Finite Group Databasebeta

← #14297286

Subgroups — #14297286

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66283C211yesmaximal, characteristic
2#11751334C211yesmaximal, characteristic, complemented
3C5×#5236C211yesmaximal, characteristic, complemented
4#11748624C211yesmaximal, characteristic, complemented
5#11748420C211yesmaximal, characteristic, complemented
6#11748364C211yesmaximal, characteristic, complemented
7#11748343C211yesmaximal, characteristic, complemented
8#10601206—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4150—21no—
11C3×#4150C412yescomplemented
12C3×#4149—21no—
13C3×#4149C412yescomplemented
14C3×D5×#41—22no—
15C3×D5×#41—22no—
16C3×#4147—21no—
17C3×#4144—21no—
18C3×#4144—22no—
19C2×C3×#709—22no—
20C2×C3×#709C2211yescharacteristic
21C2×C3×#709C2211yescharacteristic
22#91815C2211yescharacteristic, complemented
23C22×C3⋊#168C2211yescharacteristic, complemented
24C5×#926C2211yescharacteristic, complemented
25C2×C5×#208C2211yescharacteristic, complemented
26#91119—21no—
27#91116—21no—
28C5×#837—22no—
29#90995—22no—
30#90976—22no—
31#90970—21no—
32#90964—21no—
33#90955—22no—
34#72146—51nomaximal, Hall
35#66283D311yescharacteristic
36C5×#421—31no—
37#65522—31no—
38#65428—31no—
39#65418—31no—
40#65295—31no—
41#65291—31no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41C2×C412yes—
45C3×C5×#41D412yes—
46C2×C3×C5×Q8D411yescharacteristic
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4D411yescharacteristic
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×C3×C22⋊D5—24no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5D412yes—
54C3×#713—22no—
55C3×#713—22no—
56C3×Q8×D5—22no—
57C3×Q8×D5—22no—
58C3×#711—24no—
59C3×#711—22no—
60C3×#711—22no—
61C3×#711—24no—
62C3×D4×D5—24no—
63C3×D4×D5—22no—
64C3×D4×D5—24no—
65C3×D4×D5—22no—
66C3×#709—24no—
67C3×#709—24no—
68C3×#709—21no—
69C3×#709—21no—
70C3×#709—21no—
71C3×#709—21no—
72C3×#709—21no—
73C3×#709—21no—
74C3×#709—22no—
75C3×#709—22no—
76C3×#709C2×C412yes—
77C3×#709D412yes—
78C2×C3×D20—22no—
79C2×C3×D20C2×C411yescharacteristic
80C2×C3×D20D411yescharacteristic
81C2×C3×C4×D5—24no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5D412yes—
84C2×C3×Dic10—22no—
85C2×C3×Dic10C2×C411yescharacteristic
86C2×C3×Dic10D411yescharacteristic
87#6719—21no—
88C4⋊Dic15—21no—
89C4×Dic15—21no—
90C2×C3⋊#168—21no—
91C2×C3⋊#168—21no—
92C2×C3⋊#168—21no—
93C5×#217—21no—
94C5×C4⋊Dic3—21no—
95C4×C5×Dic3—21no—
96C5×#208—21no—
97C5×#208—21no—
98C2×C5×C3⋊C8—21no—
99C3×#585—51no—
100#5240—51no—
101#5236—51no—
102#5236D511yescharacteristic, complemented
103#5234—51no—
104#5233—51no—
105#5233—51no—
106C2×C5×#41C2×D311yescharacteristic
107#4150—21no—
108#4150Dic312yescomplemented
109#4149—21no—
110#4149Dic312yescomplemented
111D5×#41—22no—
112D5×#41—22no—
113#4147—21no—
114#4144—21no—
115#4144—22no—
116C2×#709—22no—
117C2×#709C2×D311yescharacteristic
118C2×#709C2×D311yescharacteristic
119C2×C5×M16—31no—
120C5×#117—31no—
121#4072—31no—
122C22×#168—31no—
123C5×#104—62no—
124#3967—61no—
125#3964—61no—
126#3957—62no—
127#3952—62no—
128#3942—61no—
129#3941—61no—
130#3938—62no—
131#1794—151noSylow
132C23×C3×C5—21no—
133C23×C3×C5C2×D411yescharacteristic
134C22×C3×D5—24no—
135C22×C3×D5—21no—
136C22×C3×D5C22⋊C412yes—
137C3×C5×Q8—21no—
138C3×C5×Q8C22⋊C412yes—
139C3×C5×D4—22no—
140C3×C5×D4—22no—
141C3×C5×D4—21no—
142C3×C5×D4C22⋊C412yes—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C22×C411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×Dic15—41no—
153C2×C5×Dic3—41no—
154C3×C22⋊D5—24no—
155C3×C22⋊D5—24no—
156C3×C22⋊D5—22no—
157C3×C22⋊D5—22no—
158C3×C22⋊D5—22no—
159C3×C22⋊D5—22no—
160C2×C3×Dic5—24no—
161C2×C3×Dic5—21no—
162C2×C3×Dic5C22⋊C412yes—
163C3×D20—24no—
164C3×D20—21no—
165C3×D20—21no—
166C3×D20—21no—
167C3×D20C22⋊C412yes—
168C3×C4×D5—24no—
169C3×C4×D5—24no—
170C3×C4×D5—22no—
171C3×C4×D5—22no—
172C3×C4×D5—22no—
173C3×C4×D5—22no—
174C3×Dic10—24no—
175C3×Dic10—21no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C3×Dic10C22⋊C412yes—
179C3⋊#168—41no—
180C5×C3⋊C8—41no—
181C3×2−1+4—52no—
182C3×2−1+4—101no—
183C3×2−1+4—101no—
184C3×H(5,𝔽2)—52no—
185C3×H(5,𝔽2)—102no—
186C3×H(5,𝔽2)—101no—
187C3×H(5,𝔽2)—101no—
188C2×C3×#41—51no—
189C2×C3×#41—51no—
190C2×C3×#41—102no—
191C2×C3×#41—102no—
192C2×C3×#41—102no—
193C2×C3×#41C2×D511yescharacteristic
194#926—51no—
195#926C2×D511yescharacteristic, complemented
196C2×#208C2×D511yescharacteristic, complemented
197C22×C3⋊C8—51no—
198#837—22no—
199#837—102no—
200#835—101no—
201#835—101no—
202#834—102no—
203#832—101no—
204#832—101no—
205#830—102no—
206C5×#41—21no—
207C5×#41—21no—
208C5×#41C2×Dic312yes—
209C5×#41#6712yes—
210C2×C5×Q8#6711yescharacteristic
211C2×C5×D4—21no—
212C2×C5×D4#6711yescharacteristic
213C22×C4×C5—21no—
214C22×C4×C5C22×D311yescharacteristic
215C2×C22⋊D5—24no—
216C2×C22⋊D5—21no—
217C2×C22⋊D5#6712yes—
218#713—22no—
219#713—22no—
220Q8×D5—22no—
221Q8×D5—22no—
222#711—24no—
223#711—22no—
224#711—22no—
225#711—24no—
226D4×D5—24no—
227D4×D5—22no—
228D4×D5—24no—
229D4×D5—22no—
230#709—24no—
231#709—24no—
232#709—21no—
233#709—21no—
234#709—21no—
235#709—21no—
236#709—21no—
237#709—21no—
238#709—22no—
239#709—22no—
240#709C2×Dic312yes—
241#709#6712yes—
242C2×D20—22no—
243C2×D20C2×Dic311yescharacteristic
244C2×D20#6711yescharacteristic
245C2×C4×D5—24no—
246C2×C4×D5—21no—
247C2×C4×D5#6712yes—
248C2×Dic10—22no—
249C2×Dic10C2×Dic311yescharacteristic
250C2×Dic10#6711yescharacteristic
251C5×M16—61no—
252C5×M16—61no—
253C2×C5×C8—61no—
254C5×C4⋊C4—61no—
255C5×C22⋊C4—61no—
256C42×C5—61no—
257C22⋊Dic5—61no—
258C4⋊Dic5—61no—
259C4×Dic5—61no—
260C2×#168—61no—
261C2×#168—61no—
262C2×#168—61no—
263#585—51no—
264#421—31no—
265#421—151no—
266#416—151no—
267#416—151no—
268#410—151no—
269#408—151no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—81no—
273C22×C3×C5C2×C22⋊C411yescharacteristic
274C22×C3×C5#12011yescharacteristic
275C22×C3×C5#12011yescharacteristic
276C2×C3×D5—22no—
277C2×C3×D5—22no—
278C2×C3×D5—42no—
279C2×C3×D5—81no—
280C2×C3×D5—84no—
281C3×C4×C5—22no—
282C3×C4×C5C2×C22⋊C411yescharacteristic
283C3×C4×C5C2×C22⋊C411yescharacteristic
284C3×C4×C5#12011yescharacteristic
285C3×C4×C5#12011yescharacteristic
286Dic15—81no—
287C3×Dic5—22no—
288C3×Dic5—22no—
289C5×Dic3—81no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—52no—
293C3×#41—52no—
294C3×#41—102no—
295C3×#41—102no—
296C3×#41—104no—
297C3×#41—104no—
298C3×#41—104no—
299C3×#41—104no—
300C3×#41—102no—
301C3×#41—102no—
302C3×#41—102no—
303C3×#41—102no—
304C3×#41—101no—
305C3×#41—101no—
306C3×#41—101no—
307C3×#41—101no—
308C3×#41—101no—
309C3×#41—101no—
310C3×#41C4×D512yes—
311C3×#41C22⋊D512yes—
312C2×C3×Q8—51no—
313C2×C3×Q8—51no—
314C2×C3×Q8—102no—
315C2×C3×Q8—102no—
316C2×C3×Q8—102no—
317C2×C3×Q8D2011yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4—52no—
320C2×C3×D4—51no—
321C2×C3×D4—51no—
322C2×C3×D4—102no—
323C2×C3×D4—104no—
324C2×C3×D4—104no—
325C2×C3×D4—102no—
326C2×C3×D4—104no—
327C2×C3×D4—101no—
328C2×C3×D4—102no—
329C2×C3×D4D2011yescharacteristic
330C22×C3×C4—21no—
331C22×C3×C4—52no—
332C22×C3×C4—104no—
333C22×C3×C4—101no—
334C22×C3×C4C22×D511yescharacteristic
335#217—21no—
336#217—101no—
337C4⋊Dic3—21no—
338C4⋊Dic3—101no—
339C4×Dic3—21no—
340C4×Dic3—101no—
341#208—21no—
342#208—21no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—101no—
345C2×C3⋊C8—101no—
346C2×C3⋊C8—101no—
347C23×C5—21no—
348C23×C5C2×#6711yescharacteristic
349C22×D5—24no—
350C22×D5—21no—
351C22×D5#21712yes—
352C5×Q8—21no—
353C5×Q8#21712yes—
354C5×D4—22no—
355C5×D4—22no—
356C5×D4—21no—
357C5×D4#21712yes—
358C2×C4×C5—21no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—121no—
362C2×C4×C5C22×Dic311yescharacteristic
363C2×C4×C5C2×#6711yescharacteristic
364C2×C4×C5C2×#6711yescharacteristic
365C2×C4×C5C2×#6711yescharacteristic
366C2×C4×C5C2×#6711yescharacteristic
367C2×C4×C5C2×#6711yescharacteristic
368C22⋊D5—24no—
369C22⋊D5—24no—
370C22⋊D5—22no—
371C22⋊D5—22no—
372C22⋊D5—22no—
373C22⋊D5—22no—
374C2×Dic5—24no—
375C2×Dic5—21no—
376C2×Dic5—121no—
377C2×Dic5#21712yes—
378D20—24no—
379D20—21no—
380D20—21no—
381D20—21no—
382D20#21712yes—
383C4×D5—24no—
384C4×D5—24no—
385C4×D5—22no—
386C4×D5—22no—
387C4×D5—22no—
388C4×D5—22no—
389Dic10—24no—
390Dic10—21no—
391Dic10—21no—
392Dic10—21no—
393Dic10#21712yes—
394C5×C8—121no—
395#168—121no—
3962−1+4—52no—
3972−1+4—101no—
3982−1+4—101no—
399H(5,𝔽2)—52no—
400H(5,𝔽2)—102no—
401H(5,𝔽2)—101no—
402H(5,𝔽2)—101no—
403C2×#41—51no—
404C2×#41—51no—
405C2×#41—102no—
406C2×#41—102no—
407C2×#41—102no—
408C2×#41D3×D511yescharacteristic
409C2×M16—31no—
410C22×C8—151no—
411#117—31no—
412#117—151no—
413#104—62no—
414#104—302no—
415#103—301no—
416#103—301no—
417#102—301no—
418#102—301no—
419#99—302no—
420C22⋊C8—302no—
421C2×C3×C5—21no—
422C2×C3×C5—21no—
423C2×C3×C5—21no—
424C2×C3×C5—42no—
425C2×C3×C5#37911yescharacteristic
426C3×D5—42no—
427C3×D5—42no—
428C23×C3—21no—
429C23×C3—52no—
430C23×C3—104no—
431C23×C3—101no—
432C23×C3D4×D511yescharacteristic
433C3×Q8—21no—
434C3×Q8—52no—
435C3×Q8—104no—
436C3×Q8—101no—
437C3×Q8—101no—
438C3×Q8—101no—
439C3×Q8#68512yes—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—21no—
443C3×D4—52no—
444C3×D4—104no—
445C3×D4—104no—
446C3×D4—104no—
447C3×D4—102no—
448C3×D4—102no—
449C3×D4—102no—
450C3×D4—102no—
451C3×D4—101no—
452C3×D4—101no—
453C3×D4—101no—
454C3×D4#68512yes—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—52no—
459C2×C3×C4—104no—
460C2×C3×C4—104no—
461C2×C3×C4—104no—
462C2×C3×C4—101no—
463C2×C3×C4—102no—
464C2×C3×C4—102no—
465C2×C3×C4—102no—
466C2×C3×C4—102no—
467C2×C3×C4C2×C4×D511yescharacteristic
468C2×C3×C4C2×D2011yescharacteristic
469C2×C3×C4D4×D511yescharacteristic
470C2×C3×C4D4×D511yescharacteristic
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4C2×C22⋊D511yescharacteristic
473C2×Dic3—41no—
474C2×Dic3—201no—
475C3⋊C8—41no—
476C3⋊C8—201no—
477C22×C5—22no—
478C22×C5—41no—
479C22×C5—81no—
480C22×C5C2×#21711yescharacteristic
481C22×C5#95311yescharacteristic
482C22×C5#95311yescharacteristic
483C2×D5—22no—
484C2×D5—22no—
485C2×D5—42no—
486C2×D5—81no—
487C2×D5—84no—
488C4×C5—22no—
489C4×C5—241no—
490C4×C5C2×#21711yescharacteristic
491C4×C5C2×#21711yescharacteristic
492C4×C5#95311yescharacteristic
493C4×C5#95311yescharacteristic
494Dic5—22no—
495Dic5—22no—
496Dic5—241no—
497#41—21no—
498#41—21no—
499#41—52no—
500#41—52no—
501#41—102no—
502#41—102no—
503#41—104no—
504#41—104no—
505#41—104no—
506#41—104no—
507#41—102no—
508#41—102no—
509#41—102no—
510#41—102no—
511#41—101no—
512#41—101no—
513#41—101no—
514#41—101no—
515#41—101no—
516#41—101no—
517#41D5×Dic312yes—
518#41#120112yes—
519C2×Q8—51no—
520C2×Q8—51no—
521C2×Q8—102no—
522C2×Q8—102no—
523C2×Q8—102no—
524C2×Q8#120211yescharacteristic
525C2×D4—21no—
526C2×D4—52no—
527C2×D4—51no—
528C2×D4—51no—
529C2×D4—102no—
530C2×D4—104no—
531C2×D4—104no—
532C2×D4—102no—
533C2×D4—104no—
534C2×D4—101no—
535C2×D4—102no—
536C2×D4#120211yescharacteristic
537C22×C4—21no—
538C22×C4—52no—
539C22×C4—104no—
540C22×C4—101no—
541C22×C4C2×D3×D511yescharacteristic
542M16—61no—
543M16—61no—
544C2×C8—61no—
545C2×C8—301no—
546C2×C8—301no—
547C2×C8—301no—
548C4⋊C4—61no—
549C4⋊C4—301no—
550C22⋊C4—61no—
551C22⋊C4—301no—
552C42—61no—
553C42—301no—
554C3×C5#179411yescharacteristic, complemented, Hall
555C22×C3—22no—
556C22×C3—41no—
557C22×C3—81no—
558C22×C3—102no—
559C22×C3—102no—
560C22×C3—202no—
561C22×C3—401no—
562C22×C3—404no—
563C22×C3D5×C22⋊C411yescharacteristic
564C22×C3#402811yescharacteristic
565C22×C3#408311yescharacteristic
566C3×C4—22no—
567C3×C4—102no—
568C3×C4—102no—
569C3×C4D5×C22⋊C411yescharacteristic
570C3×C4#402811yescharacteristic
571C3×C4C2×#68511yescharacteristic
572C3×C4#408311yescharacteristic
573Dic3—81no—
574Dic3—401no—
575C2×C5—21no—
576C2×C5—21no—
577C2×C5—21no—
578C2×C5—42no—
579C2×C5#524711yescharacteristic
580D5—42no—
581D5—42no—
582C23—21no—
583C23—52no—
584C23—104no—
585C23—101no—
586C23D5×#6711yescharacteristic
587Q8—21no—
588Q8—52no—
589Q8—104no—
590Q8—101no—
591Q8—101no—
592Q8—101no—
593Q8#666512yes—
594D4—22no—
595D4—22no—
596D4—21no—
597D4—52no—
598D4—104no—
599D4—104no—
600D4—104no—
601D4—102no—
602D4—102no—
603D4—102no—
604D4—102no—
605D4—101no—
606D4—101no—
607D4—101no—
608D4#666512yes—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—52no—
613C2×C4—104no—
614C2×C4—104no—
615C2×C4—104no—
616C2×C4—101no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—121no—
622C2×C4—601no—
623C2×C4C2×D5×Dic311yescharacteristic
624C2×C4C2×#120111yescharacteristic
625C2×C4C2×#120211yescharacteristic
626C2×C4D5×#6711yescharacteristic
627C2×C4D5×#6711yescharacteristic
628C2×C4D5×#6711yescharacteristic
629C8—121no—
630C8—601no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—42no—
635C2×C3—202no—
636C2×C3—202no—
637C2×C3#6524411yescharacteristic
638C5#7214611yescharacteristic, complemented, Sylow
639C22—22no—
640C22—41no—
641C22—81no—
642C22—102no—
643C22—102no—
644C22—202no—
645C22—401no—
646C22—404no—
647C22D5×#21711yescharacteristic
648C22#9156311yescharacteristic
649C22#9156411yescharacteristic
650C4—22no—
651C4—102no—
652C4—102no—
653C4—241no—
654C4—1201no—
655C4C2×#666511yescharacteristic
656C4D5×#21711yescharacteristic
657C4#9156311yescharacteristic
658C4#9156411yescharacteristic
659C3#1060120611yescharacteristic, complemented, Sylow
660C2—21no—
661C2—21no—
662C2—21no—
663C2—42no—
664C2—202no—
665C2—202no—
666C2#1174948811yescharacteristic
subgroupG/H
centerC4#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#379
prime radicalC3×#66283C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1794
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751334C2semidirect
3. C5×#5236C2semidirect
4. #11748624C2semidirect
5. #11748420C2semidirect
6. #11748364C2semidirect
7. #11748343C2semidirect
11. C3×#4150C4semidirect
13. C3×#4149C4semidirect
22. #91815C22semidirect
23. C22×C3⋊#168C22semidirect
24. C5×#926C22semidirect
25. C2×C5×#208C22semidirect
102. #5236D5semidirect
108. #4150Dic3semidirect
110. #4149Dic3semidirect
195. #926C2×D5semidirect
196. C2×#208C2×D5semidirect
554. C3×C5#1794semidirect
638. C5#72146semidirect
659. C3#10601206semidirect

Maximal subgroups

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

subgroupindex
C3×#662832
#117513342
C5×#52362
#117486242
#117484202
#117483642
#117483432
#106012063
#721465