Finite Group Databasebeta

← #14301067

Subgroups — #14301067

Order 1920.

876 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×D40C211yesmaximal, characteristic
2C2×Dic3×D20C211yesmaximal, characteristic, complemented
3#11748785C211yesmaximal, characteristic, complemented
4C2×#90965C211yesmaximal, characteristic, complemented
5C2×#90965C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7C5×#4550C211yesmaximal, characteristic, complemented
8#10599466—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C22×D5×Dic3—21no—
12C22×C3×C5×C8C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×C5×Dic3C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×D40—22no—
18C2×C3×D40—22no—
19C2×C3×D40C414yescomplemented
20C2×#6665—21no—
21C2×#6665—21no—
22C2×#6665—21no—
23Dic3×D20—22no—
24Dic3×D20—22no—
25#90965—22no—
26#90965—22no—
27#72037—51nomaximal, Hall
28C22×D40D311yescharacteristic
29C2×C4×D20—31no—
30C2×#3953—31no—
31C2×#3953—31no—
32#65228—31no—
33C5×#336—31no—
34#64771—31no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15—21no—
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C2×C3×D20—21no—
43C2×C3×D20—21no—
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20C2×C412yes—
51C2×C3×D20C2×C412yescomplemented
52C2×C3×D20D412yes—
53C2×C3×D20D412yes—
54C2×D5×Dic3—24no—
55C2×D5×Dic3—42no—
56C2×D5×Dic3—42no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8C2×C412yescomplemented
60C4⋊Dic15—21no—
61C4⋊Dic15—21no—
62C4⋊Dic15—21no—
63C4⋊Dic15D412yes—
64C4×C5×Dic3—21no—
65C4×C5×Dic3—21no—
66C2×C5×C3⋊C8—21no—
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8—21no—
69C3×D40—28no—
70#6665—24no—
71#6665—42no—
72#6665—42no—
73C22×C3×D8—51no—
74C2×D4×Dic3—51no—
75#5221—51no—
76C2×#832—51no—
77C2×#832—51no—
78#4551—51no—
79#4550D511yescharacteristic, complemented
80C22×D20C2×D311yescharacteristic
81C22×D20C2×D311yescharacteristic
82C22×C4×D5—61no—
83C22×C5×C8—31no—
84C22×C5×C8C2×D311yescharacteristic
85C2×C42×C5—31no—
86C2×#685—61no—
87C2×#685—61no—
88C2×#685—61no—
89C2×C4⋊Dic5—31no—
90C2×C4⋊Dic5—31no—
91C2×D40—22no—
92C2×D40—22no—
93C2×D40Dic314yescomplemented
94C4×D20—62no—
95C4×D20—62no—
96#3953—62no—
97#3953—62no—
98#1879—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5—22no—
103C22×C3×D5—22no—
104C22×C3×D5—41no—
105C22×C3×D5—41no—
106C22×C3×D5—41no—
107C22×C3×D5—41no—
108C22×C3×D5—41no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×Dic15—22no—
121C2×Dic15—41no—
122C2×Dic15—41no—
123C2×Dic15—41no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×C5×Dic3—21no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3—21no—
129C2×C5×Dic3—21no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3D812yescomplemented
132C3×D20—22no—
133C3×D20—22no—
134C3×D20—22no—
135C3×D20—22no—
136C3×D20—22no—
137C3×D20—41no—
138C3×D20—41no—
139C3×D20C22⋊C414yescomplemented
140D5×Dic3—48no—
141C3×C5×C8—22no—
142C5×C3⋊C8—41no—
143C22×C3×D4—51no—
144C22×C3×D4—51no—
145C23×Dic3—101no—
146C2×C3×D8—54no—
147C2×C3×D8—102no—
148C2×C3×D8—102no—
149C22×C3×C8C2×D511yescharacteristic
150C2×#217—101no—
151C2×#217—101no—
152C2×#217—101no—
153D4×Dic3—102no—
154D4×Dic3—102no—
155C2×C4⋊Dic3—51no—
156C2×C4⋊Dic3—51no—
157C2×C4×Dic3C2×D511yescharacteristic
158C22×C3⋊C8C2×D511yescharacteristic
159#832—102no—
160#832—102no—
161C23×D5—21no—
162C23×D5—21no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5C22×D311yescharacteristic
166C22×Dic5—61no—
167C22×Dic5—61no—
168C2×D20—21no—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20—21no—
173C2×D20—21no—
174C2×D20—21no—
175C2×D20—21no—
176C2×D20C2×Dic312yes—
177C2×D20C2×Dic312yescomplemented
178C2×D20#6712yes—
179C2×D20#6712yes—
180C2×C4×D5—64no—
181C2×C4×D5—122no—
182C2×C4×D5—122no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—61no—
186C2×C5×C8—61no—
187C2×C5×C8—61no—
188C2×C5×C8C2×Dic312yescomplemented
189C42×C5—61no—
190C42×C5—61no—
191#685—64no—
192#685—122no—
193#685—122no—
194C4⋊Dic5—32no—
195C4⋊Dic5—61no—
196C4⋊Dic5—61no—
197C4⋊Dic5—61no—
198D40—28no—
199C22×D8—51no—
200C2×C4×D4—151no—
201C2×#102—151no—
202C2×#102—151no—
203#390—151no—
204#340—151no—
205#336—31no—
206C22×C3×C5C4×D411yescharacteristic
207C22×C3×C5#12011yescharacteristic
208C22×C3×C5#12111yescharacteristic
209C22×C3×C5C2×D811yescharacteristic
210C22×C3×C5#13511yescharacteristic
211C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
212C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
213C2×C3×D5—24no—
214C2×C3×D5—42no—
215C2×C3×D5—42no—
216C2×C3×D5—42no—
217C2×C3×D5—42no—
218C2×C3×D5—42no—
219C2×C3×D5—42no—
220C2×C3×D5—42no—
221C2×C3×D5—42no—
222C2×C3×D5—42no—
223C2×C3×D5—81no—
224C2×C3×D5—81no—
225C2×C3×D5—81no—
226C2×C3×D5—81no—
227C3×C4×C5C2×C22⋊C411yescharacteristic
228C3×C4×C5C4×D411yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×C4×C5#12311yescharacteristic
231Dic15—42no—
232Dic15—81no—
233C5×Dic3—22no—
234C5×Dic3—41no—
235C24×C3—101no—
236C24×C3—101no—
237C2×C3×D4—52no—
238C2×C3×D4—52no—
239C2×C3×D4—52no—
240C2×C3×D4—52no—
241C2×C3×D4—101no—
242C2×C3×D4—101no—
243C2×C3×D4—101no—
244C2×C3×D4—101no—
245C2×C3×D4—101no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C2×C3×D4—101no—
249C22×C3×C4C22×D511yescharacteristic
250C22×Dic3—104no—
251C22×Dic3—101no—
252C22×Dic3—101no—
253C22×Dic3—202no—
254C22×Dic3—202no—
255C22×Dic3D2011yescharacteristic
256C22×Dic3D2011yescharacteristic
257C3×D8—108no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8C4×D512yescomplemented
261#217—104no—
262#217—202no—
263#217—202no—
264C4⋊Dic3—52no—
265C4⋊Dic3—101no—
266C4⋊Dic3—101no—
267C4⋊Dic3—101no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272C2×C3⋊C8—21no—
273C23×C5D3×D411yescharacteristic
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—41no—
279C22×D5—41no—
280C22×D5—41no—
281C22×D5—41no—
282C22×D5—41no—
283C22×D5—41no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C2×C4×C5—32no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—61no—
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5#23711yescharacteristic
296C2×C4×C5#23711yescharacteristic
297C2×C4×C5C22×Dic311yescharacteristic
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C2×#6711yescharacteristic
300C2×Dic5—62no—
301C2×Dic5—121no—
302C2×Dic5—121no—
303C2×Dic5—121no—
304C2×Dic5—121no—
305C2×Dic5—121no—
306D20—22no—
307D20—22no—
308D20—22no—
309D20—22no—
310D20—22no—
311D20—41no—
312D20—41no—
313D20#21714yescomplemented
314C4×D5—128no—
315C5×C8—22no—
316C5×C8—121no—
317C22×D4—51no—
318C22×D4—51no—
319C23×C4—301no—
320C2×D8—54no—
321C2×D8—102no—
322C2×D8—102no—
323C22×C8—31no—
324C22×C8D3×D511yescharacteristic
325C4×D4—302no—
326C4×D4—302no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4—151no—
329C2×C22⋊C4—301no—
330C2×C22⋊C4—301no—
331C2×C22⋊C4—301no—
332C2×C42—31no—
333#102—302no—
334#102—302no—
335C2×C3×C5#38611yescharacteristic
336C2×C3×C5C4×D811yescharacteristic
337C2×C3×C5#44211yescharacteristic
338C2×C3×C5#44711yescharacteristic
339C2×C3×C5#44911yescharacteristic
340C2×C3×C5#45911yescharacteristic
341C2×C3×C5#46311yescharacteristic
342C3×D5—44no—
343C3×D5—82no—
344C23×C3—102no—
345C23×C3—102no—
346C23×C3—102no—
347C23×C3—102no—
348C23×C3—201no—
349C23×C3—201no—
350C23×C3—201no—
351C23×C3—201no—
352C23×C3—201no—
353C23×C3—201no—
354C23×C3—201no—
355C23×C3—201no—
356C23×C3—201no—
357C23×C3—201no—
358C23×C3C2×D2011yescharacteristic
359C3×D4—54no—
360C3×D4—102no—
361C3×D4—102no—
362C3×D4—102no—
363C3×D4—102no—
364C3×D4—102no—
365C3×D4—201no—
366C3×D4—201no—
367C2×C3×C4C2×C4×D511yescharacteristic
368C2×C3×C4#70911yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4#71311yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—102no—
379C2×Dic3—208no—
380C2×Dic3—201no—
381C2×Dic3—201no—
382C2×Dic3—201no—
383C2×Dic3—201no—
384C2×Dic3—201no—
385C2×Dic3D4012yescomplemented
386C3×C8—22no—
387C3⋊C8—41no—
388C22×C5D3×D811yescharacteristic
389C22×C5#91111yescharacteristic
390C22×C5#91111yescharacteristic
391C22×C5#91211yescharacteristic
392C22×C5D4×Dic311yescharacteristic
393C22×C5#93711yescharacteristic
394C22×C5#93911yescharacteristic
395C2×D5—24no—
396C2×D5—42no—
397C2×D5—42no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—42no—
405C2×D5—81no—
406C2×D5—81no—
407C2×D5—81no—
408C2×D5—81no—
409C4×C5—62no—
410C4×C5—121no—
411C4×C5D4×Dic311yescharacteristic
412C4×C5#93511yescharacteristic
413C4×C5#93911yescharacteristic
414C4×C5C2×#21711yescharacteristic
415Dic5—122no—
416Dic5—241no—
417C24—101no—
418C24—101no—
419C2×D4—52no—
420C2×D4—52no—
421C2×D4—52no—
422C2×D4—52no—
423C2×D4—101no—
424C2×D4—101no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—304no—
434C22×C4—301no—
435C22×C4—301no—
436C22×C4—602no—
437C22×C4—602no—
438C22×C4C2×D3×D511yescharacteristic
439D8—108no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8D5×Dic312yescomplemented
446C4⋊C4—152no—
447C4⋊C4—301no—
448C4⋊C4—301no—
449C4⋊C4—301no—
450C22⋊C4—304no—
451C22⋊C4—602no—
452C22⋊C4—602no—
453C42—61no—
454C42—61no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—104no—
457C22×C3—202no—
458C22×C3—202no—
459C22×C3—202no—
460C22×C3—202no—
461C22×C3—202no—
462C22×C3—202no—
463C22×C3—202no—
464C22×C3—202no—
465C22×C3—202no—
466C22×C3—401no—
467C22×C3—401no—
468C22×C3—401no—
469C22×C3—401no—
470C22×C3C4×D2011yescharacteristic
471C22×C3#402811yescharacteristic
472C22×C3#404111yescharacteristic
473C22×C3C2×D4011yescharacteristic
474C22×C3#405011yescharacteristic
475C22×C3#405411yescharacteristic
476C22×C3#405411yescharacteristic
477C3×C4D5×C22⋊C411yescharacteristic
478C3×C4#403011yescharacteristic
479C3×C4#403911yescharacteristic
480C3×C4#404011yescharacteristic
481Dic3—22no—
482Dic3—41no—
483Dic3—202no—
484Dic3—401no—
485C2×C5Dic3×D811yescharacteristic
486C2×C5#515011yescharacteristic
487C2×C5#515211yescharacteristic
488C2×C5#515311yescharacteristic
489C2×C5#515611yescharacteristic
490C2×C5#515811yescharacteristic
491C2×C5#522011yescharacteristic
492D5—44no—
493D5—82no—
494C23—102no—
495C23—102no—
496C23—102no—
497C23—102no—
498C23—201no—
499C23—201no—
500C23—201no—
501C23—201no—
502C23—201no—
503C23—201no—
504C23—201no—
505C23—201no—
506C23—201no—
507C23—201no—
508C23D3×D2011yescharacteristic
509D4—54no—
510D4—102no—
511D4—102no—
512D4—102no—
513D4—102no—
514D4—102no—
515D4—201no—
516D4—201no—
517C2×C4—32no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—302no—
524C2×C4—608no—
525C2×C4—601no—
526C2×C4—601no—
527C2×C4—601no—
528C2×C4—601no—
529C2×C4—601no—
530C2×C4#676511yescharacteristic
531C2×C4#676611yescharacteristic
532C2×C4#677711yescharacteristic
533C2×C4C2×D5×Dic311yescharacteristic
534C2×C4D5×#6711yescharacteristic
535C2×C4D5×#6711yescharacteristic
536C8—22no—
537C8—121no—
538C2×C3—204no—
539C2×C3—402no—
540C2×C3#6495411yescharacteristic
541C2×C3C4×D4011yescharacteristic
542C2×C3#6500011yescharacteristic
543C2×C3#6502111yescharacteristic
544C2×C3#6502311yescharacteristic
545C2×C3#6513211yescharacteristic
546C2×C3#6513311yescharacteristic
547C5#7203711yescharacteristic, complemented, Sylow
548C22—104no—
549C22—202no—
550C22—202no—
551C22—202no—
552C22—202no—
553C22—202no—
554C22—202no—
555C22—202no—
556C22—202no—
557C22—202no—
558C22—401no—
559C22—401no—
560C22—401no—
561C22—401no—
562C22D3×D4011yescharacteristic
563C22#9125411yescharacteristic
564C22#9125411yescharacteristic
565C22#9127311yescharacteristic
566C22#9140911yescharacteristic
567C22Dic3×D2011yescharacteristic
568C22#9147411yescharacteristic
569C4—62no—
570C4—121no—
571C4—602no—
572C4—1201no—
573C4#9140711yescharacteristic
574C4#9140811yescharacteristic
575C4#9143411yescharacteristic
576C4D5×#21711yescharacteristic
577C3#1059946611yescharacteristic, complemented, Sylow
578C2—204no—
579C2—402no—
580C2#1174775411yescharacteristic
581C2#1174775611yescharacteristic
582C2Dic3×D4011yescharacteristic
583C2#1174779911yescharacteristic
584C2#1174811211yescharacteristic
585C2#1174814911yescharacteristic
586C2#1174889611yescharacteristic
subgroupG/H
centerC23D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×D40C2
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1879
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×D20C2semidirect
3. #11748785C2semidirect
4. C2×#90965C2semidirect
5. C2×#90965C2semidirect
6. #11746372C2semidirect
7. C5×#4550C2semidirect
19. C2×C3×D40C4semidirect
51. C2×C3×D20C2×C4semidirect
59. C2×C3×C5×C8C2×C4semidirect
79. #4550D5semidirect
93. C2×D40Dic3semidirect
131. C2×C5×Dic3D8semidirect
139. C3×D20C22⋊C4semidirect
177. C2×D20C2×Dic3semidirect
188. C2×C5×C8C2×Dic3semidirect
260. C2×C3×C8C4×D5semidirect
313. D20#217semidirect
385. C2×Dic3D40semidirect
445. C2×C8D5×Dic3semidirect
455. C3×C5#1879semidirect
547. C5#72037semidirect
577. C3#10599466semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D402
C2×Dic3×D202
#117487852
C2×#909652
#117463722
C5×#45502
#105994663
#720375