Finite Group Databasebeta

← #14300695

Subgroups — #14300695

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91456C211yesmaximal, characteristic
2C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C2×C5×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#3953C211yesmaximal, characteristic, complemented
5C2×#90965C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11745980C211yesmaximal, characteristic, complemented
8#10600725—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C22×#1201—21no—
12C22×D3×Dic5—21no—
13C22×C3×C5×C8C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4⋊Dic15C2211yescharacteristic
16C22×C5×C3⋊C8C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×Dic3⋊Dic5—21no—
19C2×#6665—21no—
20#91456—22no—
21#91456C414yescomplemented
22D3×C4⋊Dic5—22no—
23D3×C4⋊Dic5—22no—
24C5×(C2×D3)⋊C8—22no—
25C3×#3953—22no—
26#90965—22no—
27#70200—51nomaximal, Hall
28C2×#4076—31no—
29C22×C4⋊Dic5—31no—
30C2×C5×C22⋊C8—31no—
31C2×#3953—31no—
32C2×#3953D311yescharacteristic, complemented
33#64771—31no—
34#64771—31no—
35C23×C5×D3D411yescharacteristic
36C23×C3×D5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×Dic15—21no—
40C22×C5×Dic3D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3C2×C412yes—
46C2×C4×C5×D3D412yes—
47C22×C3×Dic5—21no—
48C2×C3×D20—21no—
49C2×C3×D20—21no—
50C2×C3×D20—21no—
51C2×C3×D20—21no—
52C2×C3×D20—21no—
53C2×C3×D20C2×C412yescomplemented
54C2×#1201—24no—
55C2×#1201—42no—
56C2×#1201—42no—
57C2×D3×Dic5—24no—
58C2×D3×Dic5—42no—
59C2×D3×Dic5—42no—
60C2×C3×C5×C8—21no—
61C2×C3×C5×C8—21no—
62C2×C3×C5×C8—21no—
63C4⋊Dic15—21no—
64C4⋊Dic15—21no—
65C4⋊Dic15C2×C412yescomplemented
66C4⋊Dic15D412yescomplemented
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8—21no—
69C2×C5×C3⋊C8—21no—
70C3×C4⋊Dic5—21no—
71C3×C4⋊Dic5D412yescomplemented
72Dic3⋊Dic5—24no—
73#6665—24no—
74C2×#938—51no—
75C2×D3×C4⋊C4—51no—
76C2×C3×#102—51no—
77C2×#832—51no—
78C2×(C2×D3)⋊C8D511yescharacteristic, complemented
79#4551—51no—
80#4529—51no—
81C23×C4×C5—31no—
82C22×C22⋊D5—61no—
83C23×Dic5—61no—
84C22×D20C2×D311yescharacteristic
85C22×C5×C8—31no—
86C22×C5×C8C2×D311yescharacteristic
87#4076—34no—
88#4076—62no—
89C2×#685—61no—
90C2×C4⋊Dic5—31no—
91C2×C4⋊Dic5—31no—
92C2×C4⋊Dic5—62no—
93C2×C4⋊Dic5—61no—
94C2×C4⋊Dic5—62no—
95C2×C4⋊Dic5C2×D311yescharacteristic
96C5×C22⋊C8—62no—
97#3953—22no—
98#3953—62no—
99#1874—151noSylow
100C23×C3×C5C2×D411yescharacteristic
101C22×C5×D3—21no—
102C22×C5×D3—21no—
103C22×C5×D3—21no—
104C22×C5×D3—21no—
105C22×C5×D3C22⋊C412yes—
106C22×C5×D3D812yes—
107C22×C5×D3SD1612yes—
108C22×C3×D5—22no—
109C22×C3×D5—41no—
110C22×C3×D5—41no—
111C22×C3×D5—41no—
112C22×C3×D5—41no—
113C22×C3×D5—41no—
114C22×C3×D5—41no—
115C2×C3×C4×C5C22×C411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120C2×C3×C4×C5#4111yescharacteristic
121C2×Dic15—22no—
122C2×Dic15—22no—
123C2×Dic15—41no—
124C2×Dic15—41no—
125C2×Dic15—41no—
126C2×Dic15—41no—
127C2×C5×Dic3—21no—
128C2×C5×Dic3—21no—
129C2×C5×Dic3C22⋊C412yes—
130C4×C5×D3—22no—
131C4×C5×D3—22no—
132C4×C5×D3—22no—
133C4×C5×D3—22no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—41no—
136C2×C3×Dic5—41no—
137C3×D20—22no—
138C3×D20—22no—
139C3×D20—41no—
140C3×D20—41no—
141#1201—48no—
142D3×Dic5—48no—
143C3×C5×C8—41no—
144C5×C3⋊C8—41no—
145C22×C3×D4—51no—
146C22×#67—101no—
147C22×C4×D3—101no—
148C22×C4×D3C2×D511yescharacteristic
149C22×C3×C8C2×D511yescharacteristic
150C2×C3×C4⋊C4—51no—
151C2×#217—101no—
152#938—54no—
153#938—102no—
154C2×C4⋊Dic3—51no—
155C2×C4⋊Dic3—51no—
156C2×Dic3⋊C4—101no—
157C22×C3⋊C8C2×D511yescharacteristic
158D3×C4⋊C4—102no—
159D3×C4⋊C4—102no—
160C3×#102—102no—
161#832—102no—
162(C2×D3)⋊C8—22no—
163C24×C5—31no—
164C23×D5—21no—
165C22×C4×C5—31no—
166C22×C4×C5—32no—
167C22×C4×C5—32no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C22×C4×C5—61no—
171C22×C4×C5—61no—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—64no—
174C2×C22⋊D5—122no—
175C2×C22⋊D5—122no—
176C22×Dic5—21no—
177C22×Dic5—64no—
178C22×Dic5—61no—
179C22×Dic5—61no—
180C22×Dic5—122no—
181C22×Dic5—122no—
182C2×D20—21no—
183C2×D20—21no—
184C2×D20—21no—
185C2×D20—21no—
186C2×D20—21no—
187C2×D20C4×D312yescomplemented
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—61no—
192C2×C5×C8—61no—
193C2×C5×C8—61no—
194#685—64no—
195C4⋊Dic5—21no—
196C4⋊Dic5—32no—
197C4⋊Dic5—32no—
198C4⋊Dic5—64no—
199C4⋊Dic5—61no—
200C4⋊Dic5—61no—
201C4⋊Dic5#6712yescomplemented
202C2×#121—151no—
203C22×C4⋊C4—151no—
204C2×#102—51no—
205C2×#102—151no—
206C2×C22⋊C8—31no—
207#340—151no—
208#340—151no—
209C22×C3×C5C2×C22⋊C411yescharacteristic
210C22×C3×C5#12011yescharacteristic
211C22×C3×C5#12311yescharacteristic
212C22×C3×C5C2×D811yescharacteristic
213C22×C3×C5C2×SD1611yescharacteristic
214C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
215C22×C3×C5#13711yescharacteristic
216C2×C5×D3—22no—
217C2×C5×D3—22no—
218C2×C5×D3—22no—
219C2×C5×D3—22no—
220C2×C5×D3—22no—
221C2×C5×D3—22no—
222C2×C5×D3#10214yescomplemented
223C2×C3×D5—42no—
224C2×C3×D5—42no—
225C2×C3×D5—42no—
226C2×C3×D5—81no—
227C2×C3×D5—81no—
228C2×C3×D5—81no—
229C2×C3×D5—81no—
230C3×C4×C5C4×D411yescharacteristic
231C3×C4×C5C4×D411yescharacteristic
232C3×C4×C5#12111yescharacteristic
233C3×C4×C5#12111yescharacteristic
234Dic15—42no—
235Dic15—42no—
236C3×Dic5—42no—
237C5×Dic3—22no—
238C24×C3—101no—
239C23×D3D2011yescharacteristic
240C2×C3×D4—52no—
241C2×C3×D4—101no—
242C2×C3×D4—101no—
243C2×C3×D4—101no—
244C2×C3×D4—101no—
245C2×C3×D4—101no—
246C22×C3×C4—101no—
247C22×C3×C4C22×D511yescharacteristic
248C2×#67—104no—
249C2×#67—202no—
250C2×#67—202no—
251C22×Dic3—101no—
252C22×Dic3—101no—
253C22×Dic3D2011yescharacteristic
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—104no—
259C2×C4×D3—202no—
260C2×C4×D3—202no—
261C2×C4×D3C4×D512yes—
262C2×C4×D3C22⋊D512yes—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C3×C4⋊C4—52no—
267C3×C4⋊C4—101no—
268#217—104no—
269C4⋊Dic3—52no—
270C4⋊Dic3—52no—
271C4⋊Dic3—101no—
272C4⋊Dic3—101no—
273Dic3⋊C4—104no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C23×C5—32no—
278C23×C5—32no—
279C23×C5—32no—
280C23×C5—61no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—61no—
284C23×C5D3×D411yescharacteristic
285C22×D5—22no—
286C22×D5—41no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5—41no—
290C22×D5—41no—
291C22×D5—41no—
292C2×C4×C5—32no—
293C2×C4×C5—61no—
294C2×C4×C5—61no—
295C2×C4×C5—62no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5C2×C4×D311yescharacteristic
300C2×C4×C5#23511yescharacteristic
301C2×C4×C5D3×D411yescharacteristic
302C2×C4×C5D3×D411yescharacteristic
303C2×C4×C5#23711yescharacteristic
304C2×C4×C5C2×#6711yescharacteristic
305C22⋊D5—128no—
306C2×Dic5—22no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—128no—
312C2×Dic5—121no—
313C2×Dic5—121no—
314C2×Dic5—121no—
315C2×Dic5—121no—
316D20—22no—
317D20—22no—
318D20—41no—
319D20—41no—
320C5×C8—41no—
321C5×C8—121no—
322C22×D4—51no—
323C22×D4—301no—
324C23×C4—31no—
325C23×C4—301no—
326C22×C8—31no—
327C22×C8D3×D511yescharacteristic
328#121—154no—
329#121—302no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—151no—
332C2×C4⋊C4—151no—
333C2×C4⋊C4—302no—
334C2×C4⋊C4—302no—
335C2×C4⋊C4—301no—
336C2×C22⋊C4—301no—
337#102—102no—
338#102—302no—
339C22⋊C8—62no—
340C2×C3×C5#38611yescharacteristic
341C2×C3×C5C2×#10211yescharacteristic
342C2×C3×C5#41711yescharacteristic
343C2×C3×C5#44711yescharacteristic
344C2×C3×C5#44811yescharacteristic
345C2×C3×C5#48011yescharacteristic
346C2×C3×C5#48111yescharacteristic
347C3×D5—82no—
348C5×D3—24no—
349C23×C3—102no—
350C23×C3—201no—
351C23×C3—201no—
352C23×C3—201no—
353C23×C3—201no—
354C23×C3—201no—
355C23×C3—201no—
356C23×C3C2×D2011yescharacteristic
357C22×D3—21no—
358C22×D3—21no—
359C22×D3—21no—
360C22×D3—21no—
361C22×D3#67712yes—
362C22×D3D4012yes—
363C22×D3#68512yes—
364C3×D4—102no—
365C3×D4—102no—
366C3×D4—201no—
367C3×D4—201no—
368C2×C3×C4—102no—
369C2×C3×C4—201no—
370C2×C3×C4—201no—
371C2×C3×C4C2×C4×D511yescharacteristic
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4D4×D511yescharacteristic
374C2×C3×C4#71111yescharacteristic
375C2×C3×C4#71111yescharacteristic
376C2×C3×C4C2×C22⋊D511yescharacteristic
377#67—208no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—102no—
381C2×Dic3—102no—
382C2×Dic3—201no—
383C2×Dic3—201no—
384C2×Dic3—201no—
385C2×Dic3—201no—
386C2×Dic3#68512yes—
387C4×D3—22no—
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—22no—
391C4×D3—208no—
392C3×C8—41no—
393C3⋊C8—41no—
394C22×C5—34no—
395C22×C5—62no—
396C22×C5—62no—
397C22×C5—62no—
398C22×C5—62no—
399C22×C5—62no—
400C22×C5—62no—
401C22×C5D3×C22⋊C411yescharacteristic
402C22×C5#88311yescharacteristic
403C22×C5D3×D811yescharacteristic
404C22×C5#91111yescharacteristic
405C22×C5D3×SD1611yescharacteristic
406C22×C5#91511yescharacteristic
407C22×C5#93711yescharacteristic
408C2×D5—42no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—81no—
412C2×D5—81no—
413C2×D5—81no—
414C2×D5—81no—
415C4×C5—62no—
416C4×C5#67⋊C411yescharacteristic
417C4×C5#88411yescharacteristic
418C4×C5C4×#6711yescharacteristic
419C4×C5#93811yescharacteristic
420Dic5—42no—
421Dic5—122no—
422Dic5—122no—
423C24—31no—
424C24—101no—
425C2×D4—52no—
426C2×D4—101no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—304no—
432C2×D4—602no—
433C2×D4—602no—
434C22×C4—31no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—101no—
442C22×C4—304no—
443C22×C4—301no—
444C22×C4—301no—
445C22×C4—602no—
446C22×C4—602no—
447C22×C4C2×D3×D511yescharacteristic
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—61no—
452C2×C8—61no—
453C2×C8—61no—
454C4⋊C4—52no—
455C4⋊C4—101no—
456C4⋊C4—152no—
457C4⋊C4—152no—
458C4⋊C4—304no—
459C4⋊C4—301no—
460C4⋊C4—301no—
461C22⋊C4—304no—
462C3×C5#187411yescharacteristic, complemented, Hall
463C22×C3—202no—
464C22×C3—202no—
465C22×C3—202no—
466C22×C3—401no—
467C22×C3—401no—
468C22×C3—401no—
469C22×C3—401no—
470C22×C3#402811yescharacteristic
471C22×C3#403211yescharacteristic
472C22×C3C2×#67711yescharacteristic
473C22×C3C2×D4011yescharacteristic
474C22×C3#405411yescharacteristic
475C22×C3#405511yescharacteristic
476C22×C3C2×#68511yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3#395314yescomplemented
484C3×C4—202no—
485C3×C4#402711yescharacteristic
486C3×C4#402711yescharacteristic
487C3×C4#408511yescharacteristic
488C3×C4#408511yescharacteristic
489Dic3—22no—
490Dic3—202no—
491Dic3—202no—
492C2×C5—64no—
493C2×C5D3×#10211yescharacteristic
494C2×C5#477111yescharacteristic
495C2×C5#477411yescharacteristic
496C2×C5#477711yescharacteristic
497C2×C5#495611yescharacteristic
498C2×C5#515611yescharacteristic
499C2×C5#517011yescharacteristic
500D5—82no—
501C23—32no—
502C23—32no—
503C23—32no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23—102no—
509C23—201no—
510C23—201no—
511C23—201no—
512C23—201no—
513C23—201no—
514C23—201no—
515C23D3×D2011yescharacteristic
516D4—102no—
517D4—102no—
518D4—201no—
519D4—201no—
520D4—608no—
521C2×C4—32no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—102no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—608no—
534C2×C4—601no—
535C2×C4—601no—
536C2×C4—601no—
537C2×C4—601no—
538C2×C4#677211yescharacteristic
539C2×C4C4×D3×D511yescharacteristic
540C2×C4#677711yescharacteristic
541C2×C4#678011yescharacteristic
542C2×C4D5×#6711yescharacteristic
543C2×C4D3×C22⋊D511yescharacteristic
544C8—41no—
545C8—121no—
546C2×C3—402no—
547C2×C3#6502111yescharacteristic
548C2×C3#6502411yescharacteristic
549C2×C3#6502511yescharacteristic
550C2×C3#6502711yescharacteristic
551C2×C3#6524711yescharacteristic
552C2×C3C2×#395311yescharacteristic
553C2×C3#6542211yescharacteristic
554D3—24no—
555C5#7020011yescharacteristic, complemented, Sylow
556C22—34no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—62no—
563C22—202no—
564C22—202no—
565C22—202no—
566C22—401no—
567C22—401no—
568C22—401no—
569C22—401no—
570C22D3×#67711yescharacteristic
571C22D3×D4011yescharacteristic
572C22#9125411yescharacteristic
573C22#9127411yescharacteristic
574C22#9145711yescharacteristic
575C22D3×#68511yescharacteristic
576C22#9147411yescharacteristic
577C4—62no—
578C4—202no—
579C4—602no—
580C4—602no—
581C4#9144011yescharacteristic
582C4#9144211yescharacteristic
583C4#9145311yescharacteristic
584C4#9156511yescharacteristic
585C3#1060072511yescharacteristic, complemented, Sylow
586C2—64no—
587C2—402no—
588C2#1174791311yescharacteristic
589C2#1174791611yescharacteristic
590C2D3×#395311yescharacteristic
591C2#1174811211yescharacteristic
592C2#1174812411yescharacteristic
593C2#1174813811yescharacteristic
594C2#1174891111yescharacteristic
subgroupG/H
centerC23D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC2×#91456C2
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1874
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×D3×C4⋊Dic5C2semidirect
3. C2×C5×(C2×D3)⋊C8C2semidirect
4. C2×C3×#3953C2semidirect
5. C2×#90965C2semidirect
6. #11746372C2semidirect
7. #11745980C2semidirect
21. #91456C4semidirect
32. C2×#3953D3semidirect
53. C2×C3×D20C2×C4semidirect
65. C4⋊Dic15C2×C4semidirect
66. C4⋊Dic15D4semidirect
71. C3×C4⋊Dic5D4semidirect
78. C2×(C2×D3)⋊C8D5semidirect
187. C2×D20C4×D3semidirect
201. C4⋊Dic5#67semidirect
222. C2×C5×D3#102semidirect
462. C3×C5#1874semidirect
483. C2×D3#3953semidirect
555. C5#70200semidirect
585. C3#10600725semidirect

Maximal subgroups

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

subgroupindex
C2×#914562
C2×D3×C4⋊Dic52
C2×C5×(C2×D3)⋊C82
C2×C3×#39532
C2×#909652
#117463722
#117459802
#106007253
#702005