Finite Group Databasebeta

← #14300546

Subgroups — #14300546

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754563C211yesmaximal, characteristic
2C2×D5×#208C211yesmaximal, characteristic, complemented
3C2×C5×#805C211yesmaximal, characteristic, complemented
4C3×C4×#685C211yesmaximal, characteristic, complemented
5C2×#90979C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10601174—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×C4×D5C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#685—21no—
16C2×C3×C4×Dic5C2211yescharacteristic
17#91563—21no—
18#91539—21no—
19#91449C411yescharacteristic, complemented
20#91449C411yescharacteristic, complemented
21C4×#1201—21no—
22C4×#1201—21no—
23#91359C411yescharacteristic, complemented
24#91359C411yescharacteristic, complemented
25C2×#6649—21no—
26D5×#208—22no—
27D5×#208—22no—
28C2×D5×C3⋊C8—21no—
29C5×#805—22no—
30C3×#3963—21no—
31#90979—22no—
32#69453—51nomaximal, Hall
33#66162—31no—
34C2×D5×M16—31no—
35C2×C5×#104—31no—
36C2×#3969—31no—
37C4×#685D311yescharacteristic, complemented
38#64775—31no—
39#64743—31no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×C5×#67—21no—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12C2×C411yescharacteristic
49C2×C4×C5×D3—21no—
50C2×C5×Dic6C2×C411yescharacteristic
51C22×C3×Dic5—21no—
52C22×C3×Dic5D411yescharacteristic
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5—21no—
57C2×C3×C4×D5C2×C411yescharacteristic
58C2×C3×C4×D5C2×C411yescharacteristic
59C2×C3×C4×D5D411yescharacteristic
60C2×C3×C4×D5D411yescharacteristic
61C2×#1201—21no—
62C2×#1201—21no—
63C3×C42×C5—21no—
64C3×C42×C5—21no—
65#6719—21no—
66C4⋊Dic15C2×C411yescharacteristic
67C4⋊Dic15C2×C411yescharacteristic
68C4×Dic15—21no—
69#6710—21no—
70#6710D412yescomplemented
71C2×C3⋊#168—21no—
72C5×#208—21no—
73C5×#208D412yescomplemented
74C2×C5×C3⋊C8—21no—
75C3×#685—24no—
76C3×C4×Dic5—21no—
77C3×C4×Dic5—21no—
78#6669—21no—
79#6669—21no—
80(C2×D3)⋊Dic5—21no—
81(C2×D3)⋊Dic5—21no—
82#6665—21no—
83#6665—21no—
84#6649—24no—
85D5×C3⋊C8—24no—
86#5791—51no—
87C22×#208—51no—
88C3×C4×C22⋊C4—51no—
89C2×#805—51no—
90C2×#805D511yescharacteristic, complemented
91#4523—51no—
92#4523—51no—
93C2×C5×#41—31no—
94C22×C4×D5C2×D311yescharacteristic
95C2×C5×M16—31no—
96C2×C42×C5C2×D311yescharacteristic
97#4092—31no—
98#4092—31no—
99#4084—31no—
100#4084—31no—
101#4083—61no—
102#4081—61no—
103C4×C22⋊D5—61no—
104C4×C22⋊D5—61no—
105C2×#685—21no—
106#4072—31no—
107C2×C4×Dic5C2×D311yescharacteristic
108C2×#681—31no—
109D5×M16—62no—
110D5×M16—62no—
111C2×#676—61no—
112C2×C8×D5—61no—
113C5×#104—62no—
114#3969—62no—
115#3963—21no—
116#1871—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C5×D3—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—22no—
122C22×C3×D5—41no—
123C22×C3×D5C22⋊C411yescharacteristic
124C22×C3×D5C22⋊C411yescharacteristic
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×C3×C4×C5#4111yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136C5×#67—41no—
137C5×#67—41no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12—21no—
141C4×C5×D3—41no—
142C4×C5×D3—41no—
143C5×Dic6—21no—
144C5×Dic6—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—41no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5C22⋊C411yescharacteristic
151C2×C3×Dic5C22⋊C411yescharacteristic
152C3×C4×D5—21no—
153C3×C4×D5—21no—
154C3×C4×D5—21no—
155C3×C4×D5—21no—
156C3×C4×D5—21no—
157C3×C4×D5—21no—
158C3×C4×D5—21no—
159C3×C4×D5—21no—
160#1201—42no—
161#1201—42no—
162C3⋊#168—22no—
163C5×C3⋊C8—22no—
164C23×C3×C4—51no—
165C2×#235C2×D511yescharacteristic
166C2×C3×C22⋊C4—101no—
167C2×C3×C42—51no—
168C2×C3×C42C2×D511yescharacteristic
169#953—101no—
170#930—51no—
171#930—51no—
172#929—101no—
173C4×#67—101no—
174C4×#67—101no—
175#926—51no—
176#924—51no—
177#924—51no—
178C2×#208—51no—
179C2×#208—101no—
180C2×#208—102no—
181C2×#208—102no—
182C2×#208C2×D511yescharacteristic
183C22×C3⋊C8—101no—
184C3×#95—101no—
185#805—22no—
186#805—102no—
187C23×D5#6711yescharacteristic
188C5×#41—61no—
189C5×#41—61no—
190C5×#41—61no—
191C5×#41—61no—
192C2×C5×Q8—31no—
193C2×C5×D4—31no—
194C2×C5×D4—61no—
195C22×C4×C5—21no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C2×C22⋊D5—61no—
200C22×Dic5—21no—
201C22×Dic5#6711yescharacteristic
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5C4×D311yescharacteristic
207C2×C4×D5C4×D311yescharacteristic
208C2×C4×D5D1211yescharacteristic
209C2×C4×D5D1211yescharacteristic
210C5×M16—32no—
211C5×M16—61no—
212C2×C5×C8—61no—
213C42×C5—21no—
214C42×C5—21no—
215C22⋊Dic5—61no—
216C22⋊Dic5—61no—
217C22⋊Dic5—61no—
218#685—24no—
219#685—61no—
220#685—61no—
221C4⋊Dic5—31no—
222C4⋊Dic5—31no—
223#683—61no—
224#683—61no—
225C4×Dic5—21no—
226C4×Dic5—21no—
227C4×Dic5—61no—
228#681—32no—
229#681—61no—
230C2×#168—61no—
231#676—64no—
232C8×D5—64no—
233C22×M16—151no—
234#525—151no—
235C2×#104—31no—
236C2×#104—151no—
237C4×C22⋊C4—51no—
238#339—151no—
239#339—151no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5C2×C22⋊C411yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5#12111yescharacteristic
245C2×C5×D3—41no—
246C2×C5×D3—41no—
247C2×C5×D3—41no—
248C2×C3×D5—21no—
249C2×C3×D5—21no—
250C2×C3×D5—21no—
251C2×C3×D5—21no—
252C2×C3×D5—21no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5#10412yescomplemented
256C3×C4×C5—42no—
257C3×C4×C5C4×D411yescharacteristic
258C3×C4×C5C4×D411yescharacteristic
259C3×C4×C5#12011yescharacteristic
260C3×C4×C5#12311yescharacteristic
261Dic15—41no—
262Dic15—41no—
263C3×Dic5—21no—
264C3×Dic5—21no—
265C3×Dic5—42no—
266C5×Dic3—41no—
267C24×C3—51no—
268C22×C3×C4—21no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C22×C3×C4—101no—
277C22×C3×C4—101no—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281C2×#67—101no—
282C2×#67—101no—
283#235—21no—
284#235—21no—
285#235—21no—
286#235—21no—
287C2×D12C4×D511yescharacteristic
288C2×C4×D3—21no—
289C2×Dic6C4×D511yescharacteristic
290C3×C22⋊C4—104no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42—101no—
294C3×C42—101no—
295#217—101no—
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—101no—
299(C2×D3)⋊C4—101no—
300C4⋊Dic3—51no—
301C4⋊Dic3—51no—
302Dic3⋊C4—101no—
303Dic3⋊C4—101no—
304C4×Dic3—101no—
305#208—21no—
306#208—52no—
307#208—104no—
308#208—101no—
309#208C22⋊D512yescomplemented
310C2×C3⋊C8—21no—
311C2×C3⋊C8—104no—
312C2×C3⋊C8—101no—
313C23×C5—61no—
314C23×C5C2×#6711yescharacteristic
315C22×D5—21no—
316C22×D5—21no—
317C22×D5—22no—
318C22×D5—41no—
319C22×D5(C2×D3)⋊C411yescharacteristic
320C22×D5(C2×D3)⋊C411yescharacteristic
321C5×Q8—61no—
322C5×Q8—61no—
323C5×D4—61no—
324C5×D4—61no—
325C5×D4—121no—
326C5×D4—121no—
327C2×C4×C5—22no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—61no—
331C2×C4×C5—121no—
332C2×C4×C5—121no—
333C2×C4×C5C2×C4×D311yescharacteristic
334C2×C4×C5C2×D1211yescharacteristic
335C2×C4×C5D3×D411yescharacteristic
336C2×C4×C5D3×D411yescharacteristic
337C2×C4×C5#23711yescharacteristic
338C2×C4×C5#23711yescharacteristic
339C22⋊D5—122no—
340C22⋊D5—122no—
341C2×Dic5—21no—
342C2×Dic5—21no—
343C2×Dic5—22no—
344C2×Dic5—41no—
345C2×Dic5—41no—
346C2×Dic5—61no—
347C2×Dic5—61no—
348C2×Dic5(C2×D3)⋊C411yescharacteristic
349C2×Dic5(C2×D3)⋊C411yescharacteristic
350C4×D5—21no—
351C4×D5—21no—
352C4×D5—21no—
353C4×D5—21no—
354C4×D5—21no—
355C4×D5—21no—
356C4×D5—21no—
357C4×D5—21no—
358C5×C8—62no—
359#168—62no—
360C2×#41—31no—
361C23×C4—51no—
362C2×M16—31no—
363C2×M16—151no—
364C2×M16—301no—
365C2×M16—302no—
366C2×M16—302no—
367C22×C8—301no—
368#123—301no—
369C22⋊Q8—151no—
370C22⋊Q8—151no—
371#121—151no—
372#121—151no—
373#120—301no—
374C4×D4—301no—
375C4×D4—301no—
376#117—151no—
377C2×C22⋊C4—101no—
378C2×C42—51no—
379C2×C42D3×D511yescharacteristic
380#104—62no—
381#104—302no—
382#95—101no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5#38611yescharacteristic
386C2×C3×C5C2×#10411yescharacteristic
387C2×C3×C5#42111yescharacteristic
388C3×D5—22no—
389C3×D5—41no—
390C5×D3—81no—
391C23×C3—51no—
392C23×C3—51no—
393C23×C3—102no—
394C23×C3—101no—
395C23×C3—101no—
396C23×C3—201no—
397C23×C3D4×D511yescharacteristic
398C22×D3—21no—
399C2×C3×C4—22no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—51no—
403C2×C3×C4—51no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—101no—
407C2×C3×C4—101no—
408C2×C3×C4—101no—
409C2×C3×C4—101no—
410C2×C3×C4—101no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4—101no—
414C2×C3×C4—102no—
415C2×C3×C4—201no—
416C2×C3×C4—201no—
417C2×C3×C4C2×C4×D511yescharacteristic
418C2×C3×C4#70911yescharacteristic
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4#71111yescharacteristic
422C2×C3×C4C2×C22⋊D511yescharacteristic
423#67—41no—
424#67—41no—
425#67—202no—
426#67—202no—
427C2×Dic3—21no—
428C2×Dic3—101no—
429C2×Dic3—101no—
430D12—21no—
431D12—21no—
432C4×D3—41no—
433C4×D3—41no—
434Dic6—21no—
435Dic6—21no—
436C3⋊C8—22no—
437C3⋊C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—121no—
441C22×C5—121no—
442C22×C5—121no—
443C22×C5C2×(C2×D3)⋊C411yescharacteristic
444C22×C5#93911yescharacteristic
445C22×C5#93911yescharacteristic
446C2×D5—21no—
447C2×D5—21no—
448C2×D5—21no—
449C2×D5—21no—
450C2×D5—21no—
451C2×D5—42no—
452C2×D5—42no—
453C2×D5#80512yescomplemented
454C4×C5—42no—
455C4×C5—121no—
456C4×C5#67⋊C411yescharacteristic
457C4×C5#67⋊C411yescharacteristic
458C4×C5#88211yescharacteristic
459C4×C5#88611yescharacteristic
460Dic5—21no—
461Dic5—21no—
462Dic5—42no—
463Dic5—121no—
464Dic5—121no—
465C24—51no—
466#41—61no—
467#41—61no—
468#41—61no—
469#41—61no—
470C2×Q8—31no—
471C2×D4—31no—
472C2×D4—61no—
473C2×D4—301no—
474C2×D4—301no—
475C22×C4—21no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—51no—
481C22×C4—61no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—101no—
487C22×C4C2×D3×D511yescharacteristic
488M16—32no—
489M16—61no—
490M16—152no—
491M16—304no—
492M16—301no—
493C2×C8—61no—
494C2×C8—304no—
495C2×C8—301no—
496C4⋊C4—151no—
497C4⋊C4—151no—
498C4⋊C4—301no—
499C4⋊C4—301no—
500C22⋊C4—104no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C22⋊C4—301no—
504C22⋊C4—301no—
505C22⋊C4—301no—
506C42—21no—
507C42—21no—
508C42—101no—
509C42—101no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—52no—
515C22×C3—101no—
516C22×C3—101no—
517C22×C3—101no—
518C22×C3—101no—
519C22×C3—101no—
520C22×C3—202no—
521C22×C3—202no—
522C22×C3D5×C22⋊C411yescharacteristic
523C22×C3#403011yescharacteristic
524C22×C3#408411yescharacteristic
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—41no—
528C3×C4—42no—
529C3×C4—101no—
530C3×C4—101no—
531C3×C4—202no—
532C3×C4#402711yescharacteristic
533C3×C4#402911yescharacteristic
534C3×C4C4×C22⋊D511yescharacteristic
535C3×C4#408311yescharacteristic
536Dic3—41no—
537Dic3—201no—
538Dic3—201no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5—241no—
542C2×C5C2×#80511yescharacteristic
543C2×C5#495811yescharacteristic
544C2×C5#500511yescharacteristic
545D5—22no—
546D5—41no—
547C23—51no—
548C23—51no—
549C23—61no—
550C23—102no—
551C23—101no—
552C23—101no—
553C23—201no—
554C23D5×#6711yescharacteristic
555Q8—61no—
556Q8—61no—
557D4—61no—
558D4—61no—
559D4—121no—
560D4—121no—
561D4—602no—
562D4—602no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—51no—
567C2×C4—51no—
568C2×C4—61no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—102no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4#676511yescharacteristic
587C2×C4C4×D3×D511yescharacteristic
588C2×C4D5×D1211yescharacteristic
589C2×C4#677711yescharacteristic
590C2×C4#678011yescharacteristic
591C2×C4D3×C22⋊D511yescharacteristic
592C8—62no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—102no—
597C2×C3—201no—
598C2×C3D5×#10411yescharacteristic
599C2×C3#6511011yescharacteristic
600C2×C3#6524511yescharacteristic
601D3—81no—
602C5#6945311yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—52no—
606C22—101no—
607C22—101no—
608C22—101no—
609C22—101no—
610C22—101no—
611C22—121no—
612C22—121no—
613C22—121no—
614C22—202no—
615C22—202no—
616C22#9140811yescharacteristic
617C22D5×(C2×D3)⋊C411yescharacteristic
618C22#9154911yescharacteristic
619C4—42no—
620C4—101no—
621C4—101no—
622C4—121no—
623C4—202no—
624C4—601no—
625C4—601no—
626C4#9141411yescharacteristic
627C4#9144111yescharacteristic
628C4#9144211yescharacteristic
629C4#9147511yescharacteristic
630C3#1060117411yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—102no—
634C2—201no—
635C2—241no—
636C2D5×#80511yescharacteristic
637C2#1174710911yescharacteristic
638C2#1174890611yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754563C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D5×#208C2semidirect
3. C2×C5×#805C2semidirect
4. C3×C4×#685C2semidirect
5. C2×#90979C2semidirect
6. #11746344C2semidirect
7. #11745978C2semidirect
19. #91449C4semidirect
20. #91449C4semidirect
23. #91359C4semidirect
24. #91359C4semidirect
37. C4×#685D3semidirect
70. #6710D4semidirect
73. C5×#208D4semidirect
90. C2×#805D5semidirect
255. C2×C3×D5#104semidirect
309. #208C22⋊D5semidirect
453. C2×D5#805semidirect
511. C3×C5#1871semidirect
602. C5#69453semidirect
630. C3#10601174semidirect

Maximal subgroups

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

subgroupindex
#117545632
C2×D5×#2082
C2×C5×#8052
C3×C4×#6852
C2×#909792
#117463442
#117459782
#106011743
#694535