Finite Group Databasebeta

← #14424110

Subgroups — #14424110

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×C5×#41C211yesmaximal, characteristic
2C2×#91840C212yesmaximal, complemented
3C2×#91813C211yesmaximal, characteristic, complemented
4#11751340C214yesmaximal, complemented
5#11751333C212yesmaximal, complemented
6#11751329C212yesmaximal, complemented
7#11751319C212yesmaximal, complemented
8#11751308C211yesmaximal, characteristic, complemented
9#10615815—31nomaximal, Hall
10C2×C3×C5×#41—28no—
11C2×C3×C5×#41—21no—
12C2×C3×C5×#41—21no—
13C2×C3×C5×#41C2212yes—
14C2×C3×C5×#41C2212yes—
15C22×C3×C5×Q8C2211yescharacteristic
16C22×C3×C5×D4—21no—
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5—21no—
19C23×C3×C4×C5C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C2×#6719—21no—
22#91840—28no—
23C2×#6718C2214yescomplemented
24C2×#6716C2214yescomplemented
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26#91813—21no—
27#91813—21no—
28#91813C2212yes—
29#91813C2212yescomplemented
30C2×#6712—21no—
31C2×#6710C2212yescomplemented
32#91119C2214yescomplemented
33#91116C2214yescomplemented
34#91114C2212yes—
35#91114C2212yescomplemented
36#84084—51nomaximal, Hall
37C22×C5×#41D311yescharacteristic
38C2×#4097—32no—
39C2×#4070—31no—
40#65528—34no—
41#65521—32no—
42#65517—32no—
43#65507—32no—
44#65496—31no—
45C24×C3×C5—21no—
46C24×C3×C5D411yescharacteristic
47C3×C5×#41—28no—
48C3×C5×#41—28no—
49C3×C5×#41—24no—
50C3×C5×#41—24no—
51C3×C5×#41—24no—
52C3×C5×#41D418yes—
53C2×C3×C5×Q8—24no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56C2×C3×C5×D4—28no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—24no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5—28no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—22no—
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5D411yescharacteristic
68C22×C3×C4×C5D411yescharacteristic
69C22×C3×C4×C5D411yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×Dic15—21no—
74C22×Dic15—21no—
75C2×Dic30—24no—
76C2×Dic30—21no—
77C2×Dic30C2312yes—
78#6719—22no—
79#6719—22no—
80#6718—28no—
81#6716—28no—
82C4⋊Dic15—21no—
83C4⋊Dic15C2312yes—
84#6712—22no—
85#6712—22no—
86#6710—24no—
87C2×C3⋊#168C2314yes—
88C22×C3×#41D511yescharacteristic
89C2×#951—52no—
90C2×#924—51no—
91#5239—54no—
92#5232—52no—
93#5228—52no—
94#5218—52no—
95#5207—51no—
96C2×C5×#41—28no—
97C2×C5×#41—21no—
98C2×C5×#41—21no—
99C2×C5×#41C2×D312yes—
100C2×C5×#41C2×D312yes—
101C22×C5×Q8C2×D311yescharacteristic
102C22×C5×D4—21no—
103C22×C5×D4C2×D311yescharacteristic
104C23×C4×C5—21no—
105C23×C4×C5C2×D311yescharacteristic
106C22×Dic10—31no—
107C2×C22⋊Dic5—61no—
108#4097—68no—
109C2×#689—34no—
110C2×#687—34no—
111C2×C4⋊Dic5—31no—
112#4070—32no—
113#4070—32no—
114#4070—61no—
115#4070—61no—
116C2×#683—61no—
117C2×#681—32no—
118#3967—34no—
119#3964—34no—
120C22⋊#168—32no—
121C22⋊#168—32no—
122#3007—151noSylow
123C23×C3×C5—24no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—41no—
128C23×C3×C5—42no—
129C23×C3×C5—42no—
130C23×C3×C5C2×D411yescharacteristic
131C23×C3×C5C2×D411yescharacteristic
132C23×C3×C5C2×D411yescharacteristic
133C3×C5×Q8—24no—
134C3×C5×Q8—22no—
135C3×C5×Q8C2×D414yes—
136C3×C5×D4—28no—
137C3×C5×D4—24no—
138C3×C5×D4—28no—
139C3×C5×D4—22no—
140C3×C5×D4C2×D414yes—
141C2×C3×C4×C5—24no—
142C2×C3×C4×C5—28no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—28no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D414yes—
154C2×C3×C4×C5C2411yescharacteristic
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—42no—
158C2×Dic15—42no—
159Dic30—24no—
160Dic30—42no—
161C3⋊#168—24no—
162C2×C3×#41—28no—
163C2×C3×#41—21no—
164C2×C3×#41—21no—
165C2×C3×#41C2×D512yes—
166C2×C3×#41C2×D512yes—
167C22×C3×Q8C2×D511yescharacteristic
168C22×C3×D4—21no—
169C22×C3×D4C2×D511yescharacteristic
170C23×C3×C4—21no—
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×#208—52no—
184#835—54no—
185#832—54no—
186#830—52no—
187#830—52no—
188C24×C5—21no—
189C24×C5#6711yescharacteristic
190C5×#41—28no—
191C5×#41—28no—
192C5×#41—24no—
193C5×#41—24no—
194C5×#41—24no—
195C5×#41#6718yes—
196C2×C5×Q8—24no—
197C2×C5×Q8—21no—
198C2×C5×Q8C22×D312yes—
199C2×C5×D4—28no—
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4C22×D312yes—
205C22×C4×C5—28no—
206C22×C4×C5—21no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—24no—
210C22×C4×C5#6711yescharacteristic
211C22×C4×C5#6711yescharacteristic
212C22×C4×C5#6711yescharacteristic
213C22×C4×C5C22×D311yescharacteristic
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D311yescharacteristic
216C22×Dic5—61no—
217C22×Dic5—61no—
218C2×Dic10—32no—
219C2×Dic10—64no—
220C2×Dic10—61no—
221C22⋊Dic5—62no—
222C22⋊Dic5—62no—
223#689—68no—
224#687—68no—
225C4⋊Dic5—32no—
226C4⋊Dic5—61no—
227#683—62no—
228#683—62no—
229#681—64no—
230C2×#168—34no—
231C22×#41D1511yescharacteristic
232C2×#137—152no—
233C2×C22⋊Q8—151no—
234#452—154no—
235#451—152no—
236#450—152no—
237#417—152no—
238#407—151no—
239C22×C3×C5—21no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—21no—
243C22×C3×C5—21no—
244C22×C3×C5—24no—
245C22×C3×C5—21no—
246C22×C3×C5—21no—
247C22×C3×C5—44no—
248C22×C3×C5—48no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5#12012yes—
252C22×C3×C5#13712yescomplemented
253C22×C3×C5C22×D411yescharacteristic
254C3×C4×C5—21no—
255C3×C4×C5—24no—
256C3×C4×C5—21no—
257C3×C4×C5#12012yes—
258C3×C4×C5C22×D412yes—
259Dic15—42no—
260Dic15—42no—
261C24×C3—21no—
262C24×C3C22⋊D511yescharacteristic
263C3×#41—28no—
264C3×#41—28no—
265C3×#41—24no—
266C3×#41—24no—
267C3×#41—24no—
268C3×#41C22⋊D518yes—
269C2×C3×Q8—24no—
270C2×C3×Q8—21no—
271C2×C3×Q8C22×D512yes—
272C2×C3×D4—28no—
273C2×C3×D4—22no—
274C2×C3×D4—22no—
275C2×C3×D4—24no—
276C2×C3×D4—21no—
277C2×C3×D4C22×D512yes—
278C22×C3×C4—28no—
279C22×C3×C4—21no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—24no—
283C22×C3×C4C22⋊D511yescharacteristic
284C22×C3×C4C22⋊D511yescharacteristic
285C22×C3×C4C22⋊D511yescharacteristic
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—104no—
303C2×C3⋊C8—54no—
304C23×C5—24no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—41no—
309C23×C5—42no—
310C23×C5—42no—
311C23×C5C2×#6711yescharacteristic
312C23×C5C2×#6711yescharacteristic
313C23×C5C2×#6711yescharacteristic
314C5×Q8—24no—
315C5×Q8—22no—
316C5×Q8C2×#6714yes—
317C5×D4—28no—
318C5×D4—24no—
319C5×D4—28no—
320C5×D4—22no—
321C5×D4C2×#6714yes—
322C2×C4×C5—24no—
323C2×C4×C5—28no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—28no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5C2×#6711yescharacteristic
332C2×C4×C5C2×#6711yescharacteristic
333C2×C4×C5C2×#6711yescharacteristic
334C2×C4×C5C2×#6714yes—
335C2×C4×C5C23×D311yescharacteristic
336C2×Dic5—62no—
337C2×Dic5—62no—
338C2×Dic5—122no—
339C2×Dic5—122no—
340Dic10—64no—
341Dic10—122no—
342#168—64no—
343C2×#41—28no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41C2×D1512yes—
347C2×#41C2×D1512yes—
348C22×Q8—151no—
349C22×Q8C2×D1511yescharacteristic
350C22×D4—21no—
351C22×D4C2×D1511yescharacteristic
352C23×C4—21no—
353C23×C4C2×D1511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—152no—
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—152no—
368C22⋊C8—152no—
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5—44no—
373C2×C3×C5C2×#12011yescharacteristic
374C2×C3×C5C2×#13711yescharacteristic
375C2×C3×C5#57511yescharacteristic
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—41no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3C2×C22⋊D511yescharacteristic
384C23×C3C2×C22⋊D511yescharacteristic
385C23×C3C2×C22⋊D511yescharacteristic
386C3×Q8—24no—
387C3×Q8—22no—
388C3×Q8C2×C22⋊D514yes—
389C3×D4—28no—
390C3×D4—24no—
391C3×D4—28no—
392C3×D4—22no—
393C3×D4C2×C22⋊D514yes—
394C2×C3×C4—24no—
395C2×C3×C4—28no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—28no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4C2×C22⋊D511yescharacteristic
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C2×C22⋊D514yes—
407C2×C3×C4C23×D511yescharacteristic
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—202no—
411C2×Dic3—202no—
412Dic6—104no—
413Dic6—202no—
414C3⋊C8—104no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—24no—
423C22×C5—44no—
424C22×C5—48no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5#95112yescomplemented
428C22×C5#95312yes—
429C22×C5C22×#6711yescharacteristic
430C4×C5—21no—
431C4×C5—24no—
432C4×C5—21no—
433C4×C5#95312yes—
434C4×C5C22×#6712yes—
435Dic5—122no—
436Dic5—122no—
437C24—21no—
438C24#122011yescharacteristic
439#41—28no—
440#41—28no—
441#41—24no—
442#41—24no—
443#41—24no—
444#41#122018yes—
445C2×Q8—24no—
446C2×Q8—21no—
447C2×Q8—152no—
448C2×Q8—301no—
449C2×Q8—304no—
450C2×Q8C22×D1512yes—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—21no—
456C2×D4C22×D1512yes—
457C22×C4—28no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—301no—
463C22×C4—301no—
464C22×C4#122011yescharacteristic
465C22×C4#122011yescharacteristic
466C22×C4#122011yescharacteristic
467C22×C4C22×D1511yescharacteristic
468C22×C4C22×D1511yescharacteristic
469C22×C4C22×D1511yescharacteristic
470Q16—308no—
471SD16—308no—
472M16—304no—
473C2×C8—154no—
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—24no—
489C22×C3—44no—
490C22×C3—48no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3#409712yescomplemented
494C22×C3#409912yes—
495C22×C3C22×C22⋊D511yescharacteristic
496C3×C4—21no—
497C3×C4—24no—
498C3×C4—21no—
499C3×C4#409912yes—
500C3×C4C22×C22⋊D512yes—
501Dic3—202no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5—44no—
507C2×C5#582211yescharacteristic
508C2×C5C2×#95111yescharacteristic
509C2×C5C2×#95311yescharacteristic
510C23—24no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—41no—
515C23—42no—
516C23—42no—
517C23C2×#122011yescharacteristic
518C23C2×#122011yescharacteristic
519C23C2×#122011yescharacteristic
520Q8—24no—
521Q8—22no—
522Q8—304no—
523Q8—602no—
524Q8C2×#122014yes—
525D4—28no—
526D4—24no—
527D4—28no—
528D4—22no—
529D4C2×#122014yes—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—28no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—602no—
542C2×C4—602no—
543C2×C4C2×#122011yescharacteristic
544C2×C4C2×#122011yescharacteristic
545C2×C4C2×#122011yescharacteristic
546C2×C4C2×#122014yes—
547C2×C4C23×D1511yescharacteristic
548C8—304no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3—44no—
553C2×C3#6615611yescharacteristic
554C2×C3C2×#409711yescharacteristic
555C2×C3C2×#409911yescharacteristic
556C5#8408411yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—44no—
566C22—48no—
567C22—42no—
568C22—42no—
569C22#9184012yescomplemented
570C22#9184212yes—
571C22C22×#122011yescharacteristic
572C4—21no—
573C4—24no—
574C4—21no—
575C4—602no—
576C4—602no—
577C4#9184212yes—
578C4C22×#122012yes—
579C3#1061581511yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—44no—
584C2#1175658111yescharacteristic
585C2C2×#9184011yescharacteristic
586C2C2×#9184211yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC22×C3×C5×#41C2
socleC22×C3×C5C22×D4
hypercenterC22×#41D15
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91840C2semidirect
3. C2×#91813C2semidirect
4. #11751340C2semidirect
5. #11751333C2semidirect
6. #11751329C2semidirect
7. #11751319C2semidirect
8. #11751308C2semidirect
20. C22×Dic30C22semidirect
23. C2×#6718C22semidirect
24. C2×#6716C22semidirect
25. C2×C4⋊Dic15C22semidirect
29. #91813C22semidirect
31. C2×#6710C22semidirect
32. #91119C22semidirect
33. #91116C22semidirect
35. #91114C22semidirect
252. C22×C3×C5#137semidirect
427. C22×C5#951semidirect
480. C3×C5#3007semidirect
493. C22×C3#4097semidirect
556. C5#84084semidirect
569. C22#91840semidirect
579. C3#10615815semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C2×#918402
C2×#918132
#117513402
#117513332
#117513292
#117513192
#117513082
#106158153
#840845