Finite Group Databasebeta

← #14424156

Subgroups — #14424156

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×C5×#924C211yesmaximal, characteristic, complemented
3C2×#91307C212yesmaximal, complemented
4#11751308C211yesmaximal, characteristic, complemented
5#11748555C212yesmaximal, complemented
6#11748528C214yesmaximal, complemented
7#11748527C212yesmaximal, complemented
8#11748368C212yesmaximal, complemented
9#10614466—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic, 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×#6710C2212yescomplemented
22C2×C5×#217—21no—
23C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
24C5×#924—21no—
25C5×#924—21no—
26C5×#924C2212yes—
27C5×#924C2212yescomplemented
28C2×C5×Dic3⋊C4—21no—
29C2×#6661C2214yescomplemented
30#91307—28no—
31C2×#6655C2214yescomplemented
32#91114C2212yes—
33#91114C2212yescomplemented
34#90970C2214yescomplemented
35#90964C2214yescomplemented
36#84084—51nomaximal, Hall
37C22×#709D311yescharacteristic
38C2×C5×C22⋊Q8—31no—
39C2×#4088—32no—
40#65496—31no—
41#65339—32no—
42#65336—34no—
43#65335—32no—
44#65255—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×C5×Dic3—21no—
55C22×C5×Dic3—21no—
56C2×C5×Dic6—24no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6C2312yes—
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#6710—24no—
79C2×C3⋊#168C2314yes—
80C5×#217—22no—
81C5×#217—22no—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3C2312yes—
84C5×Dic3⋊C4—22no—
85C5×Dic3⋊C4—22no—
86#6661—28no—
87#6655—28no—
88C22×C3×#41—51no—
89C2×#951—52no—
90C2×#924D511yescharacteristic, complemented
91#5239—54no—
92#5232—52no—
93#5228—52no—
94#5218—52no—
95#5207—51no—
96C22×C5×Q8—31no—
97C23×C4×C5C2×D311yescharacteristic
98C22×C22⋊D5—21no—
99C2×#709—21no—
100C2×#709—21no—
101C2×#709—28no—
102C2×#709C2×D312yes—
103C2×#709C2×D312yes—
104C22×D20C2×D311yescharacteristic
105C22×C4×D5—21no—
106C22×Dic10C2×D311yescharacteristic
107C5×C22⋊Q8—32no—
108C5×C22⋊Q8—32no—
109C5×C22⋊Q8—61no—
110C5×C22⋊Q8—61no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—61no—
113C2×C5×C22⋊C4—61no—
114C2×#689—34no—
115#4088—68no—
116C2×#688—34no—
117C2×#681—32no—
118C22⋊#168—32no—
119C22⋊#168—32no—
120#3942—34no—
121#3941—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×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—42no—
146C2×C5×Dic3—42no—
147C5×Dic6—24no—
148C5×Dic6—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—
161C3⋊#168—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×Dic6C2×D511yescharacteristic, complemented
173C2×#217—21no—
174#951—108no—
175C2×#216—54no—
176C2×#214—54no—
177C2×C4⋊Dic3C2×D511yescharacteristic, complemented
178#924—21no—
179#924—21no—
180#924C2×D512yes—
181#924C2×D512yescomplemented
182C2×Dic3⋊C4—21no—
183C2×#208—52no—
184#835—54no—
185#832—54no—
186#830—52no—
187#830—52no—
188C24×C5#6711yescharacteristic
189C23×D5—21no—
190C2×C5×Q8—32no—
191C2×C5×Q8—61no—
192C2×C5×Q8—64no—
193C22×C4×C5—24no—
194C22×C4×C5—61no—
195C22×C4×C5—61no—
196C22×C4×C5#6711yescharacteristic
197C22×C4×C5#6711yescharacteristic
198C22×C4×C5#6711yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×C4×C5C22×D311yescharacteristic
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—28no—
203C2×C22⋊D5—22no—
204C2×C22⋊D5—22no—
205C22×Dic5—21no—
206#709—28no—
207#709—28no—
208#709—24no—
209#709—24no—
210#709—24no—
211#709#6718yes—
212C2×D20—21no—
213C2×D20—24no—
214C2×D20C22×D312yes—
215C2×C4×D5—28no—
216C2×C4×D5—22no—
217C2×C4×D5—22no—
218C2×Dic10—21no—
219C2×Dic10—24no—
220C2×Dic10C22×D312yes—
221C5×C4⋊C4—32no—
222C5×C4⋊C4—61no—
223C5×C4⋊C4—62no—
224C5×C4⋊C4—62no—
225C5×C22⋊C4—62no—
226C5×C22⋊C4—62no—
227#689—68no—
228#688—68no—
229#681—64no—
230C2×#168—34no—
231C22×#41—51no—
232C2×#137—152no—
233C2×C22⋊Q8—31no—
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×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—
258C3×Dic5—24no—
259C5×Dic3—42no—
260C5×Dic3—42no—
261C24×C3—101no—
262C24×C3C22⋊D511yescharacteristic
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×C4C22⋊D511yescharacteristic
284C22×C3×C4C22⋊D511yescharacteristic
285C22×C3×C4C22⋊D511yescharacteristic
286C22×C3×C4C22×D511yescharacteristic
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D511yescharacteristic
289C22×Dic3—21no—
290C22×Dic3—21no—
291C2×Dic6—24no—
292C2×Dic6—21no—
293C2×Dic6C22×D512yes—
294#217—22no—
295#217—22no—
296#216—108no—
297#214—108no—
298C4⋊Dic3—21no—
299C4⋊Dic3C22×D512yes—
300Dic3⋊C4—22no—
301Dic3⋊C4—22no—
302#208—104no—
303C2×C3⋊C8—54no—
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—
314C5×Q8—64no—
315C5×Q8—122no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—62no—
322C2×C4×C5—62no—
323C2×C4×C5—122no—
324C2×C4×C5—122no—
325C2×C4×C5C2×#6711yescharacteristic
326C2×C4×C5C2×#6711yescharacteristic
327C2×C4×C5C2×#6711yescharacteristic
328C2×C4×C5C2×#6714yes—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—28no—
331C22⋊D5—28no—
332C2×Dic5—24no—
333C2×Dic5—22no—
334D20—24no—
335D20—22no—
336D20C2×#6714yes—
337C4×D5—28no—
338C4×D5—28no—
339Dic10—24no—
340Dic10—22no—
341Dic10C2×#6714yes—
342#168—64no—
343C2×#41—52no—
344C2×#41—52no—
345C2×#41—108no—
346C2×#41—101no—
347C2×#41—101no—
348C22×Q8—31no—
349C22×Q8—51no—
350C22×D4—51no—
351C22×D4—101no—
352C23×C4—101no—
353C23×C4D3×D511yescharacteristic
354#137—308no—
355C2×Q16—154no—
356C2×SD16—154no—
357C2×M16—152no—
358C22⋊Q8—32no—
359C22⋊Q8—32no—
360C22⋊Q8—61no—
361C22⋊Q8—61no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C22⋊C4—61no—
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
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×C22⋊D511yescharacteristic
384C23×C3C2×C22⋊D511yescharacteristic
385C23×C3C2×C22⋊D511yescharacteristic
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×C4D4×D514yes—
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C2×C22⋊D511yescharacteristic
406C2×C3×C4C2×C22⋊D511yescharacteristic
407C2×C3×C4C23×D511yescharacteristic
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412Dic6—24no—
413Dic6—42no—
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#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—122no—
433C4×C5—122no—
434C4×C5#95312yes—
435C4×C5C22×#6712yes—
436Dic5—24no—
437C24—101no—
438C24#120111yescharacteristic
439#41—58no—
440#41—104no—
441#41—104no—
442#41—108no—
443#41—108no—
444#41—104no—
445C2×Q8—32no—
446C2×Q8—52no—
447C2×Q8—61no—
448C2×Q8—64no—
449C2×Q8—104no—
450C2×Q8—101no—
451C2×D4—52no—
452C2×D4—104no—
453C2×D4—108no—
454C2×D4—102no—
455C2×D4—102no—
456C2×D4—101no—
457C22×C4—24no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—108no—
461C22×C4—101no—
462C22×C4—102no—
463C22×C4—102no—
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—32no—
475C4⋊C4—61no—
476C4⋊C4—62no—
477C4⋊C4—62no—
478C22⋊C4—62no—
479C22⋊C4—62no—
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#408312yes—
494C22×C3#408812yescomplemented
495C22×C3C22×C22⋊D511yescharacteristic
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—104no—
499C3×C4#408312yes—
500C3×C4C2×D4×D512yes—
501Dic3—42no—
502Dic3—42no—
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×#120111yescharacteristic
518C23C2×#120111yescharacteristic
519C23C2×#120111yescharacteristic
520Q8—54no—
521Q8—64no—
522Q8—104no—
523Q8—102no—
524Q8—122no—
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—62no—
536C2×C4—62no—
537C2×C4—108no—
538C2×C4—104no—
539C2×C4—102no—
540C2×C4—108no—
541C2×C4—122no—
542C2×C4—122no—
543C2×C4C2×#120111yescharacteristic
544C2×C4C2×#120111yescharacteristic
545C2×C4C2×#120111yescharacteristic
546C2×C4D5×#6714yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—304no—
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—41no—
552C2×C3—204no—
553C2×C3C2×#408311yescharacteristic
554C2×C3C2×#408811yescharacteristic
555C2×C3#6615611yescharacteristic
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#9130712yescomplemented
570C22#9156312yes—
571C22C22×#120111yescharacteristic
572C4—21no—
573C4—21no—
574C4—104no—
575C4—122no—
576C4—122no—
577C4#9156312yes—
578C4C2×D5×#6712yes—
579C3#1061446611yescharacteristic, complemented, Sylow
580C2—22no—
581C2—22no—
582C2—41no—
583C2—204no—
584C2#1175413811yescharacteristic
585C2C2×#9130711yescharacteristic
586C2C2×#9156311yescharacteristic
subgroupG/H
centerC22C22×#1201
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×C5×#924C2semidirect
3. C2×#91307C2semidirect
4. #11751308C2semidirect
5. #11748555C2semidirect
6. #11748528C2semidirect
7. #11748527C2semidirect
8. #11748368C2semidirect
11. C22×C5×Dic6C22semidirect
21. C2×#6710C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
27. C5×#924C22semidirect
29. C2×#6661C22semidirect
31. C2×#6655C22semidirect
33. #91114C22semidirect
34. #90970C22semidirect
35. #90964C22semidirect
90. C2×#924D5semidirect
172. C22×Dic6C2×D5semidirect
177. C2×C4⋊Dic3C2×D5semidirect
181. #924C2×D5semidirect
248. C22×C3×C5#137semidirect
423. C22×C5#951semidirect
480. C3×C5#3007semidirect
494. C22×C3#4088semidirect
556. C5#84084semidirect
569. C22#91307semidirect
579. C3#10614466semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C5×#9242
C2×#913072
#117513082
#117485552
#117485282
#117485272
#117483682
#106144663
#840845