGL(1,𝔽5)—44no—
437AGL(1,𝔽5)—124no—
438C4×C5—22no—
439C4×C5—34no—
440C4×C5—62no—
441Dic5—32no—
442Dic5—32no—
443C24—51no—
444C24—51no—
445C24—151no—
446#41—308no—
447#41—308no—
448#41—308no—
449#41—308no—
450C2×Q8—34no—
451C2×Q8—62no—
452C2×Q8—62no—
453C2×D4—52no—
454C2×D4—52no—
455C2×D4—102no—
456C2×D4—102no—
457C2×D4—152no—
458C2×D4—154no—
459C2×D4—152no—
460C2×D4—302no—
461C2×D4—302no—
462C2×D4—302no—
463C2×D4—302no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—102no—
467C22×C4—152no—
468C22×C4—152no—
469C22×C4—152no—
470C22×C4—154no—
471C22×C4—152no—
472C22×C4—154no—
473C22×C4—151no—
474C22×C4—154no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4—301no—
478C22×C4—302no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4—302no—
482C22×C4D3×AGL(1,𝔽5)11yescharacteristic
483C4⋊C4—308no—
484C22⋊C4—54no—
485C22⋊C4—102no—
486C22⋊C4—154no—
487C22⋊C4—302no—
488C42—308no—
489C3×C5C2×#41011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—52no—
492C22×C3—52no—
493C22×C3—104no—
494C22×C3—102no—
495C22×C3—202no—
496C22×C3—201no—
497C22×C3—201no—
498C22×C3—202no—
499C22×C3—202no—
500C22×C3—202no—
501C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
502C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
503C22×C3C23×AGL(1,𝔽5)11yescharacteristic
504C2×D3—102no—
505C2×D3—202no—
506C2×D3—202no—
507C2×D3—202no—
508C3×C4—22no—
509C3×C4—204no—
510Dic3—22no—
511Dic3—52no—
512Dic3—52no—
513Dic3—204no—
514Dic3C2×C22⋊AGL(1,𝔽5)14yes—
515C2×C5—21no—
516C2×C5—21no—
517C2×C5#474012yescomplemented
518C2×C5C2×D3×C22⋊C411yescharacteristic
519D5—22no—
520D5—22no—
521D5—42no—
522D5—122no—
523C23—52no—
524C23—52no—
525C23—51no—
526C23—51no—
527C23—52no—
528C23—101no—
529C23—101no—
530C23—152no—
531C23—202no—
532C23—202no—
533C23—301no—
534C23—301no—
535C23—602no—
536C23C2×D3×AGL(1,𝔽5)11yescharacteristic
537Q8—68no—
538D4—104no—
539D4—104no—
540D4—308no—
541D4—304no—
542D4—304no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—104no—
552C2×C4—154no—
553C2×C4—154no—
554C2×C4—154no—
555C2×C4—154no—
556C2×C4—152no—
557C2×C4—151no—
558C2×C4—151no—
559C2×C4—152no—
560C2×C4—204no—
561C2×C4—304no—
562C2×C4—304no—
563C2×C4—304no—
564C2×C4—304no—
565C2×C4—304no—
566C2×C4—604no—
567C2×C4C2×D3×AGL(1,𝔽5)12yes—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—102no—
571C2×C3—102no—
572C2×C3—202no—
573C2×C3#6578512yescomplemented
574C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
575D3—202no—
576C5C2×#474011yescharacteristic, complemented, Sylow
577C22—22no—
578C22—52no—
579C22—52no—
580C22—104no—
581C22—102no—
582C22—202no—
583C22—201no—
584C22—201no—
585C22—202no—
586C22—202no—
587C22—202no—
588C22—302no—
589C22—602no—
590C22—602no—
591C22—602no—
592C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
593C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
594C22C22×D3×AGL(1,𝔽5)11yescharacteristic
595C4—22no—
596C4—34no—
597C4—62no—
598C4—152no—
599C4—152no—
600C4—204no—
601C4—604no—
602C3C2×#6578511yescharacteristic, complemented, Sylow
603C2—21no—
604C2—21no—
605C2—102no—
606C2—102no—
607C2—202no—
608C2—602no—
609C2#1175186312yesdirect product factor
610C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6766C2
cosocleC22×C3×D5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91923C2semidirect
3. C2×#91228C2semidirect
4. C2×C3×#3999C2semidirect
5. C2×#91173C2semidirect
6. #11751863C2direct (N × H)
8. C22×C4×D15C4semidirect
9. C22×C5×Dic6C4semidirect
11. C22×#1202C4semidirect
13. C22×D5×Dic3C4semidirect
18. C2×#6766C4semidirect
24. #91923C22semidirect
26. #91228C22semidirect
27. C3×#3999C22semidirect
28. #91173C22semidirect
35. C2×#3999D3semidirect
46. C2×C4×D15C2×C4semidirect
51. C2×C5×Dic6C2×C4semidirect
61. C2×#1202C2×C4semidirect
67. C2×D5×Dic3C2×C4semidirect
108. #3999C2×D3semidirect
166. C22×Dic6AGL(1,𝔽5)semidirect
292. C2×Dic6C2×AGL(1,𝔽5)semidirect
367. C2×C3×C5#410semidirect
489. C3×C5C2×#410semidirect
517. C2×C5#4740semidirect
573. C2×C3#65785semidirect
576. C5C2×#4740semidirect
602. C3C2×#65785semidirect
609. C2#11751863direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67662
C2×#919232
C2×#912282
C2×C3×#39992
C2×#911732
#117518632
C2×#657853
C2×#47405