Finite Group Databasebeta

← #14424159

Subgroups — #14424159

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×C5×#235C211yesmaximal, characteristic
2C2×#91813C211yesmaximal, characteristic, complemented
3C2×#91322C212yesmaximal, complemented
4C3×#65496C211yesmaximal, characteristic, complemented
5#11748561C212yesmaximal, complemented
6#11748543C212yesmaximal, complemented
7#11748390C212yesmaximal, complemented
8#11748361C214yesmaximal, complemented
9#10615815—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×Dic30C2211yescharacteristic, complemented
12C22×C5×#67—21no—
13C2×C5×#235—21no—
14C2×C5×#235—21no—
15C2×C5×#235—28no—
16C2×C5×#235C2212yes—
17C2×C5×#235C2212yes—
18C22×C5×D12C2211yescharacteristic
19C22×C4×C5×D3—21no—
20C22×C5×Dic6C2211yescharacteristic
21C2×#6719—21no—
22C2×C4⋊Dic15C2211yescharacteristic, complemented
23#91813—21no—
24#91813—21no—
25#91813C2212yes—
26#91813C2212yescomplemented
27C2×#6712—21no—
28C2×C3×#681C2212yescomplemented
29#91322—28no—
30C2×#6663C2214yescomplemented
31C2×#6659C2214yescomplemented
32C3×C22⋊#168C2212yes—
33C3×C22⋊#168C2212yescomplemented
34#90973C2214yescomplemented
35#90967C2214yescomplemented
36#78640—51nomaximal, Hall
37C22×C5×#41—31no—
38C2×#4097—32no—
39C2×#4070—31no—
40#65528—34no—
41#65521—32no—
42#65517—32no—
43#65507—32no—
44#65496D311yescharacteristic, complemented
45C24×C3×C5D411yescharacteristic
46C23×C5×D3—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×C5×#67—28no—
60C2×C5×#67—22no—
61C2×C5×#67—22no—
62C22×C5×Dic3—21no—
63C5×#235—28no—
64C5×#235—28no—
65C5×#235—24no—
66C5×#235—24no—
67C5×#235—24no—
68C5×#235D418yes—
69C2×C5×D12—21no—
70C2×C5×D12—24no—
71C2×C5×D12C2312yes—
72C2×C4×C5×D3—28no—
73C2×C4×C5×D3—22no—
74C2×C4×C5×D3—22no—
75C2×C5×Dic6—21no—
76C2×C5×Dic6—24no—
77C2×C5×Dic6C2312yes—
78#6719—22no—
79#6719—22no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2312yes—
82#6712—22no—
83#6712—22no—
84C3×#681—24no—
85C2×C3×#168C2314yes—
86#6663—28no—
87#6659—28no—
88C22×#235D511yescharacteristic
89C2×#924—51no—
90C2×#909—52no—
91C3×#407—51no—
92#5133—52no—
93#4739—52no—
94#4733—54no—
95#4731—52no—
96C2×C5×#41—32no—
97C2×C5×#41—32no—
98C2×C5×#41—68no—
99C2×C5×#41—61no—
100C2×C5×#41—61no—
101C22×C5×Q8—31no—
102C22×C5×D4—31no—
103C22×C5×D4—61no—
104C23×C4×C5—61no—
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×#681C2×D312yescomplemented
118#3967—34no—
119#3964—34no—
120C22⋊#168C2×D312yes—
121C22⋊#168C2×D312yescomplemented
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×C5×D3—24no—
130C22×C5×D3—22no—
131C22×C5×D3—42no—
132C22×C5×D3—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—
149C5×#67—28no—
150C5×#67—28no—
151C2×C5×Dic3—24no—
152C2×C5×Dic3—22no—
153C5×D12—24no—
154C5×D12—22no—
155C5×D12C2×D414yes—
156C4×C5×D3—28no—
157C4×C5×D3—28no—
158C5×Dic6—24no—
159C5×Dic6—22no—
160C5×Dic6C2×D414yes—
161C3×#168—24no—
162C23×C3×C4C2×D511yescharacteristic
163C22×#67—21no—
164C2×#235—21no—
165C2×#235—21no—
166C2×#235—28no—
167C2×#235C2×D512yes—
168C2×#235C2×D512yes—
169C22×D12C2×D511yescharacteristic
170C22×C4×D3—21no—
171C22×Dic6—51no—
172C22×Dic6C2×D511yescharacteristic
173C2×C3×M16—52no—
174C2×#217—101no—
175C2×C4⋊Dic3—51no—
176#924—52no—
177#924—52no—
178#924—101no—
179#924—101no—
180C2×Dic3⋊C4—101no—
181#909—108no—
182C2×Dic12—54no—
183C2×#204—54no—
184C3×C22⋊C8—52no—
185C3×C22⋊C8—52no—
186#821—54no—
187#816—54no—
188C24×C5—61no—
189C24×C5D1211yescharacteristic
190C5×#41—38no—
191C5×#41—64no—
192C5×#41—64no—
193C5×#41—68no—
194C5×#41—68no—
195C5×#41—64no—
196C2×C5×Q8—32no—
197C2×C5×Q8—64no—
198C2×C5×Q8—61no—
199C2×C5×D4—32no—
200C2×C5×D4—64no—
201C2×C5×D4—68no—
202C2×C5×D4—62no—
203C2×C5×D4—62no—
204C2×C5×D4—61no—
205C22×C4×C5—24no—
206C22×C4×C5—68no—
207C22×C4×C5—61no—
208C22×C4×C5—62no—
209C22×C4×C5—62no—
210C22×C4×C5D1211yescharacteristic
211C22×C4×C5D1211yescharacteristic
212C22×C4×C5D1211yescharacteristic
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—24no—
230C2×#168C22×D314yes—
231C22×#41—31no—
232C2×#137—152no—
233C2×C22⋊Q8—151no—
234#452—154no—
235#451—152no—
236#450—152no—
237#417—152no—
238#407—51no—
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×C5×D3—24no—
251C2×C5×D3—48no—
252C2×C5×D3—42no—
253C2×C5×D3—42no—
254C3×C4×C5—21no—
255C3×C4×C5—21no—
256C3×C4×C5#12012yes—
257C3×C4×C5C22×D412yes—
258Dic15—42no—
259Dic15—42no—
260C5×Dic3—24no—
261C24×C3C22⋊D511yescharacteristic
262C23×D3—21no—
263C22×C3×C4—24no—
264C22×C3×C4C22⋊D511yescharacteristic
265C22×C3×C4C22⋊D511yescharacteristic
266C22×C3×C4C22⋊D511yescharacteristic
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—28no—
271C2×#67—22no—
272C2×#67—22no—
273C22×Dic3—21no—
274C22×Dic3—101no—
275C22×Dic3—101no—
276#235—28no—
277#235—28no—
278#235—24no—
279#235—24no—
280#235—24no—
281#235C22⋊D518yes—
282C2×D12—21no—
283C2×D12—24no—
284C2×D12C22×D512yes—
285C2×C4×D3—28no—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×Dic6—21no—
289C2×Dic6—24no—
290C2×Dic6—52no—
291C2×Dic6—104no—
292C2×Dic6—101no—
293C2×Dic6C22×D512yes—
294C3×M16—104no—
295C2×C3×C8—54no—
296#217—102no—
297#217—102no—
298C4⋊Dic3—52no—
299C4⋊Dic3—101no—
300Dic3⋊C4—102no—
301Dic3⋊C4—102no—
302Dic12—108no—
303#204—108no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—41no—
307C23×C5—64no—
308C23×C5—62no—
309C23×C5—122no—
310C23×C5—122no—
311C23×C5C2×D1211yescharacteristic
312C23×C5C2×D1211yescharacteristic
313C23×C5C2×D1211yescharacteristic
314C5×Q8—34no—
315C5×Q8—64no—
316C5×Q8—62no—
317C5×D4—34no—
318C5×D4—64no—
319C5×D4—68no—
320C5×D4—68no—
321C5×D4—62no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—68no—
328C2×C4×C5—64no—
329C2×C4×C5—62no—
330C2×C4×C5—68no—
331C2×C4×C5C2×D1211yescharacteristic
332C2×C4×C5C2×D1211yescharacteristic
333C2×C4×C5C2×D1211yescharacteristic
334C2×C4×C5D3×D414yes—
335C2×C4×C5C23×D311yescharacteristic
336C2×Dic5—62no—
337C2×Dic5—62no—
338C2×Dic5—122no—
339C2×Dic5—122no—
340Dic10—64no—
341Dic10—122no—
342#168—24no—
343C2×#41—32no—
344C2×#41—32no—
345C2×#41—68no—
346C2×#41—61no—
347C2×#41—61no—
348C22×Q8—31no—
349C22×Q8—151no—
350C22×D4—31no—
351C22×D4—61no—
352C23×C4—61no—
353C23×C4D3×D511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—52no—
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—52no—
368C22⋊C8—52no—
369C2×C3×C5—22no—
370C2×C3×C5—22no—
371C2×C3×C5—41no—
372C2×C3×C5C2×#12011yescharacteristic
373C2×C3×C5C2×#13711yescharacteristic
374C2×C3×C5#57511yescharacteristic
375C5×D3—44no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3C2×C22⋊D511yescharacteristic
380C23×C3C2×C22⋊D511yescharacteristic
381C23×C3C2×C22⋊D511yescharacteristic
382C22×D3—24no—
383C22×D3—22no—
384C22×D3—42no—
385C22×D3—42no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4C2×C22⋊D511yescharacteristic
392C2×C3×C4C2×C22⋊D511yescharacteristic
393C2×C3×C4C2×C22⋊D511yescharacteristic
394C2×C3×C4C2×C22⋊D514yes—
395C2×C3×C4C23×D511yescharacteristic
396#67—28no—
397#67—28no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—202no—
403C2×Dic3—202no—
404D12—24no—
405D12—22no—
406D12C2×C22⋊D514yes—
407C4×D3—28no—
408C4×D3—28no—
409Dic6—24no—
410Dic6—22no—
411Dic6—104no—
412Dic6—202no—
413Dic6C2×C22⋊D514yes—
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—44no—
423C22×C5—64no—
424C22×C5—128no—
425C22×C5—122no—
426C22×C5—122no—
427C22×C5#88212yes—
428C22×C5#90912yescomplemented
429C22×C5C22×D1211yescharacteristic
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—64no—
433C4×C5#88212yes—
434C4×C5C2×D3×D412yes—
435Dic5—122no—
436Dic5—122no—
437C24—61no—
438C24#120311yescharacteristic
439#41—38no—
440#41—64no—
441#41—64no—
442#41—68no—
443#41—68no—
444#41—64no—
445C2×Q8—32no—
446C2×Q8—64no—
447C2×Q8—61no—
448C2×Q8—152no—
449C2×Q8—301no—
450C2×Q8—304no—
451C2×D4—32no—
452C2×D4—64no—
453C2×D4—68no—
454C2×D4—62no—
455C2×D4—62no—
456C2×D4—61no—
457C22×C4—24no—
458C22×C4—68no—
459C22×C4—61no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—301no—
463C22×C4—301no—
464C22×C4#120311yescharacteristic
465C22×C4#120311yescharacteristic
466C22×C4#120311yescharacteristic
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470Q16—308no—
471SD16—308no—
472M16—104no—
473C2×C8—54no—
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#409712yescomplemented
490C22×C3#409912yes—
491C22×C3C22×C22⋊D511yescharacteristic
492C2×D3—24no—
493C2×D3—48no—
494C2×D3—42no—
495C2×D3—42no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4#409912yes—
499C3×C4C22×C22⋊D512yes—
500Dic3—24no—
501Dic3—202no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5—124no—
507C2×C5C2×#88211yescharacteristic
508C2×C5C2×#90911yescharacteristic
509C2×C5#574811yescharacteristic
510C23—22no—
511C23—22no—
512C23—41no—
513C23—64no—
514C23—62no—
515C23—122no—
516C23—122no—
517C23C2×#120311yescharacteristic
518C23C2×#120311yescharacteristic
519C23C2×#120311yescharacteristic
520Q8—34no—
521Q8—64no—
522Q8—62no—
523Q8—304no—
524Q8—602no—
525D4—34no—
526D4—64no—
527D4—68no—
528D4—68no—
529D4—62no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—68no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—68no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—602no—
542C2×C4—602no—
543C2×C4C2×#120311yescharacteristic
544C2×C4C2×#120311yescharacteristic
545C2×C4C2×#120311yescharacteristic
546C2×C4D3×C22⋊D514yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—104no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3#6615611yescharacteristic
553C2×C3C2×#409711yescharacteristic
554C2×C3C2×#409911yescharacteristic
555D3—44no—
556C5#7864011yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—44no—
565C22—64no—
566C22—128no—
567C22—122no—
568C22—122no—
569C22#9132212yescomplemented
570C22#9157012yes—
571C22C22×#120311yescharacteristic
572C4—21no—
573C4—21no—
574C4—64no—
575C4—602no—
576C4—602no—
577C4#9157012yes—
578C4C2×D3×C22⋊D512yes—
579C3#1061581511yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—124no—
584C2#1175414511yescharacteristic
585C2C2×#9132211yescharacteristic
586C2C2×#9157011yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×#235C2
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×#91322C2semidirect
4. C3×#65496C2semidirect
5. #11748561C2semidirect
6. #11748543C2semidirect
7. #11748390C2semidirect
8. #11748361C2semidirect
11. C22×Dic30C22semidirect
22. C2×C4⋊Dic15C22semidirect
26. #91813C22semidirect
28. C2×C3×#681C22semidirect
30. C2×#6663C22semidirect
31. C2×#6659C22semidirect
33. C3×C22⋊#168C22semidirect
34. #90973C22semidirect
35. #90967C22semidirect
44. #65496D3semidirect
117. C2×#681C2×D3semidirect
121. C22⋊#168C2×D3semidirect
248. C22×C3×C5#137semidirect
428. C22×C5#909semidirect
480. C3×C5#3007semidirect
489. C22×C3#4097semidirect
556. C5#78640semidirect
569. C22#91322semidirect
579. C3#10615815semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C2×#918132
C2×#913222
C3×#654962
#117485612
#117485432
#117483902
#117483612
#106158153
#786405