Finite Group Databasebeta

← #14480654

Subgroups — #14480654

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×D3×#711C212yesmaximal, complemented
2#11756355C211yesmaximal, characteristic, complemented
3C5×#5605C211yesmaximal, characteristic, complemented
4C3×#65931C211yesmaximal, characteristic, complemented
5#11755067C212yesmaximal, complemented
6#11755046C212yesmaximal, complemented
7#11754820C212yesmaximal, complemented
8#11754797C212yesmaximal, complemented
9#11754768C212yesmaximal, complemented
10#11754660C211yesmaximal, characteristic, complemented
11#11754386C211yesmaximal, characteristic, complemented
12#11754331C211yesmaximal, characteristic, complemented
13C2×#91400C211yesmaximal, characteristic, complemented
14#11753864C212yesmaximal, complemented
15#11753420C212yesmaximal, complemented
16#11753246C212yesmaximal, complemented
17#11753245C212yesmaximal, complemented
18#11752844C212yesmaximal, complemented
19#11752842C212yesmaximal, complemented
20#10618195—31nomaximal, Hall
21C2×#6819C2212yescomplemented
22C2×C5×D3×D4C2212yes—
23C2×C3×#711C2212yescomplemented
24C2×D3×C22⋊D5C2212yes—
25C2×D3×C22⋊D5C2212yescomplemented
26C2×#6782C2212yes—
27C2×#6782C2212yescomplemented
28C22×D3×Dic5C2211yescharacteristic
29C22×D3×Dic5C2212yescomplemented
30C2×#6780C2212yes—
31C2×#6780C2212yescomplemented
32D3×#711—216no—
33C2×C4×D3×D5C2212yescomplemented
34C2×#6772C2212yes—
35C2×#6768C2212yes—
36C2×D3×Dic10C2212yescomplemented
37C3×C5×#121C2211yescharacteristic, complemented
38#91829C2211yescharacteristic, complemented
39#91828C2212yescomplemented
40D4×Dic15C2211yescharacteristic, complemented
41#91819C2211yescharacteristic, complemented
42C2×C4×Dic15C2211yescharacteristic, complemented
43#91782C2211yescharacteristic, complemented
44#91777C2211yescharacteristic, complemented
45#91774C2212yescomplemented
46#91770C2212yescomplemented
47C5×#939C2212yescomplemented
48C5×#937C2212yescomplemented
49C5×#930C2211yescharacteristic, complemented
50C2×C5×(C2×D3)⋊C4C2211yescharacteristic
51C5×#894C2212yescomplemented
52C5×#883C2212yescomplemented
53C5×#882C2212yescomplemented
54C3×#4085C2212yescomplemented
55C3×#4085C2212yescomplemented
56C3×#4076C2211yescharacteristic, complemented
57C2×C3×#683C2211yescharacteristic, complemented
58C3×#4042C2212yescomplemented
59C3×#4030C2212yescomplemented
60C3×#4024C2212yescomplemented
61#91577C2212yescomplemented
62#91574C2212yescomplemented
63#91571C2212yescomplemented
64#91570C2212yescomplemented
65#91569C2212yescomplemented
66#91568C2212yescomplemented
67#91567C2212yescomplemented
68#91566C2212yescomplemented
69#91566C2212yescomplemented
70#91565C2212yescomplemented
71#67⋊Dic5C2212yescomplemented
72#91559C2212yescomplemented
73#91555C2212yescomplemented
74C2×#6668C2211yescharacteristic, complemented
75C2×(C2×D3)⋊Dic5C2211yescharacteristic
76#91533C2212yescomplemented
77C2×Dic3×Dic5C2211yescharacteristic, complemented
78#91526C2212yescomplemented
79#91476C2212yescomplemented
80#91475C2212yescomplemented
81#91474C2212yescomplemented
82#91470C2211yescharacteristic, complemented
83#91464C2212yescomplemented
84#91463C2211yescharacteristic, complemented
85#91462C2212yescomplemented
86#91457C2212yescomplemented
87#91452C2212yescomplemented
88#91448C2212yescomplemented
89#91442C2212yescomplemented
90#91435C2211yescharacteristic, complemented
91#91434C2211yescharacteristic, complemented
92#91427C2212yescomplemented
93#91423C2212yescomplemented
94#91420C2212yescomplemented
95#91419C2212yescomplemented
96#91417C2212yescomplemented
97#91416C2212yescomplemented
98#91411C2212yescomplemented
99#91410C2212yescomplemented
100#91406C2212yescomplemented
101#91400C2212yescomplemented
102#91400C2212yescomplemented
103#91400C2212yescomplemented
104#91400C2212yescomplemented
105#91396C2212yescomplemented
106#91351C2212yescomplemented
107#91349C2212yescomplemented
108#91328C2212yescomplemented
109#86363—51nomaximal, Hall
110C22×#711—32no—
111C5×#534—31no—
112#66138—32no—
113#65990—32no—
114#65990—32no—
115#65982—32no—
116#65982—32no—
117#65931—31no—
118#65931—32no—
119#65931D311yescharacteristic, complemented
120#65930—32no—
121#65930—31no—
122#65930—31no—
123#65926—32no—
124#65926—32no—
125#65920—32no—
126#65920—32no—
127#65827—31no—
128C2×#4023—31no—
129C23×C5×D3C2312yes—
130C23×C5×D3C2311yescharacteristic
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×Dic3C2311yescharacteristic
149C5×D3×D4—28no—
150C2×C5×D12C2312yes—
151C2×C5×D12C2311yescharacteristic
152C2×C4×C5×D3C2312yes—
153C2×C3×C22⋊D5C2312yes—
154C2×C3×C22⋊D5C2312yes—
155C2×C3×C22⋊D5C2312yes—
156C22×C3×Dic5C2312yes—
157C22×C3×Dic5C2311yescharacteristic
158C22×C3×Dic5C2311yescharacteristic
159C3×#711—28no—
160C2×C3×D20C2311yescharacteristic
161C2×C3×C4×D5C2312yes—
162C2×C3×Dic10C2312yes—
163D3×C22⋊D5—28no—
164D3×C22⋊D5—28no—
165C2×#1204C2312yes—
166C2×#1204C2312yes—
167C2×#1203C2312yes—
168C2×#1203C2312yes—
169C2×#1203C2312yes—
170C2×#1202C2312yes—
171C2×#1201C2312yes—
172C2×#1201C2312yes—
173C2×#1201C2312yes—
174C2×#1200C2312yes—
175#6782—28no—
176#6782—28no—
177C2×D3×Dic5—28no—
178C2×D3×Dic5D418yescomplemented
179C2×D3×Dic5C2312yes—
180C2×D3×Dic5C2312yes—
181C2×D3×Dic5C2312yes—
182C2×D3×Dic5C2312yes—
183C2×D3×Dic5C2312yes—
184#6780—28no—
185#6780—28no—
186C2×D5×Dic3C2312yes—
187C4×D3×D5—28no—
188#6772—28no—
189#6768—28no—
190D3×Dic10—28no—
191C3×C5×C4⋊C4C2311yescharacteristic
192C3×C5×C22⋊C4C2312yes—
193#6719C2312yes—
194#6714C2312yes—
195#6714C2312yes—
196C4⋊Dic15C2311yescharacteristic
197#6712C2312yes—
198C4×Dic15C2311yescharacteristic
199C4×Dic15C2311yescharacteristic
200C4×Dic15C2311yescharacteristic
201C4×Dic15C2311yescharacteristic
202C5×#217C2312yes—
203C5×(C2×D3)⋊C4C2312yes—
204C5×(C2×D3)⋊C4C2312yes—
205C5×(C2×D3)⋊C4C2312yes—
206C5×(C2×D3)⋊C4C2312yes—
207C5×C4⋊Dic3C2311yescharacteristic
208C5×Dic3⋊C4C2312yes—
209C3×C22⋊Dic5C2312yes—
210C3×#685C2312yes—
211C3×#685C2312yes—
212C3×C4⋊Dic5C2311yescharacteristic
213C3×#683C2312yes—
214C3×#683C2312yes—
215C3×#683C2312yes—
216Dic3⋊Dic5C2312yes—
217#6669C2312yes—
218#6668C2312yes—
219#6668C2312yes—
220#6668C2312yes—
221#6667C2312yes—
222#6667C2312yes—
223(C2×D3)⋊Dic5C2312yes—
224(C2×D3)⋊Dic5C2312yes—
225(C2×D3)⋊Dic5C2312yes—
226(C2×D3)⋊Dic5C2312yes—
227#6665C2312yes—
228#6665C2312yes—
229Dic3×Dic5C2312yes—
230Dic3×Dic5C2312yes—
231C2×D3×#41—52no—
232C3×#537—51no—
233#5833—52no—
234#5628—52no—
235#5628—52no—
236#5627—52no—
237#5627—52no—
238#5607—52no—
239#5607—52no—
240#5606—52no—
241#5606—52no—
242#5605—52no—
243#5605—51no—
244#5605D511yescharacteristic, complemented
245#5596—51no—
246#5596—52no—
247#5596—51no—
248#5510—51no—
249C2×#892—51no—
250C22×C5×D4—32no—
251C22×C22⋊D5—32no—
252C22×C22⋊D5—32no—
253C23×Dic5—31no—
254C23×Dic5—32no—
255C2×#711—32no—
256C2×#711—32no—
257C2×#711—32no—
258C2×#711—32no—
259C2×#711—32no—
260C2×#711—32no—
261C2×#711—32no—
262C2×#711—616no—
263C2×#711C2×D312yescomplemented
264C22×C4×D5—32no—
265C22×Dic10—32no—
266C5×#123—32no—
267C5×#123—32no—
268C5×#121—32no—
269C5×#121—31no—
270C5×#121C2×D311yescharacteristic, complemented
271C5×#120—32no—
272C5×#120—32no—
273C2×C5×C22⋊C4—31no—
274#4099—32no—
275#4099—32no—
276C2×C22⋊Dic5—31no—
277#4086—31no—
278#4086—32no—
279#4086—31no—
280#4085—32no—
281#4085—32no—
282#4085—32no—
283#4085—32no—
284#4085—32no—
285#4085—32no—
286#4085C2×D312yescomplemented
287#4085C2×D312yescomplemented
288#4083—32no—
289#4083—32no—
290#4081—32no—
291#4081—32no—
292D4×Dic5—31no—
293D4×Dic5—32no—
294D4×Dic5—31no—
295#4076—31no—
296#4076—32no—
297#4076C2×D311yescharacteristic, complemented
298#4075—32no—
299#4075—32no—
300C2×#683—31no—
301C2×#683C2×D311yescharacteristic, complemented
302C2×C4×Dic5—31no—
303C2×C4×Dic5—31no—
304#4042—32no—
305#4042—32no—
306#4042—32no—
307#4042C2×D312yescomplemented
308#4039—31no—
309#4039—31no—
310#4039—32no—
311#4034—31no—
312#4034—31no—
313#4034—32no—
314#4032—32no—
315#4032—32no—
316#4031—32no—
317#4031—32no—
318#4031—32no—
319#4031—32no—
320#4030—32no—
321#4030—32no—
322#4030—32no—
323#4030C2×D312yescomplemented
324#4028—32no—
325#4028—32no—
326#4027—32no—
327#4027—32no—
328#4027—32no—
329#4027—32no—
330#4024—32no—
331#4024—32no—
332#4024—32no—
333#4024C2×D312yescomplemented
334#4023—32no—
335#4023—32no—
336#4023—32no—
337#4023—32no—
338#3449—151noSylow
339C23×C3×C5C2412yes—
340C23×C3×C5C2411yescharacteristic
341C22×D15C2412yes—
342C22×C5×D3—24no—
343C22×C5×D3—41no—
344C22×C5×D3—41no—
345C22×C5×D3—42no—
346C22×C5×D3—42no—
347C22×C5×D3C2×D414yes—
348C22×C5×D3C2412yes—
349C22×C5×D3C2412yes—
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×C5C2411yescharacteristic
358C2×C3×C4×C5C2411yescharacteristic
359C2×C3×C4×C5C2412yes—
360#1220—24no—
361#1220—24no—
362#1220—42no—
363C2×Dic15—24no—
364C2×Dic15—41no—
365C2×Dic15C2×D414yes—
366C2×Dic15C2411yescharacteristic
367C2×Dic15C2412yes—
368C2×Dic15C2411yescharacteristic
369C2×Dic15C2411yescharacteristic
370C2×Dic15C2411yescharacteristic
371D60—41no—
372C4×D15—24no—
373Dic30—24no—
374C5×#67—24no—
375C5×#67—24no—
376C5×#67—42no—
377C2×C5×Dic3—41no—
378C2×C5×Dic3C2412yes—
379C2×C5×Dic3C2412yes—
380C5×D12—24no—
381C5×D12—41no—
382C4×C5×D3—24no—
383C3×C22⋊D5—24no—
384C3×C22⋊D5—24no—
385C3×C22⋊D5—42no—
386C2×C3×Dic5—24no—
387C2×C3×Dic5—41no—
388C2×C3×Dic5C2×D414yes—
389C2×C3×Dic5C2412yes—
390C2×C3×Dic5C2412yes—
391C2×C3×Dic5C2412yes—
392C3×D20—41no—
393C3×C4×D5—24no—
394C3×Dic10—24no—
395#1204—24no—
396#1204—24no—
397#1203—24no—
398#1203—24no—
399#1203—42no—
400#1202—42no—
401#1201—24no—
402#1201—24no—
403#1201—42no—
404#1200—24no—
405D3×Dic5—24no—
406D3×Dic5—24no—
407D3×Dic5—24no—
408D3×Dic5C2×D418yes—
409D3×Dic5C2×D418yes—
410D5×Dic3—24no—
411C2×C3×#41—52no—
412D3×#41—1016no—
413C2×#239—52no—
414C2×D3×Q8—52no—
415C2×#237—52no—
416C2×#237—52no—
417C2×#237—52no—
418C2×D3×D4—52no—
419C2×D3×D4—52no—
420C2×D3×D4C2×D512yes—
421C2×#235—52no—
422C2×#235—52no—
423C2×#235—52no—
424C22×C4×D3—51no—
425C22×C4×D3—52no—
426C22×C4×D3—52no—
427C3×C22⋊Q8—52no—
428C3×C22⋊Q8—52no—
429C3×#121—52no—
430C3×#121—52no—
431C3×#121—51no—
432C3×#121—52no—
433C3×#121C2×D511yescharacteristic, complemented
434C2×C3×C4⋊C4—51no—
435#946—52no—
436#946—52no—
437#940—51no—
438#940—52no—
439#940—51no—
440#939—52no—
441#939—52no—
442#939—52no—
443#939C2×D512yescomplemented
444#938—52no—
445#938—52no—
446#937—52no—
447#937—52no—
448#937—52no—
449#937C2×D512yescomplemented
450D4×Dic3—51no—
451D4×Dic3—52no—
452D4×Dic3—51no—
453#930—51no—
454#930—52no—
455#930—52no—
456#930—52no—
457#930C2×D511yescharacteristic, complemented
458C2×(C2×D3)⋊C4—51no—
459C2×(C2×D3)⋊C4C2×D511yescharacteristic
460C2×C4⋊Dic3—51no—
461#924—52no—
462#924—52no—
463C2×C4×Dic3—51no—
464C2×C4×Dic3—51no—
465#897—52no—
466#897—52no—
467#895—52no—
468#895—52no—
469#894—52no—
470#894—52no—
471#894—52no—
472#894C2×D512yescomplemented
473#893—51no—
474#893—51no—
475#893—52no—
476#892—52no—
477#892—52no—
478#892—52no—
479#892—52no—
480#888—51no—
481#888—51no—
482#888—52no—
483#885—52no—
484#885—52no—
485#885—52no—
486#885—52no—
487#883—52no—
488#883—52no—
489#883—52no—
490#883C2×D512yescomplemented
491#882—52no—
492#882—52no—
493#882—52no—
494#882C2×D512yescomplemented
495#67⋊C4—52no—
496#67⋊C4—52no—
497#67⋊C4—52no—
498#67⋊C4—52no—
499C24×C5—31no—
500C24×C5—32no—
501C23×D5—32no—
502C2×C5×D4—32no—
503C2×C5×D4—32no—
504C2×C5×D4—32no—
505C2×C5×D4—32no—
506C2×C5×D4—31no—
507C2×C5×D4—68no—
508C2×C5×D4C22×D312yes—
509C2×C5×D4C22×D311yescharacteristic
510C22×C4×C5—31no—
511C22×C4×C5—32no—
512C22×C4×C5C22×D311yescharacteristic
513C2×C22⋊D5—32no—
514C2×C22⋊D5—32no—
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⋊D5—68no—
523C2×C22⋊D5—68no—
524C2×C22⋊D5C22×D312yes—
525C2×C22⋊D5C22×D312yes—
526C2×C22⋊D5C22×D312yes—
527C22×Dic5—31no—
528C22×Dic5—38no—
529C22×Dic5—32no—
530C22×Dic5—32no—
531C22×Dic5—32no—
532C22×Dic5—31no—
533C22×Dic5—32no—
534C22×Dic5—32no—
535C22×Dic5—32no—
536C22×Dic5—68no—
537C22×Dic5C22×D312yes—
538C22×Dic5C22×D311yescharacteristic
539C22×Dic5C22×D311yescharacteristic
540#711—28no—
541#711—68no—
542#711—68no—
543#711—68no—
544#711—68no—
545#711—68no—
546#711—68no—
547#711—68no—
548C2×D20—32no—
549C2×D20—31no—
550C2×D20C22×D311yescharacteristic
551C2×C4×D5—32no—
552C2×C4×D5—32no—
553C2×C4×D5—32no—
554C2×C4×D5—68no—
555C2×C4×D5C22×D312yes—
556C2×Dic10—32no—
557C2×Dic10—32no—
558C2×Dic10—32no—
559C2×Dic10—68no—
560C2×Dic10C22×D312yes—
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⋊C4—32no—
568C5×C22⋊C4—32no—
569C5×C22⋊C4C22×D312yes—
570C22⋊Dic5—32no—
571C22⋊Dic5—32no—
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#685C22×D312yes—
583#685C22×D312yes—
584C4⋊Dic5—31no—
585C4⋊Dic5—32no—
586C4⋊Dic5C22×D311yescharacteristic
587#683—32no—
588#683—32no—
589#683—32no—
590#683—32no—
591#683—32no—
592#683C22×D312yes—
593#683C22×D312yes—
594#683C22×D312yes—
595C4×Dic5—31no—
596C4×Dic5—31no—
597C4×Dic5—31no—
598C4×Dic5—31no—
599C4×Dic5—32no—
600C4×Dic5—32no—
601C22×#41—152no—
602#537—51no—
603#537—151no—
604#537—152no—
605#536—152no—
606#536—152no—
607#535—152no—
608#535—152no—
609#534—31no—
610#534—151no—
611#534—152no—
612#532—152no—
613#532—151no—
614#532—151no—
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×C5×D3—22no—
634C2×C5×D3—22no—
635C2×C5×D3—44no—
636C2×C5×D3—48no—
637C2×C5×D3C22×D414yes—
638C2×C3×D5—22no—
639C2×C3×D5—22no—
640C2×C3×D5—22no—
641D3×D5—48no—
642C3×C4×C5—22no—
643C3×C4×C5—21no—
644C3×C4×C5—21no—
645Dic15—22no—
646Dic15—21no—
647Dic15—21no—
648Dic15C22×D412yes—
649Dic15C22×D412yes—
650C3×Dic5—22no—
651C3×Dic5—22no—
652C3×Dic5C22×D414yes—
653C5×Dic3—22no—
654C5×Dic3—22no—
655C23×D3—52no—
656C23×D3C22×D512yes—
657C23×D3C22×D511yescharacteristic
658C3×#41—108no—
659C2×C3×Q8—52no—
660C2×C3×D4—52no—
661C2×C3×D4—52no—
662C2×C3×D4—52no—
663C2×C3×D4—51no—
664C2×C3×D4C22×D512yes—
665C2×C3×D4C22×D511yescharacteristic
666C22×C3×C4—51no—
667C22×C3×C4—52no—
668C22×C3×C4—51no—
669C22×C3×C4—52no—
670C22×C3×C4C22×D511yescharacteristic
671C2×#67—52no—
672C2×#67—52no—
673C2×#67—52no—
674C2×#67—52no—
675C2×#67—52no—
676C2×#67—52no—
677C2×#67—52no—
678C2×#67C22×D512yes—
679C2×#67C22×D512yes—
680C2×#67C22×D512yes—
681C22×Dic3—51no—
682C22×Dic3—52no—
683C22×Dic3—51no—
684C22×Dic3—52no—
685C22×Dic3C22×D511yescharacteristic
686#239—108no—
687D3×Q8—108no—
688#237—108no—
689#237—108no—
690#237—108no—
691D3×D4—28no—
692D3×D4—108no—
693D3×D4—108no—
694#235—108no—
695#235—108no—
696#235—108no—
697C2×D12—52no—
698C2×D12—52no—
699C2×D12—52no—
700C2×D12—51no—
701C2×D12C22×D512yes—
702C2×D12C22×D511yescharacteristic
703C2×C4×D3—58no—
704C2×C4×D3—52no—
705C2×C4×D3—52no—
706C2×C4×D3—52no—
707C2×C4×D3—52no—
708C2×C4×D3—52no—
709C2×C4×D3—52no—
710C2×C4×D3—52no—
711C2×C4×D3—108no—
712C2×C4×D3—108no—
713C2×C4×D3C22×D512yes—
714C2×Dic6—52no—
715C2×Dic6—52no—
716C2×Dic6—52no—
717C3×C4⋊C4—52no—
718C3×C4⋊C4—52no—
719C3×C4⋊C4—52no—
720C3×C4⋊C4—51no—
721C3×C4⋊C4C22×D511yescharacteristic
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#217C22×D512yes—
730(C2×D3)⋊C4—52no—
731(C2×D3)⋊C4—52no—
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—
740(C2×D3)⋊C4C22×D512yes—
741(C2×D3)⋊C4C22×D512yes—
742C4⋊Dic3—51no—
743C4⋊Dic3—52no—
744C4⋊Dic3—52no—
745C4⋊Dic3—52no—
746C4⋊Dic3C22×D511yescharacteristic
747Dic3⋊C4—52no—
748Dic3⋊C4—52no—
749Dic3⋊C4—52no—
750Dic3⋊C4C22×D512yes—
751C4×Dic3—51no—
752C4×Dic3—51no—
753C4×Dic3—51no—
754C4×Dic3—51no—
755C4×Dic3—52no—
756C4×Dic3—52no—
757C23×C5—32no—
758C23×C5—34no—
759C23×C5—32no—
760C23×C5—64no—
761C23×C5—121no—
762C23×C5—121no—
763C23×C5—122no—
764C23×C5—122no—
765C23×C5C23×D312yes—
766C23×C5C23×D311yescharacteristic
767C22×D5—32no—
768C22×D5—64no—
769C22×D5—122no—
770C22×D5—122no—
771C22×D5C23×D312yes—
772C5×D4—24no—
773C5×D4—41no—
774C5×D4—64no—
775C5×D4—64no—
776C5×D4—64no—
777C5×D4—121no—
778C5×D4—122no—
779C2×C4×C5—32no—
780C2×C4×C5—32no—
781C2×C4×C5—41no—
782C2×C4×C5—64no—
783C2×C4×C5—121no—
784C2×C4×C5C23×D311yescharacteristic
785C2×C4×C5C23×D311yescharacteristic
786C2×C4×C5C23×D312yes—
787C22⋊D5—24no—
788C22⋊D5—24no—
789C22⋊D5—42no—
790C22⋊D5—64no—
791C22⋊D5—64no—
792C22⋊D5—64no—
793C22⋊D5—64no—
794C22⋊D5—64no—
795C22⋊D5—64no—
796C22⋊D5—122no—
797C22⋊D5—122no—
798C22⋊D5—122no—
799C2×Dic5—24no—
800C2×Dic5—34no—
801C2×Dic5—31no—
802C2×Dic5—31no—
803C2×Dic5—38no—
804C2×Dic5—38no—
805C2×Dic5—31no—
806C2×Dic5—31no—
807C2×Dic5—32no—
808C2×Dic5—41no—
809C2×Dic5—64no—
810C2×Dic5—64no—
811C2×Dic5—64no—
812C2×Dic5—64no—
813C2×Dic5—121no—
814C2×Dic5D3×D414yes—
815C2×Dic5C23×D312yes—
816C2×Dic5C23×D312yes—
817C2×Dic5C23×D312yes—
818D20—41no—
819D20—121no—
820D20—122no—
821C4×D5—24no—
822C4×D5—64no—
823C4×D5—64no—
824C4×D5—64no—
825Dic10—24no—
826Dic10—64no—
827Dic10—64no—
828Dic10—64no—
829C2×#41—52no—
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—32no—
840C22×D4—152no—
841C22×D4—152no—
842C23×C4—152no—
843C23×C4—151no—
844C23×C4—152no—
845C4⋊Q8—152no—
846C4⋊Q8—151no—
847C4⋊Q8—151no—
848#127—152no—
849#127—151no—
850#127—151no—
851#124—152no—
852#124—152no—
853#124—152no—
854#124—152no—
855#123—32no—
856#123—32no—
857#123—152no—
858#123—152no—
859#123—152no—
860#123—152no—
861#123—152no—
862#123—152no—
863C22⋊Q8—52no—
864C22⋊Q8—52no—
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—52no—
875#121—51no—
876#121—52no—
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—152no—
887#121—151no—
888#121D3×D511yescharacteristic, complemented
889#120—32no—
890#120—32no—
891#120—152no—
892#120—152no—
893#120—152no—
894#120—152no—
895#120—152no—
896#120—152no—
897C4×D4—152no—
898C4×D4—152no—
899C4×D4—152no—
900C4×D4—152no—
901C4×D4—152no—
902C4×D4—151no—
903C4×D4—151no—
904C4×D4—151no—
905C4×D4—151no—
906C4×D4—152no—
907#117—152no—
908#117—152no—
909#117—152no—
910#117—152no—
911C2×C4⋊C4—51no—
912C2×C4⋊C4—151no—
913C2×C22⋊C4—31no—
914C2×C22⋊C4—151no—
915C2×C42—151no—
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—42no—
924C5×D3—24no—
925C5×D3—42no—
926C23×C3—52no—
927C23×C3C23×D512yes—
928C23×C3C23×D511yescharacteristic
929C22×D3—24no—
930C22×D3—41no—
931C22×D3—41no—
932C22×D3—42no—
933C22×D3—42no—
934C22×D3—52no—
935C22×D3—104no—
936C22×D3—202no—
937C22×D3—202no—
938C22×D3D4×D514yes—
939C22×D3C23×D512yes—
940C22×D3C23×D512yes—
941C3×Q8—104no—
942C3×D4—24no—
943C3×D4—41no—
944C3×D4—104no—
945C3×D4—104no—
946C3×D4—201no—
947C3×D4—202no—
948C2×C3×C4—41no—
949C2×C3×C4—54no—
950C2×C3×C4—52no—
951C2×C3×C4—52no—
952C2×C3×C4—52no—
953C2×C3×C4—104no—
954C2×C3×C4—104no—
955C2×C3×C4—201no—
956C2×C3×C4C23×D511yescharacteristic
957C2×C3×C4C23×D511yescharacteristic
958C2×C3×C4C23×D512yes—
959#67—24no—
960#67—24no—
961#67—42no—
962#67—104no—
963#67—104no—
964#67—104no—
965#67—104no—
966#67—202no—
967#67—202no—
968#67—202no—
969C2×Dic3—41no—
970C2×Dic3—54no—
971C2×Dic3—51no—
972C2×Dic3—51no—
973C2×Dic3—51no—
974C2×Dic3—51no—
975C2×Dic3—52no—
976C2×Dic3—104no—
977C2×Dic3—104no—
978C2×Dic3—201no—
979C2×Dic3C23×D512yes—
980C2×Dic3C23×D512yes—
981D12—24no—
982D12—41no—
983D12—104no—
984D12—104no—
985D12—201no—
986D12—202no—
987C4×D3—24no—
988C4×D3—58no—
989C4×D3—58no—
990C4×D3—104no—
991C4×D3—104no—
992C4×D3—104no—
993C4×D3—104no—
994C4×D3—104no—
995Dic6—104no—
996Dic6—104no—
997Dic6—104no—
998C22×C5—21no—
999C22×C5—21no—
1000C22×C5—22no—
1001C22×C5—22no—
1002C22×C5—22no—
1003C22×C5—34no—
1004C22×C5—62no—
1005C22×C5—62no—
1006C22×C5—62no—
1007C22×C5—62no—
1008C22×C5—62no—
1009C22×C5—124no—
1010C22×C5—128no—
1011C22×C5C2×D3×D412yes—
1012C22×C5C24×D311yescharacteristic
1013C2×D5—22no—
1014C2×D5—22no—
1015C2×D5—22no—
1016C2×D5—62no—
1017C2×D5—62no—
1018C2×D5—62no—
1019C2×D5—128no—
1020C4×C5—22no—
1021C4×C5—21no—
1022C4×C5—21no—
1023C4×C5—62no—
1024C4×C5—62no—
1025Dic5—22no—
1026Dic5—22no—
1027Dic5—32no—
1028Dic5—32no—
1029Dic5—62no—
1030Dic5—61no—
1031Dic5—61no—
1032Dic5C2×D3×D414yes—
1033C24—31no—
1034C24—32no—
1035C24—152no—
1036#41—108no—
1037#41—308no—
1038#41—308no—
1039#41—308no—
1040#41—308no—
1041#41—308no—
1042#41—308no—
1043#41—308no—
1044C2×Q8—52no—
1045C2×Q8—152no—
1046C2×Q8—152no—
1047C2×Q8—152no—
1048C2×Q8—308no—
1049C2×D4—32no—
1050C2×D4—32no—
1051C2×D4—32no—
1052C2×D4—32no—
1053C2×D4—31no—
1054C2×D4—52no—
1055C2×D4—52no—
1056C2×D4—52no—
1057C2×D4—51no—
1058C2×D4—68no—
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—51no—
1077C22×C4—52no—
1078C22×C4—51no—
1079C22×C4—52no—
1080C22×C4—152no—
1081C22×C4—152no—
1082C22×C4—152no—
1083C22×C4—152no—
1084C22×C4—158no—
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—52no—
1099C4⋊C4—52no—
1100C4⋊C4—51no—
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—32no—
1113C22⋊C4—32no—
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—152no—
1130C42—152no—
1131C42—151no—
1132C42—151no—
1133C42—151no—
1134C42—151no—
1135C3×C5#344911yescharacteristic, complemented, Hall
1136C22×C3—21no—
1137C22×C3—21no—
1138C22×C3—22no—
1139C22×C3—22no—
1140C22×C3—22no—
1141C22×C3—102no—
1142C22×C3—102no—
1143C22×C3—102no—
1144C22×C3C2×D4×D512yes—
1145C22×C3C24×D511yescharacteristic
1146C2×D3—22no—
1147C2×D3—22no—
1148C2×D3—22no—
1149C2×D3—22no—
1150C2×D3—22no—
1151C2×D3—44no—
1152C2×D3—48no—
1153C2×D3—102no—
1154C2×D3—102no—
1155C2×D3—102no—
1156C2×D3—208no—
1157C2×D3C2×D4×D514yes—
1158C3×C4—22no—
1159C3×C4—21no—
1160C3×C4—21no—
1161C3×C4—54no—
1162C3×C4—102no—
1163C3×C4—102no—
1164Dic3—22no—
1165Dic3—22no—
1166Dic3—52no—
1167Dic3—52no—
1168Dic3—102no—
1169Dic3—101no—
1170Dic3—101no—
1171C2×C5—22no—
1172C2×C5—42no—
1173C2×C5—64no—
1174C2×C5—122no—
1175C2×C5C22×D3×D411yescharacteristic
1176C2×C5#596611yescharacteristic
1177C2×C5#596811yescharacteristic
1178D5—42no—
1179D5—122no—
1180C23—32no—
1181C23—34no—
1182C23—32no—
1183C23—52no—
1184C23—64no—
1185C23—121no—
1186C23—121no—
1187C23—122no—
1188C23—122no—
1189C23—152no—
1190C23—304no—
1191C23—602no—
1192C23—602no—
1193C23C22×D3×D512yes—
1194C23C22×D3×D511yescharacteristic
1195Q8—104no—
1196Q8—304no—
1197Q8—304no—
1198Q8—304no—
1199D4—24no—
1200D4—41no—
1201D4—64no—
1202D4—64no—
1203D4—64no—
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—32no—
1222C2×C4—32no—
1223C2×C4—41no—
1224C2×C4—54no—
1225C2×C4—52no—
1226C2×C4—52no—
1227C2×C4—52no—
1228C2×C4—64no—
1229C2×C4—104no—
1230C2×C4—104no—
1231C2×C4—121no—
1232C2×C4—158no—
1233C2×C4—158no—
1234C2×C4—154no—
1235C2×C4—151no—
1236C2×C4—151no—
1237C2×C4—151no—
1238C2×C4—151no—
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—202no—
1255C2×C3C22×D4×D511yescharacteristic
1256C2×C3#6628511yescharacteristic
1257C2×C3#6628511yescharacteristic
1258D3—24no—
1259D3—42no—
1260D3—202no—
1261C5#8636311yescharacteristic, complemented, Sylow
1262C22—21no—
1263C22—21no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—34no—
1268C22—62no—
1269C22—62no—
1270C22—62no—
1271C22—62no—
1272C22—62no—
1273C22—102no—
1274C22—102no—
1275C22—102no—
1276C22—124no—
1277C22—128no—
1278C22—302no—
1279C22—302no—
1280C22—302no—
1281C22—608no—
1282C22D3×D4×D512yes—
1283C22C23×D3×D511yescharacteristic
1284C4—22no—
1285C4—21no—
1286C4—21no—
1287C4—54no—
1288C4—62no—
1289C4—62no—
1290C4—102no—
1291C4—102no—
1292C4—152no—
1293C4—152no—
1294C4—301no—
1295C4—301no—
1296C4—302no—
1297C3#1061819511yescharacteristic, complemented, Sylow
1298C2—22no—
1299C2—42no—
1300C2—64no—
1301C2—122no—
1302C2—202no—
1303C2—602no—
1304C2C2×D3×D4×D511yescharacteristic
1305C2#1175703611yescharacteristic
1306C2#1175706411yescharacteristic
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×D3×#711C2semidirect
2. #11756355C2semidirect
3. C5×#5605C2semidirect
4. C3×#65931C2semidirect
5. #11755067C2semidirect
6. #11755046C2semidirect
7. #11754820C2semidirect
8. #11754797C2semidirect
9. #11754768C2semidirect
10. #11754660C2semidirect
11. #11754386C2semidirect
12. #11754331C2semidirect
13. C2×#91400C2semidirect
14. #11753864C2semidirect
15. #11753420C2semidirect
16. #11753246C2semidirect
17. #11753245C2semidirect
18. #11752844C2semidirect
19. #11752842C2semidirect
21. C2×#6819C22semidirect
23. C2×C3×#711C22semidirect
25. C2×D3×C22⋊D5C22semidirect
27. C2×#6782C22semidirect
29. C22×D3×Dic5C22semidirect
31. C2×#6780C22semidirect
33. C2×C4×D3×D5C22semidirect
36. C2×D3×Dic10C22semidirect
37. C3×C5×#121C22semidirect
38. #91829C22semidirect
39. #91828C22semidirect
40. D4×Dic15C22semidirect
41. #91819C22semidirect
42. C2×C4×Dic15C22semidirect
43. #91782C22semidirect
44. #91777C22semidirect
45. #91774C22semidirect
46. #91770C22semidirect
47. C5×#939C22semidirect
48. C5×#937C22semidirect
49. C5×#930C22semidirect
51. C5×#894C22semidirect
52. C5×#883C22semidirect
53. C5×#882C22semidirect
54. C3×#4085C22semidirect
55. C3×#4085C22semidirect
56. C3×#4076C22semidirect
57. C2×C3×#683C22semidirect
58. C3×#4042C22semidirect
59. C3×#4030C22semidirect
60. C3×#4024C22semidirect
61. #91577C22semidirect
62. #91574C22semidirect
63. #91571C22semidirect
64. #91570C22semidirect
65. #91569C22semidirect
66. #91568C22semidirect
67. #91567C22semidirect
68. #91566C22semidirect
69. #91566C22semidirect
70. #91565C22semidirect
71. #67⋊Dic5C22semidirect
72. #91559C22semidirect
73. #91555C22semidirect
74. C2×#6668C22semidirect
76. #91533C22semidirect
77. C2×Dic3×Dic5C22semidirect
78. #91526C22semidirect
79. #91476C22semidirect
80. #91475C22semidirect
81. #91474C22semidirect
82. #91470C22semidirect
83. #91464C22semidirect
84. #91463C22semidirect
85. #91462C22semidirect
86. #91457C22semidirect
87. #91452C22semidirect
88. #91448C22semidirect
89. #91442C22semidirect
90. #91435C22semidirect
91. #91434C22semidirect
92. #91427C22semidirect
93. #91423C22semidirect
94. #91420C22semidirect
95. #91419C22semidirect
96. #91417C22semidirect
97. #91416C22semidirect
98. #91411C22semidirect
99. #91410C22semidirect
100. #91406C22semidirect
101. #91400C22semidirect
102. #91400C22semidirect
103. #91400C22semidirect
104. #91400C22semidirect
105. #91396C22semidirect
106. #91351C22semidirect
107. #91349C22semidirect
108. #91328C22semidirect
119. #65931D3semidirect
178. C2×D3×Dic5D4semidirect
244. #5605D5semidirect
263. C2×#711C2×D3semidirect
270. C5×#121C2×D3semidirect
286. #4085C2×D3semidirect
287. #4085C2×D3semidirect
297. #4076C2×D3semidirect
301. C2×#683C2×D3semidirect
307. #4042C2×D3semidirect
323. #4030C2×D3semidirect
333. #4024C2×D3semidirect
433. C3×#121C2×D5semidirect
443. #939C2×D5semidirect
449. #937C2×D5semidirect
457. #930C2×D5semidirect
472. #894C2×D5semidirect
490. #883C2×D5semidirect
494. #882C2×D5semidirect
888. #121D3×D5semidirect
1135. C3×C5#3449semidirect
1261. C5#86363semidirect
1297. C3#10618195semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7112
#117563552
C5×#56052
C3×#659312
#117550672
#117550462
#117548202
#117547972
#117547682
#117546602
#117543862
#117543312
C2×#914002
#117538642
#117534202
#117532462
#117532452
#117528442
#117528422
#106181953
#863635