Finite Group Databasebeta

← #14480655

Subgroups — #14480655

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#237C212yesmaximal, complemented
2#11756356C211yesmaximal, characteristic, complemented
3C5×#5596C211yesmaximal, characteristic, complemented
4C3×#65939C211yesmaximal, characteristic, complemented
5#11755061C212yesmaximal, complemented
6#11755030C212yesmaximal, complemented
7#11754821C212yesmaximal, complemented
8#11754803C212yesmaximal, complemented
9#11754758C212yesmaximal, complemented
10#11754644C211yesmaximal, characteristic, complemented
11#11754387C211yesmaximal, characteristic, complemented
12#11754356C211yesmaximal, characteristic, complemented
13C2×#91393C211yesmaximal, characteristic, complemented
14#11753852C212yesmaximal, complemented
15#11753412C212yesmaximal, complemented
16#11753224C212yesmaximal, complemented
17#11753220C212yesmaximal, complemented
18#11752830C212yesmaximal, complemented
19#11752827C212yesmaximal, complemented
20#10618136—31nomaximal, Hall
21C2×#6819C2212yescomplemented
22C2×C5×#237C2212yescomplemented
23C2×C3×D4×D5C2212yes—
24C2×D5×#67C2212yes—
25C2×D5×#67C2212yescomplemented
26C2×#6780C2212yes—
27C2×#6780C2212yescomplemented
28C2×#6779C2212yes—
29C2×#6779C2212yescomplemented
30C22×D5×Dic3C2211yescharacteristic
31C22×D5×Dic3C2212yescomplemented
32D5×#237—216no—
33C2×C4×D3×D5C2212yescomplemented
34C2×#6766C2212yes—
35C2×#6765C2212yes—
36C2×D5×Dic6C2212yescomplemented
37C3×C5×#121C2211yescharacteristic, complemented
38#91828C2212yescomplemented
39#91828C2212yescomplemented
40#91819C2211yescharacteristic, complemented
41C2×#6712C2211yescharacteristic, complemented
42#91785C2212yescomplemented
43#91773C2212yescomplemented
44#91767C2212yescomplemented
45C5×#940C2211yescharacteristic, complemented
46C5×#939C2212yescomplemented
47C5×D4×Dic3C2211yescharacteristic, complemented
48C5×#930C2211yescharacteristic, complemented
49C2×C4×C5×Dic3C2211yescharacteristic, complemented
50C5×#893C2211yescharacteristic, complemented
51C5×#888C2211yescharacteristic, complemented
52C5×#885C2212yescomplemented
53C5×#67⋊C4C2212yescomplemented
54C3×#4085C2212yescomplemented
55C3×#4083C2212yescomplemented
56C3×#4076C2211yescharacteristic, complemented
57C2×C3×#685C2211yescharacteristic
58C3×#4040C2212yescomplemented
59C3×#4029C2212yescomplemented
60C3×#4028C2212yescomplemented
61#91577C2212yescomplemented
62#91576C2212yescomplemented
63#91571C2212yescomplemented
64#91571C2212yescomplemented
65#91569C2212yescomplemented
66#91567C2212yescomplemented
67#91566C2212yescomplemented
68#91564C2212yescomplemented
69#91563C2212yescomplemented
70#91558C2212yescomplemented
71#91556C2212yescomplemented
72Dic3×C22⋊D5C2212yescomplemented
73#91550C2212yescomplemented
74#91548C2212yescomplemented
75C2×#6669C2211yescharacteristic, complemented
76C2×#6665C2211yescharacteristic
77C2×Dic3×Dic5C2211yescharacteristic, complemented
78#91525C2212yescomplemented
79#91476C2212yescomplemented
80#91475C2212yescomplemented
81#91474C2212yescomplemented
82#91469C2211yescharacteristic, complemented
83#91461C2212yescomplemented
84#91458C2211yescharacteristic, complemented
85#91455C2212yescomplemented
86#91453C2212yescomplemented
87#91447C2212yescomplemented
88#91446C2212yescomplemented
89#91441C2212yescomplemented
90#91436C2212yescomplemented
91#91432C2212yescomplemented
92#91431C2212yescomplemented
93#91430C2212yescomplemented
94#91428C2211yescharacteristic, complemented
95Dic3×D20C2211yescharacteristic, complemented
96#91414C2212yescomplemented
97#91413C2212yescomplemented
98#91408C2212yescomplemented
99#91407C2212yescomplemented
100#91395C2212yescomplemented
101#91393C2212yescomplemented
102#91393C2212yescomplemented
103#91393C2212yescomplemented
104#91393C2212yescomplemented
105#91377C2212yescomplemented
106#91353C2212yescomplemented
107#91348C2212yescomplemented
108#91329C2212yescomplemented
109#86294—51nomaximal, Hall
110C2×D5×#41—32no—
111C5×#532—31no—
112#66166—32no—
113#66058—32no—
114#66049—32no—
115#66009—32no—
116#66008—32no—
117#65939—31no—
118#65939—32no—
119#65939D311yescharacteristic, complemented
120#65931—32no—
121#65931—31no—
122#65931—31no—
123#65881—32no—
124#65881—32no—
125#65881—32no—
126#65881—32no—
127#65811—31no—
128C2×#4018—31no—
129C23×C3×D5C2312yes—
130C23×C3×D5C2311yescharacteristic
131C22×D3×D5C2312yes—
132C2×C3×C5×D4C2312yes—
133C2×C3×C5×D4C2311yescharacteristic
134C22×C3×C4×C5C2311yescharacteristic
135C2×#1220C2312yes—
136C2×#1220C2312yes—
137C2×#1220C2312yes—
138C22×Dic15C2312yes—
139C22×Dic15C2311yescharacteristic
140C22×Dic15C2311yescharacteristic
141#6819—28no—
142C2×D60C2311yescharacteristic
143C2×C4×D15C2312yes—
144C2×Dic30C2312yes—
145C2×C5×#67C2312yes—
146C2×C5×#67C2312yes—
147C2×C5×#67C2312yes—
148C22×C5×Dic3C2312yes—
149C22×C5×Dic3C2311yescharacteristic
150C22×C5×Dic3C2311yescharacteristic
151C5×#237—28no—
152C2×C5×D12C2311yescharacteristic
153C2×C4×C5×D3C2312yes—
154C2×C5×Dic6C2312yes—
155C2×C3×C22⋊D5C2312yes—
156C2×C3×C22⋊D5C2312yes—
157C2×C3×C22⋊D5C2312yes—
158C22×C3×Dic5C2311yescharacteristic
159C3×D4×D5—28no—
160C2×C3×D20C2312yes—
161C2×C3×D20C2311yescharacteristic
162C2×C3×C4×D5C2312yes—
163D5×#67—28no—
164D5×#67—28no—
165C2×#1204C2312yes—
166C2×#1204C2312yes—
167C2×#1203C2312yes—
168C2×#1202C2312yes—
169C2×#1202C2312yes—
170C2×#1202C2312yes—
171C2×#1201C2312yes—
172C2×#1201C2312yes—
173C2×#1201C2312yes—
174C2×#1200C2312yes—
175C2×D3×Dic5C2312yes—
176#6780—28no—
177#6780—28no—
178#6779—28no—
179#6779—28no—
180C2×D5×Dic3—28no—
181C2×D5×Dic3D418yescomplemented
182C2×D5×Dic3C2312yes—
183C2×D5×Dic3C2312yes—
184C2×D5×Dic3C2312yes—
185C2×D5×Dic3C2312yes—
186C2×D5×Dic3C2312yes—
187C4×D3×D5—28no—
188#6766—28no—
189#6765—28no—
190D5×Dic6—28no—
191C3×C5×C4⋊C4C2311yescharacteristic
192C3×C5×C22⋊C4C2312yes—
193#6719C2312yes—
194#6714C2312yes—
195#6714C2312yes—
196C4⋊Dic15C2311yescharacteristic
197#6712C2312yes—
198#6712C2312yes—
199#6712C2312yes—
200C5×#217C2312yes—
201C5×(C2×D3)⋊C4C2312yes—
202C5×(C2×D3)⋊C4C2312yes—
203C5×C4⋊Dic3C2311yescharacteristic
204C5×Dic3⋊C4C2312yes—
205C4×C5×Dic3C2311yescharacteristic
206C4×C5×Dic3C2311yescharacteristic
207C4×C5×Dic3C2311yescharacteristic
208C4×C5×Dic3C2311yescharacteristic
209C3×C22⋊Dic5C2312yes—
210C3×#685C2312yes—
211C3×#685C2312yes—
212C3×#685C2312yes—
213C3×#685C2312yes—
214C3×C4⋊Dic5C2311yescharacteristic
215C3×#683C2312yes—
216Dic3⋊Dic5C2312yes—
217#6669C2312yes—
218#6669C2312yes—
219#6669C2312yes—
220#6668C2312yes—
221#6667C2312yes—
222#6667C2312yes—
223(C2×D3)⋊Dic5C2312yes—
224(C2×D3)⋊Dic5C2312yes—
225#6665C2312yes—
226#6665C2312yes—
227#6665C2312yes—
228#6665C2312yes—
229Dic3×Dic5C2312yes—
230Dic3×Dic5C2312yes—
231C22×#237—52no—
232C3×#534—51no—
233#5804—52no—
234#5656—52no—
235#5656—52no—
236#5648—52no—
237#5648—52no—
238#5597—51no—
239#5597—52no—
240#5597—51no—
241#5596—52no—
242#5596—51no—
243#5596D511yescharacteristic, complemented
244#5592—52no—
245#5592—52no—
246#5586—52no—
247#5586—52no—
248#5493—51no—
249C2×#877—51no—
250C2×C5×#41—32no—
251D5×#41—616no—
252C2×#713—32no—
253C2×Q8×D5—32no—
254C2×#711—32no—
255C2×#711—32no—
256C2×#711—32no—
257C2×D4×D5—32no—
258C2×D4×D5—32no—
259C2×D4×D5C2×D312yes—
260C2×#709—32no—
261C2×#709—32no—
262C2×#709—32no—
263C22×C4×D5—31no—
264C22×C4×D5—32no—
265C22×C4×D5—32no—
266C5×C4⋊Q8—31no—
267C5×#127—31no—
268C5×#124—32no—
269C5×#121—32no—
270C5×#121—31no—
271C5×#121C2×D311yescharacteristic, complemented
272C4×C5×D4—31no—
273C4×C5×D4—31no—
274C4×C5×D4—32no—
275C2×C42×C5—31no—
276#4093—32no—
277#4090—32no—
278#4086—32no—
279#4085—32no—
280#4085—32no—
281#4085—32no—
282#4085—32no—
283#4085—32no—
284#4085—32no—
285#4085—32no—
286#4085C2×D312yescomplemented
287#4083—32no—
288#4083—32no—
289#4083—32no—
290#4083C2×D312yescomplemented
291#4082—32no—
292#4076—31no—
293#4076—32no—
294#4076C2×D311yescharacteristic, complemented
295C4×C22⋊D5—32no—
296C4×C22⋊D5—32no—
297C4×C22⋊D5—32no—
298C4×C22⋊D5—32no—
299C2×#685—31no—
300C2×#685C2×D311yescharacteristic
301C2×#683—31no—
302C2×#683—31no—
303C2×C4×Dic5—31no—
304#4042—32no—
305#4042—32no—
306#4042—32no—
307#4042—32no—
308#4040—32no—
309#4040—32no—
310#4040—32no—
311#4040C2×D312yescomplemented
312#4030—32no—
313#4030—32no—
314#4030—32no—
315#4030—32no—
316#4029—32no—
317#4029—32no—
318#4029—32no—
319#4029C2×D312yescomplemented
320#4028—32no—
321#4028—32no—
322#4028—32no—
323#4028C2×D312yescomplemented
324#4024—32no—
325#4024—32no—
326#4024—32no—
327#4024—32no—
328#4021—32no—
329#4020—31no—
330C4×D20—31no—
331C4×D20—32no—
332C4×D20—31no—
333#4018—32no—
334#4018—32no—
335#4018—32no—
336#4018—32no—
337#4015—31no—
338#3449—151noSylow
339C23×C3×C5C2412yes—
340C23×C3×C5C2411yescharacteristic
341C22×D15C2412yes—
342C22×C5×D3C2412yes—
343C22×C3×D5—24no—
344C22×C3×D5—41no—
345C22×C3×D5—41no—
346C22×C3×D5—42no—
347C22×C3×D5—42no—
348C22×C3×D5C2×D414yes—
349C22×C3×D5C2412yes—
350C22×C3×D5C2412yes—
351C2×D3×D5—24no—
352C2×D3×D5—42no—
353C2×D3×D5—42no—
354C3×C5×D4—24no—
355C3×C5×D4—41no—
356C2×C3×C4×C5—41no—
357C2×C3×C4×C5C2412yes—
358C2×C3×C4×C5C2411yescharacteristic
359C2×C3×C4×C5C2411yescharacteristic
360#1220—24no—
361#1220—24no—
362#1220—42no—
363C2×Dic15—24no—
364C2×Dic15—41no—
365C2×Dic15C2×D414yes—
366C2×Dic15C2412yes—
367C2×Dic15C2412yes—
368C2×Dic15C2412yes—
369D60—41no—
370C4×D15—24no—
371Dic30—24no—
372C5×#67—24no—
373C5×#67—24no—
374C5×#67—42no—
375C2×C5×Dic3—24no—
376C2×C5×Dic3—41no—
377C2×C5×Dic3C2×D414yes—
378C2×C5×Dic3C2411yescharacteristic
379C2×C5×Dic3C2411yescharacteristic
380C2×C5×Dic3C2412yes—
381C2×C5×Dic3C2411yescharacteristic
382C2×C5×Dic3C2411yescharacteristic
383C5×D12—41no—
384C4×C5×D3—24no—
385C5×Dic6—24no—
386C3×C22⋊D5—24no—
387C3×C22⋊D5—24no—
388C3×C22⋊D5—42no—
389C2×C3×Dic5—41no—
390C2×C3×Dic5C2412yes—
391C2×C3×Dic5C2412yes—
392C3×D20—24no—
393C3×D20—41no—
394C3×C4×D5—24no—
395#1204—24no—
396#1204—24no—
397#1203—42no—
398#1202—24no—
399#1202—24no—
400#1202—42no—
401#1201—24no—
402#1201—24no—
403#1201—42no—
404#1200—24no—
405D3×Dic5—24no—
406D5×Dic3—24no—
407D5×Dic3—24no—
408D5×Dic3—24no—
409D5×Dic3C2×D418yes—
410D5×Dic3C2×D418yes—
411C22×C3×D4—52no—
412C22×#67—52no—
413C22×#67—52no—
414C23×Dic3—51no—
415C23×Dic3—52no—
416C2×#237—52no—
417C2×#237—52no—
418C2×#237—52no—
419C2×#237—52no—
420C2×#237—52no—
421C2×#237—52no—
422C2×#237—52no—
423C2×#237—1016no—
424C2×#237C2×D512yescomplemented
425C22×C4×D3—52no—
426C22×Dic6—52no—
427C3×#123—52no—
428C3×#123—52no—
429C3×#121—52no—
430C3×#121—51no—
431C3×#121C2×D511yescharacteristic, complemented
432C3×#120—52no—
433C3×#120—52no—
434C2×C3×C22⋊C4—51no—
435#953—52no—
436#953—52no—
437C2×#217—51no—
438#940—52no—
439#940—51no—
440#940C2×D511yescharacteristic, complemented
441#939—52no—
442#939—52no—
443#939—52no—
444#939—52no—
445#939—52no—
446#939—52no—
447#939—52no—
448#939C2×D512yescomplemented
449#937—52no—
450#937—52no—
451#935—52no—
452#935—52no—
453D4×Dic3—52no—
454D4×Dic3—51no—
455D4×Dic3C2×D511yescharacteristic, complemented
456#930—51no—
457#930—52no—
458#930C2×D511yescharacteristic, complemented
459#929—52no—
460#929—52no—
461C2×Dic3⋊C4—51no—
462C2×Dic3⋊C4—51no—
463C2×C4×Dic3—51no—
464C2×C4×Dic3C2×D511yescharacteristic, complemented
465#896—52no—
466#896—52no—
467#896—52no—
468#896—52no—
469#893—52no—
470#893—51no—
471#893C2×D511yescharacteristic, complemented
472#888—52no—
473#888—51no—
474#888C2×D511yescharacteristic, complemented
475#886—52no—
476#886—52no—
477#885—52no—
478#885—52no—
479#885—52no—
480#885C2×D512yescomplemented
481#884—52no—
482#884—52no—
483#884—52no—
484#884—52no—
485#882—52no—
486#882—52no—
487#67⋊C4—52no—
488#67⋊C4—52no—
489#67⋊C4—52no—
490#67⋊C4C2×D512yescomplemented
491#878—52no—
492#878—52no—
493#878—52no—
494#878—52no—
495#877—52no—
496#877—52no—
497#877—52no—
498#877—52no—
499C23×D5—32no—
500C23×D5C22×D312yes—
501C23×D5C22×D311yescharacteristic
502C5×#41—68no—
503C2×C5×Q8—32no—
504C2×C5×D4—32no—
505C2×C5×D4—32no—
506C2×C5×D4—32no—
507C2×C5×D4—31no—
508C2×C5×D4C22×D312yes—
509C2×C5×D4C22×D311yescharacteristic
510C22×C4×C5—31no—
511C22×C4×C5—32no—
512C22×C4×C5—31no—
513C22×C4×C5—32no—
514C22×C4×C5C22×D311yescharacteristic
515C2×C22⋊D5—32no—
516C2×C22⋊D5—32no—
517C2×C22⋊D5—32no—
518C2×C22⋊D5—32no—
519C2×C22⋊D5—32no—
520C2×C22⋊D5—32no—
521C2×C22⋊D5—32no—
522C2×C22⋊D5C22×D312yes—
523C2×C22⋊D5C22×D312yes—
524C2×C22⋊D5C22×D312yes—
525C22×Dic5—31no—
526C22×Dic5—32no—
527C22×Dic5—31no—
528C22×Dic5—32no—
529C22×Dic5C22×D311yescharacteristic
530#713—68no—
531Q8×D5—68no—
532#711—68no—
533#711—68no—
534#711—68no—
535D4×D5—28no—
536D4×D5—68no—
537D4×D5—68no—
538#709—68no—
539#709—68no—
540#709—68no—
541C2×D20—32no—
542C2×D20—32no—
543C2×D20—32no—
544C2×D20—31no—
545C2×D20C22×D312yes—
546C2×D20C22×D311yescharacteristic
547C2×C4×D5—38no—
548C2×C4×D5—32no—
549C2×C4×D5—32no—
550C2×C4×D5—32no—
551C2×C4×D5—32no—
552C2×C4×D5—32no—
553C2×C4×D5—32no—
554C2×C4×D5—32no—
555C2×C4×D5—68no—
556C2×C4×D5—68no—
557C2×C4×D5C22×D312yes—
558C2×Dic10—32no—
559C2×Dic10—32no—
560C2×Dic10—32no—
561C5×C4⋊C4—32no—
562C5×C4⋊C4—31no—
563C5×C4⋊C4C22×D311yescharacteristic
564C5×C22⋊C4—32no—
565C5×C22⋊C4—32no—
566C5×C22⋊C4—32no—
567C5×C22⋊C4C22×D312yes—
568C42×C5—31no—
569C42×C5—31no—
570C42×C5—31no—
571C42×C5—31no—
572C22⋊Dic5—32no—
573C22⋊Dic5—32no—
574C22⋊Dic5—32no—
575C22⋊Dic5C22×D312yes—
576#685—32no—
577#685—32no—
578#685—32no—
579#685—32no—
580#685—32no—
581#685—32no—
582#685—32no—
583#685—32no—
584#685C22×D312yes—
585#685C22×D312yes—
586#685C22×D312yes—
587#685C22×D312yes—
588C4⋊Dic5—31no—
589C4⋊Dic5—32no—
590C4⋊Dic5C22×D311yescharacteristic
591#683—32no—
592#683—32no—
593#683—32no—
594#683—32no—
595#683—32no—
596#683—32no—
597#683—32no—
598#683C22×D312yes—
599C4×Dic5—32no—
600C4×Dic5—32no—
601C22×#41—152no—
602#537—152no—
603#537—151no—
604#537—151no—
605#536—152no—
606#536—152no—
607#535—152no—
608#535—152no—
609#534—51no—
610#534—151no—
611#534—152no—
612#532—31no—
613#532—151no—
614#532—152no—
615#525—152no—
616#525—152no—
617#525—152no—
618#525—152no—
619C2×#117—151no—
620C22×C3×C5—21no—
621C22×C3×C5—21no—
622C22×C3×C5—22no—
623C22×C3×C5—22no—
624C22×C3×C5—22no—
625C22×C3×C5C22×D412yes—
626C22×C3×C5C2511yescharacteristic
627C2×D15—22no—
628C2×D15—22no—
629C2×D15—22no—
630C2×C5×D3—22no—
631C2×C5×D3—22no—
632C2×C5×D3—22no—
633C2×C3×D5—22no—
634C2×C3×D5—22no—
635C2×C3×D5—22no—
636C2×C3×D5—22no—
637C2×C3×D5—22no—
638C2×C3×D5—44no—
639C2×C3×D5—48no—
640C2×C3×D5C22×D414yes—
641D3×D5—48no—
642C3×C4×C5—22no—
643C3×C4×C5—21no—
644C3×C4×C5—21no—
645Dic15—22no—
646Dic15—22no—
647Dic15C22×D414yes—
648C3×Dic5—22no—
649C3×Dic5—22no—
650C5×Dic3—22no—
651C5×Dic3—21no—
652C5×Dic3—21no—
653C5×Dic3C22×D412yes—
654C5×Dic3C22×D412yes—
655C24×C3—51no—
656C24×C3—52no—
657C23×D3—52no—
658C2×C3×D4—52no—
659C2×C3×D4—52no—
660C2×C3×D4—52no—
661C2×C3×D4—52no—
662C2×C3×D4—51no—
663C2×C3×D4—108no—
664C2×C3×D4C22×D512yes—
665C2×C3×D4C22×D511yescharacteristic
666C22×C3×C4—51no—
667C22×C3×C4—52no—
668C22×C3×C4C22×D511yescharacteristic
669C2×#67—52no—
670C2×#67—52no—
671C2×#67—52no—
672C2×#67—52no—
673C2×#67—52no—
674C2×#67—52no—
675C2×#67—52no—
676C2×#67—52no—
677C2×#67—52no—
678C2×#67—108no—
679C2×#67—108no—
680C2×#67C22×D512yes—
681C2×#67C22×D512yes—
682C2×#67C22×D512yes—
683C22×Dic3—51no—
684C22×Dic3—58no—
685C22×Dic3—52no—
686C22×Dic3—52no—
687C22×Dic3—52no—
688C22×Dic3—51no—
689C22×Dic3—52no—
690C22×Dic3—52no—
691C22×Dic3—52no—
692C22×Dic3—108no—
693C22×Dic3C22×D512yes—
694C22×Dic3C22×D511yescharacteristic
695C22×Dic3C22×D511yescharacteristic
696#237—28no—
697#237—108no—
698#237—108no—
699#237—108no—
700#237—108no—
701#237—108no—
702#237—108no—
703#237—108no—
704C2×D12—52no—
705C2×D12—51no—
706C2×D12C22×D511yescharacteristic
707C2×C4×D3—52no—
708C2×C4×D3—52no—
709C2×C4×D3—52no—
710C2×C4×D3—108no—
711C2×C4×D3C22×D512yes—
712C2×Dic6—52no—
713C2×Dic6—52no—
714C2×Dic6—52no—
715C2×Dic6—108no—
716C2×Dic6C22×D512yes—
717C3×C4⋊C4—52no—
718C3×C4⋊C4—51no—
719C3×C4⋊C4C22×D511yescharacteristic
720C3×C22⋊C4—52no—
721C3×C22⋊C4—52no—
722C3×C22⋊C4—52no—
723C3×C22⋊C4—52no—
724C3×C22⋊C4—52no—
725C3×C22⋊C4C22×D512yes—
726#217—52no—
727#217—52no—
728#217—52no—
729#217—52no—
730#217—52no—
731#217C22×D512yes—
732(C2×D3)⋊C4—52no—
733(C2×D3)⋊C4—52no—
734(C2×D3)⋊C4—52no—
735(C2×D3)⋊C4—52no—
736(C2×D3)⋊C4—52no—
737(C2×D3)⋊C4—52no—
738(C2×D3)⋊C4C22×D512yes—
739(C2×D3)⋊C4C22×D512yes—
740C4⋊Dic3—51no—
741C4⋊Dic3—52no—
742C4⋊Dic3C22×D511yescharacteristic
743Dic3⋊C4—52no—
744Dic3⋊C4—52no—
745Dic3⋊C4—52no—
746Dic3⋊C4—52no—
747Dic3⋊C4—52no—
748Dic3⋊C4—52no—
749Dic3⋊C4—52no—
750Dic3⋊C4C22×D512yes—
751C4×Dic3—52no—
752C4×Dic3—52no—
753C4×Dic3C22×D511yescharacteristic
754C4×Dic3C22×D511yescharacteristic
755C4×Dic3C22×D511yescharacteristic
756C4×Dic3C22×D511yescharacteristic
757C23×C5—32no—
758C23×C5C23×D312yes—
759C23×C5C23×D311yescharacteristic
760C22×D5—24no—
761C22×D5—32no—
762C22×D5—41no—
763C22×D5—41no—
764C22×D5—42no—
765C22×D5—42no—
766C22×D5—64no—
767C22×D5—122no—
768C22×D5—122no—
769C22×D5D3×D414yes—
770C22×D5C23×D312yes—
771C22×D5C23×D312yes—
772C5×Q8—64no—
773C5×D4—24no—
774C5×D4—41no—
775C5×D4—64no—
776C5×D4—64no—
777C5×D4—121no—
778C5×D4—122no—
779C2×C4×C5—34no—
780C2×C4×C5—31no—
781C2×C4×C5—31no—
782C2×C4×C5—31no—
783C2×C4×C5—31no—
784C2×C4×C5—32no—
785C2×C4×C5—41no—
786C2×C4×C5—64no—
787C2×C4×C5—64no—
788C2×C4×C5—121no—
789C2×C4×C5C23×D311yescharacteristic
790C2×C4×C5C23×D311yescharacteristic
791C2×C4×C5C23×D312yes—
792C22⋊D5—24no—
793C22⋊D5—24no—
794C22⋊D5—42no—
795C22⋊D5—64no—
796C22⋊D5—64no—
797C22⋊D5—64no—
798C22⋊D5—64no—
799C22⋊D5—122no—
800C22⋊D5—122no—
801C22⋊D5—122no—
802C2×Dic5—34no—
803C2×Dic5—32no—
804C2×Dic5—32no—
805C2×Dic5—32no—
806C2×Dic5—41no—
807C2×Dic5—64no—
808C2×Dic5—64no—
809C2×Dic5—121no—
810C2×Dic5C23×D312yes—
811C2×Dic5C23×D312yes—
812D20—24no—
813D20—41no—
814D20—64no—
815D20—64no—
816D20—121no—
817D20—122no—
818C4×D5—24no—
819C4×D5—38no—
820C4×D5—38no—
821C4×D5—64no—
822C4×D5—64no—
823C4×D5—64no—
824C4×D5—64no—
825C4×D5—64no—
826Dic10—64no—
827Dic10—64no—
828Dic10—64no—
829C2×#41—32no—
830C2×#41—152no—
831C2×#41—152no—
832C2×#41—152no—
833C2×#41—152no—
834C2×#41—152no—
835C2×#41—152no—
836C2×#41—152no—
837C2×#41—3016no—
838C22×Q8—152no—
839C22×D4—52no—
840C22×D4—152no—
841C22×D4—152no—
842C23×C4—152no—
843C23×C4—151no—
844C23×C4—152no—
845C4⋊Q8—31no—
846C4⋊Q8—151no—
847C4⋊Q8—152no—
848#127—31no—
849#127—151no—
850#127—152no—
851#124—32no—
852#124—152no—
853#124—152no—
854#124—152no—
855#123—52no—
856#123—52no—
857#123—152no—
858#123—152no—
859#123—152no—
860#123—152no—
861#123—152no—
862#123—152no—
863C22⋊Q8—152no—
864C22⋊Q8—152no—
865C22⋊Q8—152no—
866C22⋊Q8—152no—
867C22⋊Q8—152no—
868C22⋊Q8—152no—
869C22⋊Q8—152no—
870C22⋊Q8—152no—
871#121—32no—
872#121—31no—
873#121—52no—
874#121—51no—
875#121—152no—
876#121—152no—
877#121—152no—
878#121—152no—
879#121—152no—
880#121—152no—
881#121—152no—
882#121—152no—
883#121—152no—
884#121—152no—
885#121—152no—
886#121—151no—
887#121—152no—
888#121D3×D511yescharacteristic, complemented
889#120—52no—
890#120—52no—
891#120—152no—
892#120—152no—
893#120—152no—
894#120—152no—
895#120—152no—
896#120—152no—
897C4×D4—31no—
898C4×D4—31no—
899C4×D4—32no—
900C4×D4—152no—
901C4×D4—151no—
902C4×D4—151no—
903C4×D4—152no—
904C4×D4—152no—
905C4×D4—152no—
906C4×D4—152no—
907#117—152no—
908#117—152no—
909#117—152no—
910#117—152no—
911C2×C4⋊C4—151no—
912C2×C4⋊C4—151no—
913C2×C22⋊C4—51no—
914C2×C22⋊C4—151no—
915C2×C42—31no—
916C2×C42—151no—
917C2×C3×C5—22no—
918C2×C3×C5—42no—
919C2×C3×C5C23×D411yescharacteristic
920C2×C3×C5#58511yescharacteristic
921C2×C3×C5#58511yescharacteristic
922D15—42no—
923C3×D5—24no—
924C3×D5—42no—
925C5×D3—42no—
926C23×C3—52no—
927C23×C3—54no—
928C23×C3—52no—
929C23×C3—104no—
930C23×C3—201no—
931C23×C3—201no—
932C23×C3—202no—
933C23×C3—202no—
934C23×C3C23×D512yes—
935C23×C3C23×D511yescharacteristic
936C22×D3—52no—
937C22×D3—104no—
938C22×D3—202no—
939C22×D3—202no—
940C22×D3C23×D512yes—
941C3×D4—24no—
942C3×D4—41no—
943C3×D4—104no—
944C3×D4—104no—
945C3×D4—104no—
946C3×D4—201no—
947C3×D4—202no—
948C2×C3×C4—41no—
949C2×C3×C4—52no—
950C2×C3×C4—52no—
951C2×C3×C4—104no—
952C2×C3×C4—201no—
953C2×C3×C4C23×D511yescharacteristic
954C2×C3×C4C23×D511yescharacteristic
955C2×C3×C4C23×D512yes—
956#67—24no—
957#67—24no—
958#67—42no—
959#67—104no—
960#67—104no—
961#67—104no—
962#67—104no—
963#67—104no—
964#67—104no—
965#67—202no—
966#67—202no—
967#67—202no—
968C2×Dic3—24no—
969C2×Dic3—41no—
970C2×Dic3—54no—
971C2×Dic3—52no—
972C2×Dic3—58no—
973C2×Dic3—58no—
974C2×Dic3—52no—
975C2×Dic3—52no—
976C2×Dic3—104no—
977C2×Dic3—104no—
978C2×Dic3—104no—
979C2×Dic3—104no—
980C2×Dic3—201no—
981C2×Dic3D4×D514yes—
982C2×Dic3C23×D511yescharacteristic
983C2×Dic3C23×D511yescharacteristic
984C2×Dic3C23×D512yes—
985C2×Dic3C23×D511yescharacteristic
986C2×Dic3C23×D511yescharacteristic
987D12—41no—
988D12—201no—
989D12—202no—
990C4×D3—24no—
991C4×D3—104no—
992C4×D3—104no—
993C4×D3—104no—
994Dic6—24no—
995Dic6—104no—
996Dic6—104no—
997Dic6—104no—
998C22×C5—21no—
999C22×C5—21no—
1000C22×C5—22no—
1001C22×C5—22no—
1002C22×C5—22no—
1003C22×C5—62no—
1004C22×C5—62no—
1005C22×C5—62no—
1006C22×C5C2×D3×D412yes—
1007C22×C5C24×D311yescharacteristic
1008C2×D5—22no—
1009C2×D5—22no—
1010C2×D5—22no—
1011C2×D5—22no—
1012C2×D5—22no—
1013C2×D5—44no—
1014C2×D5—48no—
1015C2×D5—62no—
1016C2×D5—62no—
1017C2×D5—62no—
1018C2×D5—128no—
1019C2×D5C2×D3×D414yes—
1020C4×C5—22no—
1021C4×C5—21no—
1022C4×C5—21no—
1023C4×C5—32no—
1024C4×C5—32no—
1025C4×C5—62no—
1026C4×C5—61no—
1027C4×C5—61no—
1028Dic5—22no—
1029Dic5—22no—
1030Dic5—34no—
1031Dic5—62no—
1032Dic5—62no—
1033C24—51no—
1034C24—52no—
1035C24—152no—
1036#41—68no—
1037#41—308no—
1038#41—308no—
1039#41—308no—
1040#41—308no—
1041#41—308no—
1042#41—308no—
1043#41—308no—
1044C2×Q8—32no—
1045C2×Q8—152no—
1046C2×Q8—152no—
1047C2×Q8—152no—
1048C2×Q8—308no—
1049C2×D4—32no—
1050C2×D4—32no—
1051C2×D4—32no—
1052C2×D4—31no—
1053C2×D4—52no—
1054C2×D4—52no—
1055C2×D4—52no—
1056C2×D4—52no—
1057C2×D4—51no—
1058C2×D4—108no—
1059C2×D4—152no—
1060C2×D4—152no—
1061C2×D4—152no—
1062C2×D4—152no—
1063C2×D4—152no—
1064C2×D4—152no—
1065C2×D4—152no—
1066C2×D4—152no—
1067C2×D4—152no—
1068C2×D4—152no—
1069C2×D4—151no—
1070C2×D4—308no—
1071C2×D4—308no—
1072C2×D4C2×D3×D512yes—
1073C2×D4C2×D3×D511yescharacteristic
1074C22×C4—31no—
1075C22×C4—32no—
1076C22×C4—31no—
1077C22×C4—32no—
1078C22×C4—51no—
1079C22×C4—52no—
1080C22×C4—152no—
1081C22×C4—152no—
1082C22×C4—152no—
1083C22×C4—158no—
1084C22×C4—152no—
1085C22×C4—152no—
1086C22×C4—152no—
1087C22×C4—152no—
1088C22×C4—151no—
1089C22×C4—152no—
1090C22×C4—151no—
1091C22×C4—152no—
1092C22×C4—308no—
1093C22×C4—308no—
1094C22×C4C2×D3×D511yescharacteristic
1095C4⋊C4—32no—
1096C4⋊C4—31no—
1097C4⋊C4—52no—
1098C4⋊C4—51no—
1099C4⋊C4—152no—
1100C4⋊C4—152no—
1101C4⋊C4—152no—
1102C4⋊C4—152no—
1103C4⋊C4—152no—
1104C4⋊C4—152no—
1105C4⋊C4—152no—
1106C4⋊C4—152no—
1107C4⋊C4—151no—
1108C4⋊C4C2×D3×D511yescharacteristic
1109C22⋊C4—32no—
1110C22⋊C4—32no—
1111C22⋊C4—32no—
1112C22⋊C4—52no—
1113C22⋊C4—52no—
1114C22⋊C4—52no—
1115C22⋊C4—52no—
1116C22⋊C4—52no—
1117C22⋊C4—152no—
1118C22⋊C4—152no—
1119C22⋊C4—152no—
1120C22⋊C4—152no—
1121C22⋊C4—152no—
1122C22⋊C4—152no—
1123C22⋊C4—152no—
1124C22⋊C4—152no—
1125C22⋊C4—152no—
1126C22⋊C4—152no—
1127C22⋊C4—152no—
1128C22⋊C4C2×D3×D512yes—
1129C42—31no—
1130C42—31no—
1131C42—31no—
1132C42—31no—
1133C42—152no—
1134C42—152no—
1135C3×C5#344911yescharacteristic, complemented, Hall
1136C22×C3—21no—
1137C22×C3—21no—
1138C22×C3—22no—
1139C22×C3—22no—
1140C22×C3—22no—
1141C22×C3—54no—
1142C22×C3—102no—
1143C22×C3—102no—
1144C22×C3—102no—
1145C22×C3—102no—
1146C22×C3—102no—
1147C22×C3—204no—
1148C22×C3—208no—
1149C22×C3C2×D4×D512yes—
1150C22×C3C24×D511yescharacteristic
1151C2×D3—22no—
1152C2×D3—22no—
1153C2×D3—22no—
1154C2×D3—102no—
1155C2×D3—102no—
1156C2×D3—102no—
1157C2×D3—208no—
1158C3×C4—22no—
1159C3×C4—21no—
1160C3×C4—21no—
1161C3×C4—102no—
1162C3×C4—102no—
1163Dic3—22no—
1164Dic3—21no—
1165Dic3—21no—
1166Dic3—54no—
1167Dic3—102no—
1168Dic3—102no—
1169Dic3C2×D4×D512yes—
1170Dic3C2×D4×D512yes—
1171C2×C5—22no—
1172C2×C5—42no—
1173C2×C5—122no—
1174C2×C5C22×D3×D411yescharacteristic
1175C2×C5#596611yescharacteristic
1176C2×C5#596611yescharacteristic
1177D5—24no—
1178D5—42no—
1179D5—122no—
1180C23—32no—
1181C23—52no—
1182C23—54no—
1183C23—52no—
1184C23—104no—
1185C23—152no—
1186C23—201no—
1187C23—201no—
1188C23—202no—
1189C23—202no—
1190C23—304no—
1191C23—602no—
1192C23—602no—
1193C23C22×D3×D512yes—
1194C23C22×D3×D511yescharacteristic
1195Q8—64no—
1196Q8—304no—
1197Q8—304no—
1198Q8—304no—
1199D4—24no—
1200D4—41no—
1201D4—64no—
1202D4—64no—
1203D4—104no—
1204D4—104no—
1205D4—104no—
1206D4—121no—
1207D4—122no—
1208D4—201no—
1209D4—202no—
1210D4—304no—
1211D4—304no—
1212D4—304no—
1213D4—304no—
1214D4—304no—
1215D4—304no—
1216D4—601no—
1217D4—602no—
1218D4—602no—
1219D4—602no—
1220D4—602no—
1221C2×C4—34no—
1222C2×C4—31no—
1223C2×C4—31no—
1224C2×C4—31no—
1225C2×C4—31no—
1226C2×C4—32no—
1227C2×C4—41no—
1228C2×C4—52no—
1229C2×C4—52no—
1230C2×C4—64no—
1231C2×C4—64no—
1232C2×C4—104no—
1233C2×C4—121no—
1234C2×C4—158no—
1235C2×C4—158no—
1236C2×C4—154no—
1237C2×C4—152no—
1238C2×C4—152no—
1239C2×C4—152no—
1240C2×C4—201no—
1241C2×C4—304no—
1242C2×C4—304no—
1243C2×C4—304no—
1244C2×C4—304no—
1245C2×C4—304no—
1246C2×C4—304no—
1247C2×C4—304no—
1248C2×C4—601no—
1249C2×C4C22×D3×D511yescharacteristic
1250C2×C4C22×D3×D511yescharacteristic
1251C2×C4C22×D3×D512yes—
1252C2×C3—22no—
1253C2×C3—42no—
1254C2×C3—104no—
1255C2×C3—202no—
1256C2×C3C22×D4×D511yescharacteristic
1257C2×C3#6628311yescharacteristic
1258C2×C3#6628311yescharacteristic
1259D3—42no—
1260D3—202no—
1261C5#8629411yescharacteristic, complemented, Sylow
1262C22—21no—
1263C22—21no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—54no—
1268C22—62no—
1269C22—62no—
1270C22—62no—
1271C22—102no—
1272C22—102no—
1273C22—102no—
1274C22—102no—
1275C22—102no—
1276C22—204no—
1277C22—208no—
1278C22—302no—
1279C22—302no—
1280C22—302no—
1281C22—608no—
1282C22D3×D4×D512yes—
1283C22C23×D3×D511yescharacteristic
1284C4—22no—
1285C4—21no—
1286C4—21no—
1287C4—32no—
1288C4—32no—
1289C4—61no—
1290C4—61no—
1291C4—62no—
1292C4—102no—
1293C4—102no—
1294C4—154no—
1295C4—302no—
1296C4—302no—
1297C3#1061813611yescharacteristic, complemented, Sylow
1298C2—22no—
1299C2—42no—
1300C2—104no—
1301C2—122no—
1302C2—202no—
1303C2—602no—
1304C2C2×D3×D4×D511yescharacteristic
1305C2#1175703511yescharacteristic
1306C2#1175706111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#121C22
hypercenter#121D3×D5
hypocenterC3×C5#3449
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D5×#237C2semidirect
2. #11756356C2semidirect
3. C5×#5596C2semidirect
4. C3×#65939C2semidirect
5. #11755061C2semidirect
6. #11755030C2semidirect
7. #11754821C2semidirect
8. #11754803C2semidirect
9. #11754758C2semidirect
10. #11754644C2semidirect
11. #11754387C2semidirect
12. #11754356C2semidirect
13. C2×#91393C2semidirect
14. #11753852C2semidirect
15. #11753412C2semidirect
16. #11753224C2semidirect
17. #11753220C2semidirect
18. #11752830C2semidirect
19. #11752827C2semidirect
21. C2×#6819C22semidirect
22. C2×C5×#237C22semidirect
25. C2×D5×#67C22semidirect
27. C2×#6780C22semidirect
29. C2×#6779C22semidirect
31. C22×D5×Dic3C22semidirect
33. C2×C4×D3×D5C22semidirect
36. C2×D5×Dic6C22semidirect
37. C3×C5×#121C22semidirect
38. #91828C22semidirect
39. #91828C22semidirect
40. #91819C22semidirect
41. C2×#6712C22semidirect
42. #91785C22semidirect
43. #91773C22semidirect
44. #91767C22semidirect
45. C5×#940C22semidirect
46. C5×#939C22semidirect
47. C5×D4×Dic3C22semidirect
48. C5×#930C22semidirect
49. C2×C4×C5×Dic3C22semidirect
50. C5×#893C22semidirect
51. C5×#888C22semidirect
52. C5×#885C22semidirect
53. C5×#67⋊C4C22semidirect
54. C3×#4085C22semidirect
55. C3×#4083C22semidirect
56. C3×#4076C22semidirect
58. C3×#4040C22semidirect
59. C3×#4029C22semidirect
60. C3×#4028C22semidirect
61. #91577C22semidirect
62. #91576C22semidirect
63. #91571C22semidirect
64. #91571C22semidirect
65. #91569C22semidirect
66. #91567C22semidirect
67. #91566C22semidirect
68. #91564C22semidirect
69. #91563C22semidirect
70. #91558C22semidirect
71. #91556C22semidirect
72. Dic3×C22⋊D5C22semidirect
73. #91550C22semidirect
74. #91548C22semidirect
75. C2×#6669C22semidirect
77. C2×Dic3×Dic5C22semidirect
78. #91525C22semidirect
79. #91476C22semidirect
80. #91475C22semidirect
81. #91474C22semidirect
82. #91469C22semidirect
83. #91461C22semidirect
84. #91458C22semidirect
85. #91455C22semidirect
86. #91453C22semidirect
87. #91447C22semidirect
88. #91446C22semidirect
89. #91441C22semidirect
90. #91436C22semidirect
91. #91432C22semidirect
92. #91431C22semidirect
93. #91430C22semidirect
94. #91428C22semidirect
95. Dic3×D20C22semidirect
96. #91414C22semidirect
97. #91413C22semidirect
98. #91408C22semidirect
99. #91407C22semidirect
100. #91395C22semidirect
101. #91393C22semidirect
102. #91393C22semidirect
103. #91393C22semidirect
104. #91393C22semidirect
105. #91377C22semidirect
106. #91353C22semidirect
107. #91348C22semidirect
108. #91329C22semidirect
119. #65939D3semidirect
181. C2×D5×Dic3D4semidirect
243. #5596D5semidirect
271. C5×#121C2×D3semidirect
286. #4085C2×D3semidirect
290. #4083C2×D3semidirect
294. #4076C2×D3semidirect
311. #4040C2×D3semidirect
319. #4029C2×D3semidirect
323. #4028C2×D3semidirect
424. C2×#237C2×D5semidirect
431. C3×#121C2×D5semidirect
440. #940C2×D5semidirect
448. #939C2×D5semidirect
455. D4×Dic3C2×D5semidirect
458. #930C2×D5semidirect
464. C2×C4×Dic3C2×D5semidirect
471. #893C2×D5semidirect
474. #888C2×D5semidirect
480. #885C2×D5semidirect
490. #67⋊C4C2×D5semidirect
888. #121D3×D5semidirect
1135. C3×C5#3449semidirect
1261. C5#86294semidirect
1297. C3#10618136semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2372
#117563562
C5×#55962
C3×#659392
#117550612
#117550302
#117548212
#117548032
#117547582
#117546442
#117543872
#117543562
C2×#913932
#117538522
#117534122
#117532242
#117532202
#117528302
#117528272
#106181363
#862945