Finite Group Databasebeta

← #14424158

Subgroups — #14424158

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×C3×#4070C211yesmaximal, characteristic, complemented
3C2×#91309C212yesmaximal, complemented
4#11751308C211yesmaximal, characteristic, complemented
5#11748559C212yesmaximal, complemented
6#11748538C214yesmaximal, complemented
7#11748537C212yesmaximal, complemented
8#11748384C212yesmaximal, complemented
9#10615815—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C5×#67—21no—
12C2×C5×#235—21no—
13C2×C5×#235—21no—
14C2×C5×#235—28no—
15C2×C5×#235C2212yes—
16C2×C5×#235C2212yes—
17C22×C5×D12C2211yescharacteristic
18C22×C4×C5×D3—21no—
19C22×C5×Dic6C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×#6710C2212yescomplemented
22C2×C3×C22⋊Dic5—21no—
23C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
24C3×#4070—21no—
25C3×#4070—21no—
26C3×#4070C2212yes—
27C3×#4070C2212yescomplemented
28C2×C3×#683—21no—
29C2×#6661C2214yescomplemented
30#91309—28no—
31C2×#6656C2214yescomplemented
32#91114C2212yes—
33#91114C2212yescomplemented
34#90972C2214yescomplemented
35#90966C2214yescomplemented
36#82735—51nomaximal, Hall
37C22×C5×#41—31no—
38C2×#4097—32no—
39C2×#4070D311yescharacteristic, complemented
40#65528—34no—
41#65521—32no—
42#65517—32no—
43#65507—32no—
44#65496—31no—
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
54C2×C5×#67—28no—
55C2×C5×#67—22no—
56C2×C5×#67—22no—
57C22×C5×Dic3—21no—
58C5×#235—28no—
59C5×#235—28no—
60C5×#235—24no—
61C5×#235—24no—
62C5×#235—24no—
63C5×#235D418yes—
64C2×C5×D12—21no—
65C2×C5×D12—24no—
66C2×C5×D12C2312yes—
67C2×C4×C5×D3—28no—
68C2×C4×C5×D3—22no—
69C2×C4×C5×D3—22no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6—24no—
72C2×C5×Dic6C2312yes—
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C2×C3×Dic10—24no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2312yes—
78#6710—24no—
79C2×C3⋊#168C2314yes—
80C3×C22⋊Dic5—22no—
81C3×C22⋊Dic5—22no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84C3×#683—22no—
85C3×#683—22no—
86#6661—28no—
87#6656—28no—
88C22×#235D511yescharacteristic
89C2×C3×C22⋊Q8—51no—
90C2×#942—52no—
91#5207—51no—
92#5050—52no—
93#5047—54no—
94#5046—52no—
95#4966—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×Dic10C2×D311yescharacteristic, complemented
107C2×C22⋊Dic5—21no—
108#4097—68no—
109C2×#689—34no—
110C2×#687—34no—
111C2×C4⋊Dic5C2×D311yescharacteristic, complemented
112#4070—21no—
113#4070—21no—
114#4070C2×D312yes—
115#4070C2×D312yescomplemented
116C2×#683—21no—
117C2×#681—32no—
118#3967—34no—
119#3964—34no—
120C22⋊#168—32no—
121C22⋊#168—32no—
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
143C5×#67—28no—
144C5×#67—28no—
145C2×C5×Dic3—24no—
146C2×C5×Dic3—22no—
147C5×D12—24no—
148C5×D12—22no—
149C5×D12C2×D414yes—
150C4×C5×D3—28no—
151C4×C5×D3—28no—
152C5×Dic6—24no—
153C5×Dic6—22no—
154C5×Dic6C2×D414yes—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—42no—
158C2×C3×Dic5—42no—
159C3×Dic10—24no—
160C3×Dic10—42no—
161C3⋊#168—24no—
162C22×C3×Q8—51no—
163C23×C3×C4C2×D511yescharacteristic
164C22×#67—21no—
165C2×#235—21no—
166C2×#235—21no—
167C2×#235—28no—
168C2×#235C2×D512yes—
169C2×#235C2×D512yes—
170C22×D12C2×D511yescharacteristic
171C22×C4×D3—21no—
172C22×Dic6C2×D511yescharacteristic
173C3×C22⋊Q8—52no—
174C3×C22⋊Q8—52no—
175C3×C22⋊Q8—101no—
176C3×C22⋊Q8—101no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—101no—
179C2×C3×C22⋊C4—101no—
180C2×#216—54no—
181#942—108no—
182C2×#215—54no—
183C2×#208—52no—
184#830—52no—
185#830—52no—
186#810—54no—
187#809—54no—
188C24×C5—61no—
189C24×C5#6711yescharacteristic
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×C5#6711yescharacteristic
211C22×C4×C5#6711yescharacteristic
212C22×C4×C5#6711yescharacteristic
213C22×C4×C5C22×D311yescharacteristic
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D311yescharacteristic
216C22×Dic5—21no—
217C22×Dic5—21no—
218C2×Dic10—24no—
219C2×Dic10—21no—
220C2×Dic10C22×D312yes—
221C22⋊Dic5—22no—
222C22⋊Dic5—22no—
223#689—68no—
224#687—68no—
225C4⋊Dic5—21no—
226C4⋊Dic5C22×D312yes—
227#683—22no—
228#683—22no—
229#681—64no—
230C2×#168—34no—
231C22×#41—31no—
232C2×#137—152no—
233C2×C22⋊Q8—51no—
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—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—
258C3×Dic5—42no—
259C3×Dic5—42no—
260C5×Dic3—24no—
261C24×C3C22⋊D511yescharacteristic
262C23×D3—21no—
263C2×C3×Q8—52no—
264C2×C3×Q8—101no—
265C2×C3×Q8—104no—
266C22×C3×C4—24no—
267C22×C3×C4—101no—
268C22×C3×C4—101no—
269C22×C3×C4C22⋊D511yescharacteristic
270C22×C3×C4C22⋊D511yescharacteristic
271C22×C3×C4C22⋊D511yescharacteristic
272C22×C3×C4C22×D511yescharacteristic
273C22×C3×C4C22×D511yescharacteristic
274C22×C3×C4C22×D511yescharacteristic
275C2×#67—28no—
276C2×#67—22no—
277C2×#67—22no—
278C22×Dic3—21no—
279#235—28no—
280#235—28no—
281#235—24no—
282#235—24no—
283#235—24no—
284#235C22⋊D518yes—
285C2×D12—21no—
286C2×D12—24no—
287C2×D12C22×D512yes—
288C2×C4×D3—28no—
289C2×C4×D3—22no—
290C2×C4×D3—22no—
291C2×Dic6—21no—
292C2×Dic6—24no—
293C2×Dic6C22×D512yes—
294C3×C4⋊C4—52no—
295C3×C4⋊C4—102no—
296C3×C4⋊C4—102no—
297C3×C4⋊C4—101no—
298C3×C22⋊C4—102no—
299C3×C22⋊C4—102no—
300#216—108no—
301#215—108no—
302#208—104no—
303C2×C3⋊C8—54no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—41no—
307C23×C5—64no—
308C23×C5—62no—
309C23×C5—122no—
310C23×C5—122no—
311C23×C5C2×#6711yescharacteristic
312C23×C5C2×#6711yescharacteristic
313C23×C5C2×#6711yescharacteristic
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×C5D3×D414yes—
332C2×C4×C5C2×#6711yescharacteristic
333C2×C4×C5C2×#6711yescharacteristic
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—42no—
339C2×Dic5—42no—
340Dic10—24no—
341Dic10—42no—
342#168—64no—
343C2×#41—32no—
344C2×#41—32no—
345C2×#41—68no—
346C2×#41—61no—
347C2×#41—61no—
348C22×Q8—31no—
349C22×Q8—51no—
350C22×D4—31no—
351C22×D4—61no—
352C23×C4—61no—
353C23×C4D3×D511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—152no—
358C22⋊Q8—52no—
359C22⋊Q8—52no—
360C22⋊Q8—101no—
361C22⋊Q8—101no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—101no—
364C2×C22⋊C4—101no—
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×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—
386C3×Q8—104no—
387C3×Q8—202no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—102no—
394C2×C3×C4—102no—
395C2×C3×C4—202no—
396C2×C3×C4—202no—
397C2×C3×C4C2×C22⋊D511yescharacteristic
398C2×C3×C4C2×C22⋊D511yescharacteristic
399C2×C3×C4C2×C22⋊D511yescharacteristic
400C2×C3×C4C2×C22⋊D514yes—
401C2×C3×C4C23×D511yescharacteristic
402#67—28no—
403#67—28no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406D12—24no—
407D12—22no—
408D12C2×C22⋊D514yes—
409C4×D3—28no—
410C4×D3—28no—
411Dic6—24no—
412Dic6—22no—
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#93712yes—
428C22×C5#94212yescomplemented
429C22×C5C22×#6711yescharacteristic
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—64no—
433C4×C5#93712yes—
434C4×C5C2×D3×D412yes—
435Dic5—42no—
436Dic5—42no—
437C24—61no—
438C24#120111yescharacteristic
439#41—38no—
440#41—64no—
441#41—64no—
442#41—68no—
443#41—68no—
444#41—64no—
445C2×Q8—32no—
446C2×Q8—52no—
447C2×Q8—64no—
448C2×Q8—61no—
449C2×Q8—101no—
450C2×Q8—104no—
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—101no—
463C22×C4—101no—
464C22×C4#120111yescharacteristic
465C22×C4#120111yescharacteristic
466C22×C4#120111yescharacteristic
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470Q16—308no—
471SD16—308no—
472M16—304no—
473C2×C8—154no—
474C4⋊C4—52no—
475C4⋊C4—101no—
476C4⋊C4—102no—
477C4⋊C4—102no—
478C22⋊C4—102no—
479C22⋊C4—102no—
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—202no—
499C3×C4—202no—
500C3×C4#409912yes—
501C3×C4C22×C22⋊D512yes—
502Dic3—24no—
503C2×C5—22no—
504C2×C5—22no—
505C2×C5—41no—
506C2×C5—124no—
507C2×C5C2×#93711yescharacteristic
508C2×C5C2×#94211yescharacteristic
509C2×C5#582211yescharacteristic
510C23—22no—
511C23—22no—
512C23—41no—
513C23—64no—
514C23—62no—
515C23—122no—
516C23—122no—
517C23C2×#120111yescharacteristic
518C23C2×#120111yescharacteristic
519C23C2×#120111yescharacteristic
520Q8—34no—
521Q8—64no—
522Q8—62no—
523Q8—104no—
524Q8—202no—
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—102no—
540C2×C4—102no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4C2×#120111yescharacteristic
544C2×C4C2×#120111yescharacteristic
545C2×C4C2×#120111yescharacteristic
546C2×C4D3×C22⋊D514yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—304no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3#6615611yescharacteristic
553C2×C3C2×#409711yescharacteristic
554C2×C3C2×#409911yescharacteristic
555D3—44no—
556C5#8273511yescharacteristic, 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#9130912yescomplemented
570C22#9156812yes—
571C22C22×#120111yescharacteristic
572C4—21no—
573C4—21no—
574C4—64no—
575C4—202no—
576C4—202no—
577C4#9156812yes—
578C4C2×D3×C22⋊D512yes—
579C3#1061581511yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—124no—
584C2#1175413811yescharacteristic
585C2C2×#9130911yescharacteristic
586C2C2×#9156811yescharacteristic
subgroupG/H
centerC22C22×#1201
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×C3×#4070C2semidirect
3. C2×#91309C2semidirect
4. #11751308C2semidirect
5. #11748559C2semidirect
6. #11748538C2semidirect
7. #11748537C2semidirect
8. #11748384C2semidirect
20. C22×C3×Dic10C22semidirect
21. C2×#6710C22semidirect
23. C2×C3×C4⋊Dic5C22semidirect
27. C3×#4070C22semidirect
29. C2×#6661C22semidirect
31. C2×#6656C22semidirect
33. #91114C22semidirect
34. #90972C22semidirect
35. #90966C22semidirect
39. C2×#4070D3semidirect
106. C22×Dic10C2×D3semidirect
111. C2×C4⋊Dic5C2×D3semidirect
115. #4070C2×D3semidirect
248. C22×C3×C5#137semidirect
428. C22×C5#942semidirect
480. C3×C5#3007semidirect
489. C22×C3#4097semidirect
556. C5#82735semidirect
569. C22#91309semidirect
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×C3×#40702
C2×#913092
#117513082
#117485592
#117485382
#117485372
#117483842
#106158153
#827355