Finite Group Databasebeta

← #14297331

Subgroups — #14297331

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4144C211yesmaximal, characteristic
2#11752428C212yesmaximal, complemented
3#11752426C212yesmaximal, complemented
4#11752420C211yesmaximal, characteristic, complemented
5#11752404C211yesmaximal, characteristic, complemented
6#10604929—31nomaximal, Hall
7C22×C3×C5×D4C411yescharacteristic, complemented
8C22×C3×C22⋊D5—21no—
9C22×C3×C22⋊D5—21no—
10C3×#4144—24no—
11C3×#4144—24no—
12C2×C3×#711—21no—
13C2×C3×#711C411yescharacteristic, complemented
14C2×C3×#711C2211yescharacteristic
15C2×C3×D4×D5—21no—
16C2×C3×D4×D5C411yescharacteristic, complemented
17C2×C3×D4×D5C2211yescharacteristic
18C2×C3×#709C411yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20#91989C2212yescomplemented
21D5⋊#208C2212yescomplemented
22#91242—21no—
23#91240—21no—
24#91237—24no—
25#91236—24no—
26#91234—21no—
27#91228—21no—
28#72141—51nomaximal, Hall
29C2×#4144D311yescharacteristic
30#65769—32no—
31#65767—32no—
32#65761—31no—
33#65745—31no—
34C24×C3×C5—21no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C411yescharacteristic
41C2×C3×C5×D4C2×C411yescharacteristic
42C22×C3×C4×C5C2×C411yescharacteristic
43C2×C3×C22⋊D5—28no—
44C2×C3×C22⋊D5—28no—
45C2×C3×C22⋊D5—21no—
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—21no—
48C2×C3×C22⋊D5—21no—
49C2×C3×C22⋊D5—21no—
50C2×C3×C22⋊D5D411yescharacteristic
51C2×C3×C22⋊D5D411yescharacteristic
52C22×C3×Dic5—21no—
53C22×C3×Dic5—21no—
54C3×#711—28no—
55C3×#711—22no—
56C3×#711—22no—
57C3×#711—22no—
58C3×#711D414yes—
59C3×D4×D5—28no—
60C3×D4×D5—22no—
61C3×D4×D5—22no—
62C3×D4×D5—22no—
63C3×D4×D5D414yes—
64C3×#709—22no—
65C3×#709—22no—
66C3×#709—22no—
67C3×#709—22no—
68C2×C3×D20C2×C411yescharacteristic
69C2×C3×D20D411yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5C2×C411yescharacteristic
72C2×C3×C4×D5C2311yescharacteristic
73C2×C3×Dic10C2×C411yescharacteristic
74C2×C3×Dic10D411yescharacteristic
75#6763—22no—
76#6762—22no—
77C4⋊ΓL(1,𝔽16)—22no—
78C4×ΓL(1,𝔽16)—22no—
79#6758—22no—
80D5⋊(C3⋊C8)—22no—
81C2×C3×H(5,𝔽2)—51no—
82#5240—51no—
83#5237—51no—
84#5236—52no—
85#5215—52no—
86C22×C5×D4Dic311yescharacteristic, complemented
87C22×C22⋊D5—21no—
88C22×C22⋊D5—21no—
89#4144—24no—
90#4144—24no—
91C2×#711—21no—
92C2×#711Dic311yescharacteristic, complemented
93C2×#711C2×D311yescharacteristic
94C2×D4×D5—21no—
95C2×D4×D5Dic311yescharacteristic, complemented
96C2×D4×D5C2×D311yescharacteristic
97C2×#709Dic311yescharacteristic, complemented
98C2×#709C2×D311yescharacteristic
99#4130—32no—
100D5⋊M16—32no—
101#4013—61no—
102#4011—61no—
103#4008—64no—
104#4007—64no—
105#4005—61no—
106#3999—61no—
107#1795—151noSylow
108C23×C3×C5—24no—
109C23×C3×C5—21no—
110C23×C3×C5—21no—
111C23×C3×C5—82no—
112C23×C3×C5C22⋊C411yescharacteristic
113C22×C3×D5—21no—
114C22×C3×D5—24no—
115C22×C3×D5—24no—
116C22×C3×D5—82no—
117C22×C3×D5—82no—
118C22×C3×D5C22⋊C411yescharacteristic
119C22×C3×D5C2×D411yescharacteristic
120C2×ΓL(1,𝔽16)—42no—
121C3×C5×D4—24no—
122C3×C5×D4—21no—
123C3×C5×D4—21no—
124C3×C5×D4C22⋊C412yes—
125C3×C5×D4C22⋊C412yes—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C22⋊C411yescharacteristic
129C2×C3×C4×C5C22×C411yescharacteristic
130C3×C22⋊D5—24no—
131C3×C22⋊D5—24no—
132C3×C22⋊D5—24no—
133C3×C22⋊D5—22no—
134C3×C22⋊D5—24no—
135C3×C22⋊D5—22no—
136C3×C22⋊D5—24no—
137C2×C3×Dic5—24no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—24no—
140C2×C3×Dic5C22⋊C411yescharacteristic
141C2×C3×Dic5C2×D411yescharacteristic
142C3×D20—22no—
143C3×D20—21no—
144C3×D20C22⋊C412yes—
145C3×C4×D5—24no—
146C3×C4×D5—21no—
147C3×C4×D5—21no—
148C3×C4×D5C2×D412yes—
149C3×C4×D5C2×D412yes—
150C3×Dic10—21no—
151C3×Dic10—22no—
152C3×Dic10C22⋊C412yes—
153C3⋊#170—42no—
154C3×H(5,𝔽2)—104no—
155C3×H(5,𝔽2)—104no—
156C2×C3×#41—51no—
157C2×C3×#41—51no—
158C2×C3×#41—51no—
159C2×C3×#41—51no—
160C2×C3×#41—101no—
161C22×C3×D4—51no—
162C22×C3×D4—51no—
163C22×C3×D4—101no—
164C22×C3×D4—101no—
165C22×C3×D4—101no—
166C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
167#926—52no—
168C2×#208—52no—
169#837—104no—
170#836—101no—
171#834—101no—
172#834—101no—
173#833—101no—
174#832—104no—
175C24×C5—21no—
176C23×D5—21no—
177C23×D5—21no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—21no—
181C2×C5×D4C2×Dic311yescharacteristic
182C2×C5×D4C2×Dic311yescharacteristic
183C22×C4×C5C2×Dic311yescharacteristic
184C2×C22⋊D5—28no—
185C2×C22⋊D5—28no—
186C2×C22⋊D5—21no—
187C2×C22⋊D5—21no—
188C2×C22⋊D5—21no—
189C2×C22⋊D5—21no—
190C2×C22⋊D5—21no—
191C2×C22⋊D5#6711yescharacteristic
192C2×C22⋊D5#6711yescharacteristic
193C22×Dic5—21no—
194C22×Dic5—21no—
195#711—28no—
196#711—22no—
197#711—22no—
198#711—22no—
199#711#6714yes—
200D4×D5—28no—
201D4×D5—22no—
202D4×D5—22no—
203D4×D5—22no—
204D4×D5#6714yes—
205#709—22no—
206#709—22no—
207#709—22no—
208#709—22no—
209C2×D20C2×Dic311yescharacteristic
210C2×D20#6711yescharacteristic
211C2×C4×D5—21no—
212C2×C4×D5C2×Dic311yescharacteristic
213C2×C4×D5C22×D311yescharacteristic
214C2×Dic10C2×Dic311yescharacteristic
215C2×Dic10#6711yescharacteristic
216C22⋊AGL(1,𝔽5)—62no—
217#704—62no—
218C4⋊AGL(1,𝔽5)—62no—
219C4×AGL(1,𝔽5)—62no—
220#700—62no—
221D5⋊C8—62no—
222C2×H(5,𝔽2)—51no—
223#421—152no—
224#418—152no—
225#413—151no—
226#410—151no—
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—21no—
230C22×C3×C5—41no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—84no—
234C22×C3×C5C2×C22⋊C411yescharacteristic
235C2×C3×D5—21no—
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—42no—
239C2×C3×D5—41no—
240C2×C3×D5—84no—
241C2×C3×D5—84no—
242C2×C3×D5#12012yes—
243ΓL(1,𝔽16)—82no—
244C3×C4×C5—21no—
245C3×C4×C5C2×C22⋊C411yescharacteristic
246C3×C4×C5C2×C22⋊C411yescharacteristic
247C3×Dic5—21no—
248C3×Dic5—22no—
249C3×Dic5#12012yes—
250C24×C3—21no—
251C24×C3—101no—
252C24×C3—101no—
253C3×#41—54no—
254C3×#41—102no—
255C3×#41—102no—
256C3×#41—102no—
257C3×#41—102no—
258C3×#41—102no—
259C3×#41—102no—
260C3×#41—108no—
261C3×#41—102no—
262C2×C3×Q8—51no—
263C2×C3×Q8—51no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—21no—
267C2×C3×D4—54no—
268C2×C3×D4—51no—
269C2×C3×D4—51no—
270C2×C3×D4—51no—
271C2×C3×D4—51no—
272C2×C3×D4—102no—
273C2×C3×D4—101no—
274C2×C3×D4—101no—
275C2×C3×D4—102no—
276C2×C3×D4—108no—
277C2×C3×D4—101no—
278C2×C3×D4—101no—
279C2×C3×D4—108no—
280C2×C3×D4—108no—
281C2×C3×D4—101no—
282C2×C3×D4—102no—
283C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
284C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
285C22×C3×C4—51no—
286C22×C3×C4—51no—
287C22×C3×C4—101no—
288C22×C3×C4—101no—
289C22×C3×C4—101no—
290C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
291#217—102no—
292C4⋊Dic3—102no—
293C4×Dic3—102no—
294#208—102no—
295#208—102no—
296C2×C3⋊C8—102no—
297C23×C5—24no—
298C23×C5—21no—
299C23×C5—21no—
300C23×C5—82no—
301C23×C5#21711yescharacteristic
302C22×D5—21no—
303C22×D5—24no—
304C22×D5—24no—
305C22×D5—82no—
306C22×D5—82no—
307C22×D5#21711yescharacteristic
308C22×D5C2×#6711yescharacteristic
309C2×AGL(1,𝔽5)—122no—
310C5×D4—24no—
311C5×D4—21no—
312C5×D4—21no—
313C5×D4#21712yes—
314C5×D4#21712yes—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5#21711yescharacteristic
318C2×C4×C5C22×Dic311yescharacteristic
319C22⋊D5—24no—
320C22⋊D5—24no—
321C22⋊D5—24no—
322C22⋊D5—22no—
323C22⋊D5—24no—
324C22⋊D5—22no—
325C22⋊D5—24no—
326C2×Dic5—24no—
327C2×Dic5—21no—
328C2×Dic5—24no—
329C2×Dic5#21711yescharacteristic
330C2×Dic5C2×#6711yescharacteristic
331D20—22no—
332D20—21no—
333D20#21712yes—
334C4×D5—24no—
335C4×D5—21no—
336C4×D5—21no—
337C4×D5C2×#6712yes—
338C4×D5C2×#6712yes—
339Dic10—21no—
340Dic10—22no—
341Dic10#21712yes—
342#170—122no—
343H(5,𝔽2)—104no—
344H(5,𝔽2)—104no—
345C2×#41—51no—
346C2×#41—51no—
347C2×#41—51no—
348C2×#41—51no—
349C2×#41—101no—
350C22×D4—51no—
351C22×D4—51no—
352C22×D4—101no—
353C22×D4—101no—
354C22×D4—101no—
355C22×D4ΓL(1,𝔽16)11yescharacteristic, complemented
356C2×M16—152no—
357#117—152no—
358#104—304no—
359#102—304no—
360#101—301no—
361#100—301no—
362#99—301no—
363#99—301no—
364C2×C3×C5—21no—
365C2×C3×C5—42no—
366C2×C3×C5—42no—
367C2×C3×C5—41no—
368C2×C3×C5#37911yescharacteristic
369C3×D5—22no—
370C3×D5—42no—
371C3×D5—41no—
372C23×C3—24no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—51no—
376C23×C3—51no—
377C23×C3—82no—
378C23×C3—104no—
379C23×C3—104no—
380C23×C3—101no—
381C23×C3—402no—
382C23×C3—402no—
383C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
384C3×Q8—52no—
385C3×Q8—102no—
386C3×Q8—101no—
387C3×D4—24no—
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—52no—
391C3×D4—102no—
392C3×D4—102no—
393C3×D4—104no—
394C3×D4—102no—
395C3×D4—104no—
396C3×D4—104no—
397C3×D4—104no—
398C3×D4—104no—
399C3×D4—101no—
400C3×D4C22⋊AGL(1,𝔽5)12yes—
401C3×D4C22⋊AGL(1,𝔽5)12yes—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—51no—
405C2×C3×C4—52no—
406C2×C3×C4—52no—
407C2×C3×C4—51no—
408C2×C3×C4—104no—
409C2×C3×C4—104no—
410C2×C3×C4—104no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4—101no—
414C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
415C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
416C2×Dic3—202no—
417C3⋊C8—202no—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—21no—
421C22×C5—41no—
422C22×C5—42no—
423C22×C5—42no—
424C22×C5—84no—
425C22×C5C2×#21711yescharacteristic
426C2×D5—21no—
427C2×D5—22no—
428C2×D5—41no—
429C2×D5—42no—
430C2×D5—41no—
431C2×D5—84no—
432C2×D5—84no—
433C2×D5#95312yes—
434AGL(1,𝔽5)—242no—
435C4×C5—21no—
436C4×C5C2×#21711yescharacteristic
437C4×C5C2×#21711yescharacteristic
438Dic5—21no—
439Dic5—22no—
440Dic5#95312yes—
441C24—21no—
442C24—101no—
443C24—101no—
444#41—54no—
445#41—102no—
446#41—102no—
447#41—102no—
448#41—102no—
449#41—102no—
450#41—102no—
451#41—108no—
452#41—102no—
453C2×Q8—51no—
454C2×Q8—51no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—54no—
459C2×D4—51no—
460C2×D4—51no—
461C2×D4—51no—
462C2×D4—51no—
463C2×D4—102no—
464C2×D4—101no—
465C2×D4—101no—
466C2×D4—102no—
467C2×D4—108no—
468C2×D4—101no—
469C2×D4—101no—
470C2×D4—108no—
471C2×D4—108no—
472C2×D4—101no—
473C2×D4—102no—
474C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
475C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
482M16—302no—
483M16—302no—
484C2×C8—302no—
485C4⋊C4—302no—
486C22⋊C4—302no—
487C42—302no—
488C3×C5#179511yescharacteristic, complemented, Hall
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—52no—
496C22×C3—84no—
497C22×C3—102no—
498C22×C3—101no—
499C22×C3—201no—
500C22×C3—201no—
501C22×C3—202no—
502C22×C3—404no—
503C22×C3—404no—
504C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
505C3×C4—21no—
506C3×C4—52no—
507C3×C4—101no—
508C3×C4—102no—
509C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
510C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
511Dic3—402no—
512C2×C5—21no—
513C2×C5—42no—
514C2×C5—42no—
515C2×C5—41no—
516C2×C5#524711yescharacteristic
517D5—22no—
518D5—42no—
519D5—41no—
520C23—24no—
521C23—21no—
522C23—21no—
523C23—51no—
524C23—51no—
525C23—82no—
526C23—104no—
527C23—104no—
528C23—101no—
529C23—402no—
530C23—402no—
531C23#676311yescharacteristic
532Q8—52no—
533Q8—102no—
534Q8—101no—
535D4—24no—
536D4—21no—
537D4—21no—
538D4—52no—
539D4—102no—
540D4—102no—
541D4—104no—
542D4—102no—
543D4—104no—
544D4—104no—
545D4—104no—
546D4—104no—
547D4—101no—
548D4#676312yes—
549D4#676312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—51no—
553C2×C4—52no—
554C2×C4—52no—
555C2×C4—51no—
556C2×C4—104no—
557C2×C4—104no—
558C2×C4—104no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—602no—
563C2×C4#676311yescharacteristic
564C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
565C8—602no—
566C2×C3—21no—
567C2×C3—42no—
568C2×C3—42no—
569C2×C3—41no—
570C2×C3—102no—
571C2×C3—202no—
572C2×C3—201no—
573C2×C3#6580011yescharacteristic
574C5#7214111yescharacteristic, complemented, Sylow
575C22—21no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—42no—
580C22—42no—
581C22—52no—
582C22—84no—
583C22—102no—
584C22—101no—
585C22—201no—
586C22—201no—
587C22—202no—
588C22—404no—
589C22—404no—
590C22C2×#676311yescharacteristic
591C4—21no—
592C4—52no—
593C4—101no—
594C4—102no—
595C4—1202no—
596C4C2×#676311yescharacteristic
597C4C2×#676311yescharacteristic
598C3#1060492911yescharacteristic, complemented, Sylow
599C2—21no—
600C2—42no—
601C2—42no—
602C2—41no—
603C2—102no—
604C2—202no—
605C2—201no—
606C2#1175245911yescharacteristic
subgroupG/H
centerC2#11752459
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC2×C3×C5#379
prime radicalC2×C3×#4144C2
cosocleC2×C3×C4×D5C23
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5#1795
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11752428C2semidirect
3. #11752426C2semidirect
4. #11752420C2semidirect
5. #11752404C2semidirect
7. C22×C3×C5×D4C4semidirect
13. C2×C3×#711C4semidirect
16. C2×C3×D4×D5C4semidirect
18. C2×C3×#709C4semidirect
20. #91989C22semidirect
21. D5⋊#208C22semidirect
86. C22×C5×D4Dic3semidirect
92. C2×#711Dic3semidirect
95. C2×D4×D5Dic3semidirect
97. C2×#709Dic3semidirect
166. C22×C3×D4AGL(1,𝔽5)semidirect
355. C22×D4ΓL(1,𝔽16)semidirect
488. C3×C5#1795semidirect
574. C5#72141semidirect
598. C3#10604929semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41442
#117524282
#117524262
#117524202
#117524042
#106049293
#721415