Finite Group Databasebeta

← #14301066

Subgroups — #14301066

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×D120C211yesmaximal, characteristic
2C2×#91428C211yesmaximal, characteristic, complemented
3#11748789C211yesmaximal, characteristic, complemented
4C2×#90968C211yesmaximal, characteristic, complemented
5C2×#90968C211yesmaximal, characteristic, complemented
6C5×#4550C211yesmaximal, characteristic, complemented
7C3×#64771C211yesmaximal, characteristic, complemented
8#10599466—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C22×#1200—21no—
12C22×C3×C5×C8C2211yescharacteristic
13C2×D120—22no—
14C2×D120—22no—
15C2×D120C414yescomplemented
16C2×C4×C5×Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×C4⋊Dic5C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×#6667—21no—
21C2×#6667—21no—
22C2×#6667—21no—
23#91428—22no—
24#91428—22no—
25#90968—22no—
26#90968—22no—
27#68897—51nomaximal, Hall
28C22×D40—31no—
29C2×C4×D20—31no—
30C2×#3953—31no—
31C2×#3953—31no—
32#65228—31no—
33C5×#336—31no—
34#64771D311yescharacteristic, complemented
35C23×D15—21no—
36C23×D15—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60C2×C412yes—
47C2×D60C2×C412yescomplemented
48C2×D60D412yes—
49C2×D60D412yes—
50C22×C5×Dic3D411yescharacteristic
51C22×C5×Dic3D411yescharacteristic
52C22×C3×Dic5—21no—
53C22×C3×Dic5—21no—
54C2×#1200—24no—
55C2×#1200—42no—
56C2×#1200—42no—
57C2×C3×C5×C8—21no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8C2×C412yescomplemented
60D120—28no—
61C4×C5×Dic3—21no—
62C4×C5×Dic3—21no—
63C2×C5×C3⋊C8—21no—
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C3×C4⋊Dic5—21no—
67C3×C4⋊Dic5—21no—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5D412yes—
70#6667—24no—
71#6667—42no—
72#6667—42no—
73C22×D24—51no—
74C2×#893—51no—
75#4988—51no—
76C2×#809—51no—
77C2×#809—51no—
78C3×#340—51no—
79#4550D511yescharacteristic, complemented
80C22×D20—31no—
81C22×D20—31no—
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⋊Dic5C2×D311yescharacteristic
90C2×C4⋊Dic5C2×D311yescharacteristic
91C2×D40—34no—
92C2×D40—62no—
93C2×D40—62no—
94C4×D20—62no—
95C4×D20—62no—
96#3953—62no—
97#3953—62no—
98#1879—151noSylow
99C23×C3×C5C2×D411yescharacteristic
100C22×D15—22no—
101C22×D15—22no—
102C22×D15—22no—
103C22×D15—22no—
104C22×D15—41no—
105C22×D15—41no—
106C22×D15—41no—
107C22×D15—41no—
108C22×D15—41no—
109C22×D15—41no—
110C22×D15—41no—
111C22×D15—41no—
112C22×D15—41no—
113C22×D15—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
120D60—22no—
121D60—22no—
122D60—22no—
123D60—22no—
124D60—22no—
125D60—41no—
126D60—41no—
127D60C22⋊C414yescomplemented
128C2×C5×Dic3—21no—
129C2×C5×Dic3—21no—
130C2×C5×Dic3—21no—
131C2×C5×Dic3—21no—
132C2×C5×Dic3—21no—
133C2×C5×Dic3D812yescomplemented
134C2×C3×Dic5—22no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C2×C3×Dic5—41no—
138C2×C3×Dic5—41no—
139C2×C3×Dic5—41no—
140#1200—48no—
141C3×C5×C8—22no—
142C5×C3⋊C8—41no—
143C22×D12—51no—
144C22×D12—51no—
145C22×C4×D3—101no—
146C22×C3×C8C2×D511yescharacteristic
147C2×C3×C4⋊C4—51no—
148C2×C3×C4⋊C4—51no—
149C2×(C2×D3)⋊C4—101no—
150C2×(C2×D3)⋊C4—101no—
151C2×(C2×D3)⋊C4—101no—
152C2×C4×Dic3C2×D511yescharacteristic
153C22×C3⋊C8C2×D511yescharacteristic
154C2×D24—54no—
155C2×D24—102no—
156C2×D24—102no—
157#893—102no—
158#893—102no—
159#809—102no—
160#809—102no—
161C23×D5—61no—
162C23×D5—61no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5C22×D311yescharacteristic
166C22×Dic5—21no—
167C22×Dic5—21no—
168C2×D20—32no—
169C2×D20—32no—
170C2×D20—32no—
171C2×D20—32no—
172C2×D20—61no—
173C2×D20—61no—
174C2×D20—61no—
175C2×D20—61no—
176C2×D20—61no—
177C2×D20—61no—
178C2×D20—61no—
179C2×D20—61no—
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×C8C4×D312yescomplemented
189C42×C5—61no—
190C42×C5—61no—
191#685—64no—
192#685—122no—
193#685—122no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5D1212yes—
198D40—68no—
199C22×D8—151no—
200C2×C4×D4—151no—
201C2×#102—151no—
202C2×#102—151no—
203#390—151no—
204#340—51no—
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×D15—24no—
214C2×D15—42no—
215C2×D15—42no—
216C2×D15—42no—
217C2×D15—42no—
218C2×D15—42no—
219C2×D15—42no—
220C2×D15—42no—
221C2×D15—42no—
222C2×D15—42no—
223C2×D15—81no—
224C2×D15—81no—
225C2×D15—81no—
226C2×D15—81no—
227C3×C4×C5C2×C22⋊C411yescharacteristic
228C3×C4×C5C4×D411yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×C4×C5#12311yescharacteristic
231C3×Dic5—42no—
232C3×Dic5—81no—
233C5×Dic3—22no—
234C5×Dic3—41no—
235C23×D3—101no—
236C23×D3—101no—
237C22×C3×C4—101no—
238C22×C3×C4—101no—
239C22×C3×C4C22×D511yescharacteristic
240C22×Dic3D2011yescharacteristic
241C22×Dic3D2011yescharacteristic
242C2×D12—52no—
243C2×D12—52no—
244C2×D12—52no—
245C2×D12—52no—
246C2×D12—101no—
247C2×D12—101no—
248C2×D12—101no—
249C2×D12—101no—
250C2×D12—101no—
251C2×D12—101no—
252C2×D12—101no—
253C2×D12—101no—
254C2×C4×D3—104no—
255C2×C4×D3—202no—
256C2×C4×D3—202no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8C4×D512yescomplemented
260C3×C4⋊C4—52no—
261C3×C4⋊C4—101no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—101no—
264(C2×D3)⋊C4—104no—
265(C2×D3)⋊C4—202no—
266(C2×D3)⋊C4—202no—
267C4×Dic3—21no—
268C4×Dic3—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272D24—108no—
273C23×C5D3×D411yescharacteristic
274C22×D5—62no—
275C22×D5—62no—
276C22×D5—62no—
277C22×D5—62no—
278C22×D5—121no—
279C22×D5—121no—
280C22×D5—121no—
281C22×D5—121no—
282C22×D5—121no—
283C22×D5—121no—
284C22×D5—121no—
285C22×D5—121no—
286C22×D5—121no—
287C22×D5—121no—
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×C5C2×C4×D311yescharacteristic
295C2×C4×C5C2×D1211yescharacteristic
296C2×C4×C5#23511yescharacteristic
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5#23911yescharacteristic
300C2×Dic5—22no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306D20—34no—
307D20—62no—
308D20—62no—
309D20—62no—
310D20—62no—
311D20—62no—
312D20—121no—
313D20—121no—
314C4×D5—128no—
315C5×C8—22no—
316C5×C8—121no—
317C22×D4—151no—
318C22×D4—151no—
319C23×C4—301no—
320C2×D8—154no—
321C2×D8—302no—
322C2×D8—302no—
323C22×C8—31no—
324C22×C8D3×D511yescharacteristic
325C4×D4—302no—
326C4×D4—302no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
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
342D15—44no—
343D15—82no—
344C23×C3C2×D2011yescharacteristic
345C22×D3—102no—
346C22×D3—102no—
347C22×D3—102no—
348C22×D3—102no—
349C22×D3—201no—
350C22×D3—201no—
351C22×D3—201no—
352C22×D3—201no—
353C22×D3—201no—
354C22×D3—201no—
355C22×D3—201no—
356C22×D3—201no—
357C22×D3—201no—
358C22×D3—201no—
359C2×C3×C4—102no—
360C2×C3×C4—201no—
361C2×C3×C4—201no—
362C2×C3×C4—201no—
363C2×C3×C4—201no—
364C2×C3×C4—201no—
365C2×C3×C4C2×C4×D511yescharacteristic
366C2×C3×C4#70911yescharacteristic
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4D4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4#71311yescharacteristic
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3D4012yescomplemented
377D12—54no—
378D12—102no—
379D12—102no—
380D12—102no—
381D12—102no—
382D12—102no—
383D12—201no—
384D12—201no—
385C4×D3—208no—
386C3×C8—22no—
387C3⋊C8—41no—
388C22×C5#88211yescharacteristic
389C22×C5#88411yescharacteristic
390C22×C5#89311yescharacteristic
391C22×C5D3×D811yescharacteristic
392C22×C5#91411yescharacteristic
393C22×C5#91411yescharacteristic
394C22×C5#91911yescharacteristic
395C2×D5—64no—
396C2×D5—122no—
397C2×D5—122no—
398C2×D5—122no—
399C2×D5—122no—
400C2×D5—122no—
401C2×D5—122no—
402C2×D5—122no—
403C2×D5—122no—
404C2×D5—122no—
405C2×D5—241no—
406C2×D5—241no—
407C2×D5—241no—
408C2×D5—241no—
409C4×C5—62no—
410C4×C5—121no—
411C4×C5C4×D1211yescharacteristic
412C4×C5D3×C22⋊C411yescharacteristic
413C4×C5#89411yescharacteristic
414C4×C5#89511yescharacteristic
415Dic5—42no—
416Dic5—81no—
417C24—301no—
418C24—301no—
419C2×D4—152no—
420C2×D4—152no—
421C2×D4—152no—
422C2×D4—152no—
423C2×D4—301no—
424C2×D4—301no—
425C2×D4—301no—
426C2×D4—301no—
427C2×D4—301no—
428C2×D4—301no—
429C2×D4—301no—
430C2×D4—301no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—304no—
436C22×C4—602no—
437C22×C4—602no—
438C22×C4C2×D3×D511yescharacteristic
439D8—308no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8#120012yescomplemented
446C4⋊C4—52no—
447C4⋊C4—101no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C22⋊C4—304no—
451C22⋊C4—602no—
452C22⋊C4—602no—
453C42—61no—
454C42—61no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3C4×D2011yescharacteristic
457C22×C3#402811yescharacteristic
458C22×C3#404111yescharacteristic
459C22×C3C2×D4011yescharacteristic
460C22×C3#405011yescharacteristic
461C22×C3#405411yescharacteristic
462C22×C3#405411yescharacteristic
463C2×D3—104no—
464C2×D3—202no—
465C2×D3—202no—
466C2×D3—202no—
467C2×D3—202no—
468C2×D3—202no—
469C2×D3—202no—
470C2×D3—202no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—401no—
474C2×D3—401no—
475C2×D3—401no—
476C2×D3—401no—
477C3×C4—202no—
478C3×C4—401no—
479C3×C4D5×C22⋊C411yescharacteristic
480C3×C4#403011yescharacteristic
481C3×C4#403911yescharacteristic
482C3×C4#404011yescharacteristic
483Dic3—22no—
484Dic3—41no—
485C2×C5#466511yescharacteristic
486C2×C5#477311yescharacteristic
487C2×C5#478611yescharacteristic
488C2×C5#481011yescharacteristic
489C2×C5#481911yescharacteristic
490C2×C5#486911yescharacteristic
491C2×C5#487211yescharacteristic
492D5—124no—
493D5—242no—
494C23—302no—
495C23—302no—
496C23—302no—
497C23—302no—
498C23—601no—
499C23—601no—
500C23—601no—
501C23—601no—
502C23—601no—
503C23—601no—
504C23—601no—
505C23—601no—
506C23—601no—
507C23—601no—
508C23D3×D2011yescharacteristic
509D4—154no—
510D4—302no—
511D4—302no—
512D4—302no—
513D4—302no—
514D4—302no—
515D4—601no—
516D4—601no—
517C2×C4—32no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—102no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—608no—
530C2×C4#676911yescharacteristic
531C2×C4#677311yescharacteristic
532C2×C4D5×D1211yescharacteristic
533C2×C4C2×#120011yescharacteristic
534C2×C4#679011yescharacteristic
535C2×C4#679011yescharacteristic
536C8—22no—
537C8—121no—
538C2×C3#6495411yescharacteristic
539C2×C3C4×D4011yescharacteristic
540C2×C3#6500011yescharacteristic
541C2×C3#6502111yescharacteristic
542C2×C3#6502311yescharacteristic
543C2×C3#6513211yescharacteristic
544C2×C3#6513311yescharacteristic
545D3—204no—
546D3—402no—
547C5#6889711yescharacteristic, complemented, Sylow
548C22—304no—
549C22—602no—
550C22—602no—
551C22—602no—
552C22—602no—
553C22—602no—
554C22—602no—
555C22—602no—
556C22—602no—
557C22—602no—
558C22—1201no—
559C22—1201no—
560C22—1201no—
561C22—1201no—
562C22D3×D4011yescharacteristic
563C22#9125311yescharacteristic
564C22#9125311yescharacteristic
565C22#9127511yescharacteristic
566C22#9142811yescharacteristic
567C22#9145911yescharacteristic
568C22#9147611yescharacteristic
569C4—62no—
570C4—121no—
571C4—202no—
572C4—401no—
573C4#9141811yescharacteristic
574C4#9142011yescharacteristic
575C4#9143311yescharacteristic
576C4#9156111yescharacteristic
577C3#1059946611yescharacteristic, complemented, Sylow
578C2—604no—
579C2—1202no—
580C2#1174779311yescharacteristic
581C2#1174779611yescharacteristic
582C2#1174779811yescharacteristic
583C2#1174800611yescharacteristic
584C2#1174812111yescharacteristic
585C2#1174816711yescharacteristic
586C2#1174890411yescharacteristic
subgroupG/H
centerC23D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×D120C2
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×#91428C2semidirect
3. #11748789C2semidirect
4. C2×#90968C2semidirect
5. C2×#90968C2semidirect
6. C5×#4550C2semidirect
7. C3×#64771C2semidirect
15. C2×D120C4semidirect
34. #64771D3semidirect
47. C2×D60C2×C4semidirect
59. C2×C3×C5×C8C2×C4semidirect
79. #4550D5semidirect
127. D60C22⋊C4semidirect
133. C2×C5×Dic3D8semidirect
188. C2×C5×C8C4×D3semidirect
259. C2×C3×C8C4×D5semidirect
376. C2×Dic3D40semidirect
445. C2×C8#1200semidirect
455. C3×C5#1879semidirect
547. C5#68897semidirect
577. C3#10599466semidirect

Maximal subgroups

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

subgroupindex
C22×D1202
C2×#914282
#117487892
C2×#909682
C5×#45502
C3×#647712
#105994663
#688975