Finite Group Databasebeta

← #14424161

Subgroups — #14424161

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×#91813C211yesmaximal, characteristic, complemented
3C2×#91313C212yesmaximal, complemented
4C5×#5207C211yesmaximal, characteristic, complemented
5#11748556C212yesmaximal, complemented
6#11748531C214yesmaximal, complemented
7#11748530C212yesmaximal, complemented
8#11748369C212yesmaximal, complemented
9#10610371—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×Dic30C2211yescharacteristic, complemented
12C22×C3×C22⋊D5—21no—
13C2×C3×#709—21no—
14C2×C3×#709—21no—
15C2×C3×#709—28no—
16C2×C3×#709C2212yes—
17C2×C3×#709C2212yes—
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5—21no—
20C22×C3×Dic10C2211yescharacteristic
21C2×#6719—21no—
22C2×C4⋊Dic15C2211yescharacteristic, complemented
23#91813—21no—
24#91813—21no—
25#91813C2212yes—
26#91813C2212yescomplemented
27C2×#6712—21no—
28C2×C5×#208C2212yescomplemented
29C2×#6662C2214yescomplemented
30#91313—28no—
31C2×#6657C2214yescomplemented
32C5×#830C2212yes—
33C5×#830C2212yescomplemented
34#90971C2214yescomplemented
35#90965C2214yescomplemented
36#84084—51nomaximal, Hall
37C22×#709D311yescharacteristic
38C2×#4070—31no—
39C2×#4055—32no—
40C5×#407—31no—
41#65422—32no—
42#65028—32no—
43#65022—34no—
44#65020—32no—
45C24×C3×C5D411yescharacteristic
46C23×C3×D5—21no—
47C22×C3×C4×C5—24no—
48C22×C3×C4×C5D411yescharacteristic
49C22×C3×C4×C5D411yescharacteristic
50C22×C3×C4×C5D411yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—21no—
55C22×Dic15—21no—
56C2×Dic30—24no—
57C2×Dic30—21no—
58C2×Dic30C2312yes—
59C2×C3×C22⋊D5—28no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C22×C3×Dic5—21no—
63C3×#709—28no—
64C3×#709—28no—
65C3×#709—24no—
66C3×#709—24no—
67C3×#709—24no—
68C3×#709D418yes—
69C2×C3×D20—21no—
70C2×C3×D20—24no—
71C2×C3×D20C2312yes—
72C2×C3×C4×D5—28no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×Dic10—21no—
76C2×C3×Dic10—24no—
77C2×C3×Dic10C2312yes—
78#6719—22no—
79#6719—22no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82#6712—22no—
83#6712—22no—
84C5×#208—24no—
85C2×C5×C3⋊C8C2314yes—
86#6662—28no—
87#6657—28no—
88C22×C3×#41—51no—
89C2×#951—52no—
90C2×#924—51no—
91#5239—54no—
92#5232—52no—
93#5228—52no—
94#5218—52no—
95#5207D511yescharacteristic, complemented
96C23×C4×C5C2×D311yescharacteristic
97C22×C22⋊D5—21no—
98C2×#709—21no—
99C2×#709—21no—
100C2×#709—28no—
101C2×#709C2×D312yes—
102C2×#709C2×D312yes—
103C22×D20C2×D311yescharacteristic
104C22×C4×D5—21no—
105C22×Dic10—31no—
106C22×Dic10C2×D311yescharacteristic
107C2×C5×M16—32no—
108C2×C22⋊Dic5—61no—
109C2×C4⋊Dic5—31no—
110#4070—32no—
111#4070—32no—
112#4070—61no—
113#4070—61no—
114C2×#683—61no—
115#4055—68no—
116C2×Dic20—34no—
117C2×#677—34no—
118C5×C22⋊C8—32no—
119C5×C22⋊C8—32no—
120#3953—34no—
121#3948—34no—
122#3007—151noSylow
123C23×C3×C5—22no—
124C23×C3×C5—22no—
125C23×C3×C5—41no—
126C23×C3×C5C2×D411yescharacteristic
127C23×C3×C5C2×D411yescharacteristic
128C23×C3×C5C2×D411yescharacteristic
129C22×C3×D5—24no—
130C22×C3×D5—22no—
131C22×C3×D5—42no—
132C22×C3×D5—42no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D414yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—42no—
146C2×Dic15—42no—
147Dic30—24no—
148Dic30—42no—
149C3×C22⋊D5—28no—
150C3×C22⋊D5—28no—
151C2×C3×Dic5—24no—
152C2×C3×Dic5—22no—
153C3×D20—24no—
154C3×D20—22no—
155C3×D20C2×D414yes—
156C3×C4×D5—28no—
157C3×C4×D5—28no—
158C3×Dic10—24no—
159C3×Dic10—22no—
160C3×Dic10C2×D414yes—
161C5×C3⋊C8—24no—
162C2×C3×#41—52no—
163C2×C3×#41—52no—
164C2×C3×#41—108no—
165C2×C3×#41—101no—
166C2×C3×#41—101no—
167C22×C3×Q8—51no—
168C22×C3×D4—51no—
169C22×C3×D4—101no—
170C23×C3×C4—101no—
171C23×C3×C4C2×D511yescharacteristic
172C22×Dic6—51no—
173C2×#217—101no—
174#951—108no—
175C2×#216—54no—
176C2×#214—54no—
177C2×C4⋊Dic3—51no—
178#924—52no—
179#924—52no—
180#924—101no—
181#924—101no—
182C2×Dic3⋊C4—101no—
183C2×#208C2×D512yescomplemented
184#835—54no—
185#832—54no—
186#830C2×D512yes—
187#830C2×D512yescomplemented
188C24×C5#6711yescharacteristic
189C23×D5—21no—
190C22×C4×C5—24no—
191C22×C4×C5#6711yescharacteristic
192C22×C4×C5#6711yescharacteristic
193C22×C4×C5#6711yescharacteristic
194C22×C4×C5C22×D311yescharacteristic
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—28no—
198C2×C22⋊D5—22no—
199C2×C22⋊D5—22no—
200C22×Dic5—21no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203#709—28no—
204#709—28no—
205#709—24no—
206#709—24no—
207#709—24no—
208#709#6718yes—
209C2×D20—21no—
210C2×D20—24no—
211C2×D20C22×D312yes—
212C2×C4×D5—28no—
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×Dic10—21no—
216C2×Dic10—24no—
217C2×Dic10—32no—
218C2×Dic10—64no—
219C2×Dic10—61no—
220C2×Dic10C22×D312yes—
221C5×M16—64no—
222C2×C5×C8—34no—
223C22⋊Dic5—62no—
224C22⋊Dic5—62no—
225C4⋊Dic5—32no—
226C4⋊Dic5—61no—
227#683—62no—
228#683—62no—
229Dic20—68no—
230#677—68no—
231C22×#41—51no—
232C2×#137—152no—
233C2×C22⋊Q8—151no—
234#452—154no—
235#451—152no—
236#450—152no—
237#417—152no—
238#407—31no—
239C22×C3×C5—21no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5—44no—
247C22×C3×C5#12012yes—
248C22×C3×C5#13712yescomplemented
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5—24no—
251C2×C3×D5—48no—
252C2×C3×D5—42no—
253C2×C3×D5—42no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5#12012yes—
257C3×C4×C5C22×D412yes—
258Dic15—42no—
259Dic15—42no—
260C3×Dic5—24no—
261C24×C3—101no—
262C24×C3D2011yescharacteristic
263C3×#41—58no—
264C3×#41—104no—
265C3×#41—104no—
266C3×#41—108no—
267C3×#41—108no—
268C3×#41—104no—
269C2×C3×Q8—52no—
270C2×C3×Q8—104no—
271C2×C3×Q8—101no—
272C2×C3×D4—52no—
273C2×C3×D4—104no—
274C2×C3×D4—108no—
275C2×C3×D4—102no—
276C2×C3×D4—102no—
277C2×C3×D4—101no—
278C22×C3×C4—24no—
279C22×C3×C4—108no—
280C22×C3×C4—101no—
281C22×C3×C4—102no—
282C22×C3×C4—102no—
283C22×C3×C4D2011yescharacteristic
284C22×C3×C4D2011yescharacteristic
285C22×C3×C4D2011yescharacteristic
286C22×C3×C4C22×D511yescharacteristic
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—101no—
290C22×Dic3—101no—
291C2×Dic6—52no—
292C2×Dic6—104no—
293C2×Dic6—101no—
294#217—102no—
295#217—102no—
296#216—108no—
297#214—108no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300Dic3⋊C4—102no—
301Dic3⋊C4—102no—
302#208—24no—
303C2×C3⋊C8C22×D514yes—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—41no—
307C23×C5C2×#6711yescharacteristic
308C23×C5C2×#6711yescharacteristic
309C23×C5C2×#6711yescharacteristic
310C22×D5—24no—
311C22×D5—22no—
312C22×D5—42no—
313C22×D5—42no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5C2×#6711yescharacteristic
320C2×C4×C5C2×#6711yescharacteristic
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C2×#6714yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—28no—
325C22⋊D5—28no—
326C2×Dic5—24no—
327C2×Dic5—22no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—122no—
331C2×Dic5—122no—
332D20—24no—
333D20—22no—
334D20C2×#6714yes—
335C4×D5—28no—
336C4×D5—28no—
337Dic10—24no—
338Dic10—22no—
339Dic10—64no—
340Dic10—122no—
341Dic10C2×#6714yes—
342C5×C8—64no—
343C2×#41—52no—
344C2×#41—52no—
345C2×#41—108no—
346C2×#41—101no—
347C2×#41—101no—
348C22×Q8—51no—
349C22×Q8—151no—
350C22×D4—51no—
351C22×D4—101no—
352C23×C4—101no—
353C23×C4D3×D511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—32no—
358C22⋊Q8—152no—
359C22⋊Q8—152no—
360C22⋊Q8—301no—
361C22⋊Q8—301no—
362C2×C4⋊C4—151no—
363C2×C4⋊C4—301no—
364C2×C22⋊C4—301no—
365#103—154no—
366#102—154no—
367C22⋊C8—32no—
368C22⋊C8—32no—
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5C2×#12011yescharacteristic
373C2×C3×C5C2×#13711yescharacteristic
374C2×C3×C5#57511yescharacteristic
375C3×D5—44no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—104no—
380C23×C3—102no—
381C23×C3—202no—
382C23×C3—202no—
383C23×C3C2×D2011yescharacteristic
384C23×C3C2×D2011yescharacteristic
385C23×C3C2×D2011yescharacteristic
386C3×Q8—54no—
387C3×Q8—104no—
388C3×Q8—102no—
389C3×D4—54no—
390C3×D4—104no—
391C3×D4—108no—
392C3×D4—108no—
393C3×D4—102no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—108no—
400C2×C3×C4—104no—
401C2×C3×C4—102no—
402C2×C3×C4—108no—
403C2×C3×C4C2×D2011yescharacteristic
404C2×C3×C4C2×D2011yescharacteristic
405C2×C3×C4C2×D2011yescharacteristic
406C2×C3×C4D4×D514yes—
407C2×C3×C4C23×D511yescharacteristic
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—202no—
411C2×Dic3—202no—
412Dic6—104no—
413Dic6—202no—
414C3⋊C8—24no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—44no—
423C22×C5#95112yescomplemented
424C22×C5#95312yes—
425C22×C5C22×#6711yescharacteristic
426C2×D5—24no—
427C2×D5—48no—
428C2×D5—42no—
429C2×D5—42no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5#95312yes—
433C4×C5C22×#6712yes—
434Dic5—24no—
435Dic5—122no—
436Dic5—122no—
437C24—101no—
438C24#120211yescharacteristic
439#41—58no—
440#41—104no—
441#41—104no—
442#41—108no—
443#41—108no—
444#41—104no—
445C2×Q8—52no—
446C2×Q8—104no—
447C2×Q8—101no—
448C2×Q8—152no—
449C2×Q8—301no—
450C2×Q8—304no—
451C2×D4—52no—
452C2×D4—104no—
453C2×D4—108no—
454C2×D4—102no—
455C2×D4—102no—
456C2×D4—101no—
457C22×C4—24no—
458C22×C4—108no—
459C22×C4—101no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—301no—
463C22×C4—301no—
464C22×C4#120211yescharacteristic
465C22×C4#120211yescharacteristic
466C22×C4#120211yescharacteristic
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470Q16—308no—
471SD16—308no—
472M16—64no—
473C2×C8—34no—
474C4⋊C4—152no—
475C4⋊C4—301no—
476C4⋊C4—302no—
477C4⋊C4—302no—
478C22⋊C4—302no—
479C22⋊C4—302no—
480C3×C5#300711yescharacteristic, complemented, Hall
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—44no—
489C22×C3—104no—
490C22×C3—208no—
491C22×C3—202no—
492C22×C3—202no—
493C22×C3#402812yes—
494C22×C3#405512yescomplemented
495C22×C3C22×D2011yescharacteristic
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—104no—
499C3×C4#402812yes—
500C3×C4C2×D4×D512yes—
501Dic3—202no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5#582211yescharacteristic
507C2×C5C2×#95111yescharacteristic
508C2×C5C2×#95311yescharacteristic
509D5—44no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—104no—
514C23—102no—
515C23—202no—
516C23—202no—
517C23C2×#120211yescharacteristic
518C23C2×#120211yescharacteristic
519C23C2×#120211yescharacteristic
520Q8—54no—
521Q8—104no—
522Q8—102no—
523Q8—304no—
524Q8—602no—
525D4—54no—
526D4—104no—
527D4—108no—
528D4—108no—
529D4—102no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—108no—
536C2×C4—104no—
537C2×C4—102no—
538C2×C4—108no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—602no—
542C2×C4—602no—
543C2×C4C2×#120211yescharacteristic
544C2×C4C2×#120211yescharacteristic
545C2×C4C2×#120211yescharacteristic
546C2×C4D5×#6714yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—64no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3—204no—
553C2×C3C2×#402811yescharacteristic
554C2×C3C2×#405511yescharacteristic
555C2×C3#6608211yescharacteristic
556C5#8408411yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—44no—
565C22—104no—
566C22—208no—
567C22—202no—
568C22—202no—
569C22#9131312yescomplemented
570C22#9156412yes—
571C22C22×#120211yescharacteristic
572C4—21no—
573C4—21no—
574C4—104no—
575C4—602no—
576C4—602no—
577C4#9156412yes—
578C4C2×D5×#6712yes—
579C3#1061037111yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—204no—
584C2C2×#9131311yescharacteristic
585C2#1175415411yescharacteristic
586C2C2×#9156411yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×#709C2
hypercenterC23×C4D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91813C2semidirect
3. C2×#91313C2semidirect
4. C5×#5207C2semidirect
5. #11748556C2semidirect
6. #11748531C2semidirect
7. #11748530C2semidirect
8. #11748369C2semidirect
11. C22×Dic30C22semidirect
22. C2×C4⋊Dic15C22semidirect
26. #91813C22semidirect
28. C2×C5×#208C22semidirect
29. C2×#6662C22semidirect
31. C2×#6657C22semidirect
33. C5×#830C22semidirect
34. #90971C22semidirect
35. #90965C22semidirect
95. #5207D5semidirect
183. C2×#208C2×D5semidirect
187. #830C2×D5semidirect
248. C22×C3×C5#137semidirect
423. C22×C5#951semidirect
480. C3×C5#3007semidirect
494. C22×C3#4055semidirect
556. C5#84084semidirect
569. C22#91313semidirect
579. C3#10610371semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×#918132
C2×#913132
C5×#52072
#117485562
#117485312
#117485302
#117483692
#106103713
#840845