Finite Group Databasebeta

← #14307999

Subgroups — #14307999

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756592C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C2×#91304C211yesmaximal, characteristic, complemented
4C2×C3×#3969C211yesmaximal, characteristic, complemented
5#11748764C211yesmaximal, characteristic, complemented
6C2×#90981C211yesmaximal, characteristic, complemented
7#11745987C211yesmaximal, characteristic, complemented
8#10602891—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C2×#6817C2211yescharacteristic
11C22×C5×D12C2211yescharacteristic
12#91835—21no—
13#91828—22no—
14#91827—21no—
15#91819—21no—
16C2×C4⋊Dic15C2211yescharacteristic
17#91813—21no—
18C5×#949—22no—
19C5×#949—22no—
20C2×C5×#215—21no—
21C2×C5×#213—21no—
22C2×C5×#208C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25C2×(C2×D3)⋊Dic5—22no—
26C2×#6659—21no—
27#91304—22no—
28#91304—22no—
29C2×#6654—21no—
30C3×#3969—22no—
31#90981—22no—
32#70392—51nomaximal, Hall
33C2×C5×AGL(1,ℤ/8)—31no—
34#66167—31no—
35C2×#4078—31no—
36C2×#3969D311yescharacteristic, complemented
37#65510—31no—
38C2×#3957—31no—
39#64774—31no—
40C23×C5×D3—21no—
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41—21no—
45C2×C3×C5×Q8D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4D411yescharacteristic
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C2×#1220—21no—
51C2×#1220—22no—
52C22×Dic15D412yes—
53#6817—21no—
54#6817—21no—
55#6817—21no—
56#6817—21no—
57C2×D60D411yescharacteristic
58C2×C4×D15—21no—
59C2×Dic30D411yescharacteristic
60C2×C5×D12—21no—
61C2×C5×D12—21no—
62C2×C5×D12—21no—
63C2×C5×D12—21no—
64C2×C5×D12—21no—
65C2×C5×D12D412yescomplemented
66C22×C3×Dic5—21no—
67#6719—22no—
68#6714—22no—
69C4⋊Dic15—21no—
70C4⋊Dic15—21no—
71#6712—22no—
72C5×#215—24no—
73C5×#213—24no—
74C5×#208—21no—
75C5×#208D412yescomplemented
76C2×C5×C3⋊C8—21no—
77C3×C4×Dic5—21no—
78C3×C4×Dic5—21no—
79C3×#681—21no—
80C3×#681D412yescomplemented
81C2×C3×#168—21no—
82(C2×D3)⋊Dic5—44no—
83#6659—24no—
84#6654—24no—
85#5833—51no—
86C2×#949D511yescharacteristic, complemented
87C2×#908—51no—
88C2×C3×#104—51no—
89#4939—51no—
90C2×#805—51no—
91#4554—51no—
92C2×C5×#41C2×D311yescharacteristic
93C22×C5×D4—31no—
94C2×#709—31no—
95C5×AGL(1,ℤ/8)—62no—
96C5×AGL(1,ℤ/8)—62no—
97C2×C5×SD16—61no—
98C2×C5×D8—61no—
99C2×C5×M16—31no—
100C2×C22⋊Dic5—62no—
101#4092—61no—
102#4085—62no—
103#4084—61no—
104C2×#687—61no—
105#4078—62no—
106#4078—62no—
107C2×#686—61no—
108#4076—61no—
109C2×C4⋊Dic5—31no—
110#4070—61no—
111C2×C4×Dic5C2×D311yescharacteristic
112C2×#681C2×D311yescharacteristic
113#3969—22no—
114#3957—62no—
115#2006—151noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—21no—
119C22×C5×D3—22no—
120C22×C5×D3—42no—
121C22×C5×D3—42no—
122C22×C5×D3—41no—
123C22×C5×D3—41no—
124C3×C5×Q8—21no—
125C3×C5×Q8—21no—
126C3×C5×D4—21no—
127C3×C5×D4—21no—
128C3×C5×D4—41no—
129C3×C5×D4—41no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139#1220—41no—
140#1220—41no—
141#1220—82no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—42no—
145D60—21no—
146D60—21no—
147C4×D15—41no—
148C4×D15—41no—
149Dic30—21no—
150Dic30—21no—
151C5×D12—22no—
152C5×D12—22no—
153C5×D12—41no—
154C5×D12—41no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5—41no—
158C3×#168—22no—
159C5×C3⋊C8—22no—
160C2×C3×#41C2×D511yescharacteristic
161C2×#235—51no—
162C22×D12C2×D511yescharacteristic
163C2×C3×M16—51no—
164C2×C3×C42—51no—
165#949—22no—
166#949—22no—
167#946—101no—
168C2×#215—21no—
169#939—102no—
170#938—101no—
171C2×#213—21no—
172#930—101no—
173C2×(C2×D3)⋊C4—102no—
174C2×C4⋊Dic3—51no—
175#924—101no—
176C2×#208C2×D511yescharacteristic
177#908—102no—
178#908—102no—
179C2×D24—101no—
180C2×#204—101no—
181C3×#104—102no—
182#805—102no—
183C24×C5—61no—
184C5×#41—21no—
185C5×#41—21no—
186C5×#41—21no—
187C5×#41—21no—
188C2×C5×Q8D1211yescharacteristic
189C2×C5×D4—21no—
190C2×C5×D4—32no—
191C2×C5×D4—61no—
192C2×C5×D4—61no—
193C2×C5×D4—61no—
194C2×C5×D4—61no—
195C2×C5×D4—61no—
196C2×C5×D4D1211yescharacteristic
197C22×C4×C5—21no—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—61no—
200C2×C22⋊D5—62no—
201C22×Dic5—21no—
202C22×Dic5—32no—
203#709—61no—
204#709—61no—
205#709—61no—
206#709—61no—
207C2×D20—31no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×SD16—64no—
211C5×D8—64no—
212C5×M16—32no—
213C5×M16—61no—
214C2×C5×C8—61no—
215C22⋊Dic5—62no—
216C22⋊Dic5—124no—
217#687—64no—
218#686—64no—
219#685—62no—
220C4⋊Dic5—61no—
221C4⋊Dic5—61no—
222#683—62no—
223C4×Dic5—21no—
224C4×Dic5—21no—
225#681—21no—
226#681#6712yescomplemented
227C2×#168—21no—
228C2×AGL(1,ℤ/8)—31no—
229C2×AGL(1,ℤ/8)—151no—
230#537—151no—
231C2×#104—51no—
232C2×#104—151no—
233#390—151no—
234#343—151no—
235C22×C3×C5—21no—
236C22×C3×C5—21no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5#12011yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5#12711yescharacteristic
243C2×D15—41no—
244C2×D15—41no—
245C2×D15—41no—
246C2×C5×D3—44no—
247C2×C5×D3—42no—
248C2×C5×D3—82no—
249C2×C5×D3—81no—
250C2×C5×D3—81no—
251C3×C4×C5—41no—
252C3×C4×C5#12011yescharacteristic
253C3×C4×C5#12011yescharacteristic
254C3×C4×C5#12111yescharacteristic
255C3×C4×C5#12111yescharacteristic
256Dic15—41no—
257Dic15—42no—
258C3×Dic5—42no—
259C23×D3—21no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C2×C3×Q8C22⋊D511yescharacteristic
265C2×C3×D4—21no—
266C2×C3×D4C22⋊D511yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C2×#67—102no—
272C22×Dic3—52no—
273#235—101no—
274#235—101no—
275#235—101no—
276#235—101no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—51no—
283C2×D12C22⋊D512yescomplemented
284C2×C4×D3—101no—
285C2×Dic6—51no—
286C3×M16—52no—
287C3×M16—101no—
288C2×C3×C8—101no—
289C3×C42—101no—
290C3×C42—101no—
291#217—102no—
292#215—24no—
293#213—24no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—204no—
296C4⋊Dic3—101no—
297C4⋊Dic3—101no—
298Dic3⋊C4—102no—
299#208—21no—
300#208C22⋊D512yescomplemented
301C2×C3⋊C8—21no—
302D24—104no—
303#204—104no—
304C23×C5—21no—
305C23×C5—62no—
306C23×C5—122no—
307C23×C5—122no—
308C23×C5—121no—
309C23×C5—121no—
310C23×C5D3×D411yescharacteristic
311C22×D5—61no—
312C5×Q8—21no—
313C5×Q8—21no—
314C5×D4—21no—
315C5×D4—21no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4—62no—
319C5×D4—62no—
320C5×D4—121no—
321C5×D4—121no—
322C2×C4×C5—21no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5C2×D1211yescharacteristic
326C2×C4×C5#23511yescharacteristic
327C2×C4×C5D3×D411yescharacteristic
328C2×C4×C5D3×D411yescharacteristic
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5C2×#6711yescharacteristic
331C22⋊D5—121no—
332C22⋊D5—121no—
333C22⋊D5—242no—
334C2×Dic5—22no—
335C2×Dic5—41no—
336C2×Dic5—41no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339C2×Dic5—122no—
340D20—61no—
341D20—61no—
342C4×D5—121no—
343C4×D5—121no—
344Dic10—61no—
345Dic10—61no—
346C5×C8—62no—
347#168—22no—
348C2×#41—151no—
349C2×#41D3×D511yescharacteristic
350C22×D4—31no—
351AGL(1,ℤ/8)—62no—
352AGL(1,ℤ/8)—62no—
353AGL(1,ℤ/8)—302no—
354AGL(1,ℤ/8)—302no—
355C2×SD16—61no—
356C2×SD16—301no—
357C2×D8—61no—
358C2×D8—301no—
359C2×M16—31no—
360C2×M16—51no—
361C22⋊Q8—301no—
362C22⋊Q8—301no—
363#121—301no—
364#121—302no—
365#121—301no—
366C2×C4⋊C4—151no—
367C2×C22⋊C4—302no—
368C2×C42—51no—
369#104—102no—
370#104—302no—
371C2×C3×C5—21no—
372C2×C3×C5—21no—
373C2×C3×C5—81no—
374C2×C3×C5#39211yescharacteristic
375C2×C3×C5#45311yescharacteristic
376C2×C3×C5#45411yescharacteristic
377D15—81no—
378C5×D3—82no—
379C23×C3—21no—
380C23×C3D4×D511yescharacteristic
381C22×D3—22no—
382C22×D3—42no—
383C22×D3—42no—
384C22×D3—41no—
385C22×D3—41no—
386C22×D3—101no—
387C3×Q8—21no—
388C3×Q8—21no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—41no—
392C3×D4—41no—
393C2×C3×C4—21no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—102no—
397C2×C3×C4—201no—
398C2×C3×C4—201no—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4#71111yescharacteristic
402C2×C3×C4C2×C22⋊D511yescharacteristic
403C2×C3×C4C2×C22⋊D511yescharacteristic
404C2×C3×C4C2×C22⋊D511yescharacteristic
405#67—201no—
406#67—201no—
407#67—402no—
408C2×Dic3—101no—
409C2×Dic3—102no—
410C2×Dic3—202no—
411D12—22no—
412D12—22no—
413D12—41no—
414D12—41no—
415D12—101no—
416D12—101no—
417C4×D3—201no—
418C4×D3—201no—
419Dic6—101no—
420Dic6—101no—
421C3×C8—102no—
422C3⋊C8—22no—
423C22×C5—21no—
424C22×C5—21no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—124no—
429C22×C5—122no—
430C22×C5—242no—
431C22×C5—241no—
432C22×C5—241no—
433C22×C5#88211yescharacteristic
434C22×C5#88411yescharacteristic
435C22×C5#94011yescharacteristic
436C2×D5—121no—
437C2×D5—121no—
438C2×D5—121no—
439C4×C5—41no—
440C4×C5#88211yescharacteristic
441C4×C5#88411yescharacteristic
442C4×C5#93011yescharacteristic
443C4×C5#93711yescharacteristic
444Dic5—42no—
445Dic5—121no—
446Dic5—122no—
447C24—61no—
448#41—21no—
449#41—21no—
450#41—21no—
451#41—21no—
452#41—301no—
453#41—301no—
454#41—301no—
455#41—301no—
456C2×Q8—151no—
457C2×Q8#120311yescharacteristic
458C2×D4—21no—
459C2×D4—32no—
460C2×D4—61no—
461C2×D4—61no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—151no—
466C2×D4—301no—
467C2×D4—302no—
468C2×D4#120311yescharacteristic
469C22×C4—21no—
470C22×C4—101no—
471C22×C4—152no—
472C22×C4—301no—
473C22×C4C2×D3×D511yescharacteristic
474SD16—64no—
475SD16—304no—
476D8—64no—
477D8—304no—
478M16—32no—
479M16—52no—
480M16—61no—
481M16—101no—
482C2×C8—61no—
483C2×C8—101no—
484C4⋊C4—302no—
485C4⋊C4—301no—
486C4⋊C4—301no—
487C22⋊C4—302no—
488C22⋊C4—302no—
489C22⋊C4—604no—
490C42—101no—
491C42—101no—
492C3×C5#200611yescharacteristic, complemented, Hall
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3#408311yescharacteristic
499C22×C3#408511yescharacteristic
500C22×C3#408611yescharacteristic
501C2×D3—44no—
502C2×D3—42no—
503C2×D3—82no—
504C2×D3—81no—
505C2×D3—81no—
506C2×D3—201no—
507C2×D3—201no—
508C2×D3—201no—
509C3×C4—41no—
510C3×C4—202no—
511C3×C4#408311yescharacteristic
512C3×C4#408411yescharacteristic
513C3×C4#408511yescharacteristic
514C3×C4#409911yescharacteristic
515Dic3—202no—
516Dic3—201no—
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—81no—
520C2×C5—242no—
521C2×C5#482211yescharacteristic
522C2×C5#482711yescharacteristic
523C2×C5#496011yescharacteristic
524D5—241no—
525C23—21no—
526C23—62no—
527C23—122no—
528C23—122no—
529C23—121no—
530C23—121no—
531C23—301no—
532C23#679011yescharacteristic
533Q8—21no—
534Q8—21no—
535Q8—301no—
536Q8—301no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—62no—
542D4—62no—
543D4—121no—
544D4—121no—
545D4—301no—
546D4—301no—
547D4—601no—
548D4—601no—
549D4—1202no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—102no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—302no—
557C2×C4—301no—
558C2×C4—601no—
559C2×C4—601no—
560C2×C4—602no—
561C2×C4#678211yescharacteristic
562C2×C4C2×#120311yescharacteristic
563C2×C4D5×#6711yescharacteristic
564C2×C4D3×C22⋊D511yescharacteristic
565C2×C4D3×C22⋊D511yescharacteristic
566C2×C4#679011yescharacteristic
567C8—62no—
568C8—102no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—81no—
572C2×C3#6548711yescharacteristic
573C2×C3#6549011yescharacteristic
574C2×C3#6551211yescharacteristic
575D3—82no—
576D3—401no—
577C5#7039211yescharacteristic, complemented, Sylow
578C22—21no—
579C22—21no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—124no—
584C22—122no—
585C22—242no—
586C22—241no—
587C22—241no—
588C22—601no—
589C22—601no—
590C22—601no—
591C22#9155811yescharacteristic
592C22#9156711yescharacteristic
593C22#9157311yescharacteristic
594C4—41no—
595C4—202no—
596C4—602no—
597C4—601no—
598C4#9155711yescharacteristic
599C4#9156611yescharacteristic
600C4#9157011yescharacteristic
601C4#9157711yescharacteristic
602C3#1060289111yescharacteristic, complemented, Sylow
603C2—21no—
604C2—21no—
605C2—81no—
606C2—242no—
607C2—1201no—
608C2#1174942211yescharacteristic
609C2#1174946111yescharacteristic
610C2#1174952311yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#2006
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756592C2semidirect
2. C2×C5×#949C2semidirect
3. C2×#91304C2semidirect
4. C2×C3×#3969C2semidirect
5. #11748764C2semidirect
6. C2×#90981C2semidirect
7. #11745987C2semidirect
36. C2×#3969D3semidirect
65. C2×C5×D12D4semidirect
75. C5×#208D4semidirect
80. C3×#681D4semidirect
86. C2×#949D5semidirect
226. #681#67semidirect
283. C2×D12C22⋊D5semidirect
300. #208C22⋊D5semidirect
492. C3×C5#2006semidirect
577. C5#70392semidirect
602. C3#10602891semidirect

Maximal subgroups

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

subgroupindex
#117565922
C2×C5×#9492
C2×#913042
C2×C3×#39692
#117487642
C2×#909812
#117459872
#106028913
#703925