Finite Group Databasebeta

← #14453770

Subgroups — #14453770

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756309C211yesmaximal, characteristic
2C5×D4×Dic6C211yesmaximal, characteristic, complemented
3C2×#91321C211yesmaximal, characteristic, complemented
4C22×#6660C211yesmaximal, characteristic, complemented
5C3×#65300C211yesmaximal, characteristic, complemented
6#11748566C211yesmaximal, characteristic, complemented
7#11748561C211yesmaximal, characteristic, complemented
8#11748557C211yesmaximal, characteristic, complemented
9#11748554C211yesmaximal, characteristic, complemented
10#11748544C211yesmaximal, characteristic, complemented
11#11748456C211yesmaximal, characteristic, complemented
12#11747102C211yesmaximal, characteristic, complemented
13#11747097C211yesmaximal, characteristic, complemented
14#11747087C211yesmaximal, characteristic, complemented
15#11747058C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22#91826—21no—
23#91819C2211yescharacteristic
24#91813C2211yescharacteristic
25#91783—21no—
26#91773—21no—
27C22⋊C4×D15—21no—
28#91764C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C5×D4×Dic3—21no—
31C5×#924C2211yescharacteristic
32C5×#924C2211yescharacteristic, complemented
33C5×#888—21no—
34C5×#878—21no—
35C5×#878—21no—
36C5×#869C2211yescharacteristic, complemented
37C4×C5×Dic6C2211yescharacteristic, complemented
38C2×C3×#681C2211yescharacteristic, complemented
39C22×C3×#168C2211yescharacteristic
40#91321—24no—
41C2×#6663C2211yescharacteristic, complemented
42C2×#6663C2211yescharacteristic, complemented
43C2×#6663C2211yescharacteristic, complemented
44C2×#6660—24no—
45C2×#6660C2211yescharacteristic
46C2×#6660C2211yescharacteristic
47C2×#6660C2211yescharacteristic
48C2×#6660C2211yescharacteristic
49C2×#6660C2211yescharacteristic
50C2×#6660C2211yescharacteristic
51C3×C22⋊#168C2211yescharacteristic
52C3×C22⋊#168C2211yescharacteristic, complemented
53C3×C4⋊#168C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90969C2211yescharacteristic
61#90969C2211yescharacteristic
62#79495—51nomaximal, Hall
63C5×D4×Q8—31no—
64C2×#4088—31no—
65C22×#688—31no—
66#65884—31no—
67#65517—31no—
68#65516—31no—
69#65375—31no—
70#65372—31no—
71#65340—31no—
72#65338—31no—
73#65336—31no—
74#65335—31no—
75#65317—31no—
76#65315—31no—
77#65300D311yescharacteristic, complemented
78C23×D15—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84#6817—22no—
85#6817—41no—
86C2×D60—22no—
87C2×D60—21no—
88C2×D60—41no—
89C2×D60C2311yescharacteristic
90C2×D60C2311yescharacteristic
91C2×C4×D15—21no—
92C2×C4×D15—21no—
93C2×Dic30C2311yescharacteristic
94C22×C5×Dic3—21no—
95C22×C5×Dic3—21no—
96C2×C5×Dic6—22no—
97C2×C5×Dic6—22no—
98C2×C5×Dic6—21no—
99C2×C5×Dic6—21no—
100C2×C5×Dic6—41no—
101C2×C5×Dic6—41no—
102C2×C5×Dic6C2311yescharacteristic
103C2×C5×Dic6C2311yescharacteristic
104C2×C5×Dic6C2311yescharacteristic
105C3×C5×C4⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C42×C5C2311yescharacteristic
109#6719—21no—
110#6714—21no—
111#6714—21no—
112#6714—21no—
113#6714—21no—
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
116C5×#217—21no—
117C5×#217—21no—
118C5×C4⋊Dic3—21no—
119C5×C4⋊Dic3—21no—
120C5×C4⋊Dic3C2311yescharacteristic
121C5×Dic3⋊C4—21no—
122C5×Dic3⋊C4—21no—
123C5×Dic3⋊C4—21no—
124C4×C5×Dic3—21no—
125C3×#681—22no—
126C2×C3×#168—22no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6663—22no—
132#6663—22no—
133#6663—41no—
134#6660—22no—
135#6660—22no—
136#6660—22no—
137#6660—22no—
138#6660—41no—
139#6660D414yescomplemented
140C2×#909—51no—
141C22×#204—51no—
142#5550—51no—
143D4×Dic6D511yescharacteristic, complemented
144C3×#435—51no—
145#5134—51no—
146#5116—51no—
147#4845—51no—
148#4841—51no—
149#4739—51no—
150#4738—51no—
151#4733—51no—
152#4731—51no—
153#4715—51no—
154#4710—51no—
155C22×C5×Q8—31no—
156C22×C5×Q8—31no—
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8—31no—
160C5×C4⋊Q8—61no—
161C5×C22⋊Q8—31no—
162C5×C22⋊Q8—31no—
163C5×C22⋊Q8—61no—
164C5×C22⋊Q8—61no—
165C4×C5×Q8—31no—
166C4×C5×D4—61no—
167C4×C5×D4C2×D311yescharacteristic
168C2×#689—31no—
169C2×#689—31no—
170C2×#689—31no—
171#4088—64no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—31no—
178C2×#688—64no—
179#4083—61no—
180#4076—31no—
181#4070—31no—
182C2×#681C2×D311yescharacteristic, complemented
183C22×#168C2×D311yescharacteristic
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3967—31no—
192C22⋊#168C2×D311yescharacteristic
193C22⋊#168C2×D311yescharacteristic, complemented
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3939—31no—
198C4⋊#168C2×D311yescharacteristic, complemented
199#3935C2×D311yescharacteristic, complemented
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—81no—
208C3×C5×D4—22no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—81no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224D60—21no—
225D60—42no—
226D60C2×D412yes—
227C4×D15—42no—
228C4×D15—81no—
229Dic30—21no—
230Dic30—21no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—42no—
236C2×C5×Dic3—42no—
237C5×Dic6—21no—
238C5×Dic6—21no—
239C5×Dic6—21no—
240C5×Dic6—21no—
241C5×Dic6—21no—
242C5×Dic6—42no—
243C5×Dic6—42no—
244C5×Dic6C2×D412yes—
245C3×#168—21no—
246C3×#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×#235—51no—
250C22×D12—51no—
251C22×Dic6C2×D511yescharacteristic
252C22×Dic6C2×D511yescharacteristic, complemented
253C2×C3×M16—51no—
254C22×C3×C8—51no—
255C3×C4×D4C2×D511yescharacteristic
256#937—101no—
257D4×Dic3—21no—
258#930—51no—
259#924—51no—
260#924C2×D511yescharacteristic
261#924C2×D511yescharacteristic, complemented
262#909—104no—
263C2×Dic12—51no—
264C2×Dic12—51no—
265C2×Dic12—51no—
266C2×#204—51no—
267C2×#204—51no—
268C2×#204—51no—
269C2×#204—51no—
270C2×#204—51no—
271C2×#204—51no—
272C2×#204—104no—
273#894—101no—
274#888—21no—
275#884—101no—
276D3×C22⋊C4—101no—
277#878—21no—
278#878—21no—
279#875—51no—
280C4×D12—51no—
281#869C2×D511yescharacteristic, complemented
282C4×Dic6C2×D511yescharacteristic, complemented
283C3×C4⋊C8—51no—
284C3×C22⋊C8—51no—
285C3×C22⋊C8—51no—
286C3×#97—51no—
287#821—51no—
288#821—51no—
289#818—51no—
290#816—51no—
291#816—51no—
292#816—51no—
293#816—51no—
294C23×D5—61no—
295C2×C5×Q8—31no—
296C2×C5×Q8—31no—
297C2×C5×Q8—31no—
298C2×C5×Q8—62no—
299C2×C5×Q8—62no—
300C2×C5×Q8—61no—
301C2×C5×Q8—61no—
302C2×C5×Q8—121no—
303C2×C5×Q8—121no—
304C2×C5×D4D1211yescharacteristic
305C22×C4×C5—61no—
306C22×C4×C5—61no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311#709—62no—
312#709—121no—
313C2×D20—31no—
314C2×D20—31no—
315C2×D20—62no—
316C2×D20—61no—
317C2×D20—121no—
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×Dic10—31no—
321C5×C4⋊C4—31no—
322C5×C4⋊C4—61no—
323C5×C4⋊C4—61no—
324C5×C4⋊C4—61no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4D1211yescharacteristic
328C5×C22⋊C4—61no—
329C5×C22⋊C4—61no—
330C5×C22⋊C4D1211yescharacteristic
331C5×C22⋊C4D1211yescharacteristic
332C42×C5—61no—
333C42×C5C22×D311yescharacteristic
334C22⋊Dic5—61no—
335#689—62no—
336#689—62no—
337#689—121no—
338#688—34no—
339#688—62no—
340#688—62no—
341#688—62no—
342#688—62no—
343#688—121no—
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5—31no—
349#683—61no—
350#681—22no—
351C2×#168—22no—
352C2×#168C22×D311yescharacteristic
353C2×#168C22×D311yescharacteristic
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—31no—
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—51no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×D15—22no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391Dic15—41no—
392Dic15—41no—
393C5×Dic3—22no—
394C5×Dic3—41no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C23×D3—101no—
398C2×C3×D4C22⋊D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C2×#67—101no—
402C2×#67—101no—
403C22×Dic3—21no—
404C22×Dic3—21no—
405#235—102no—
406#235—201no—
407C2×D12—51no—
408C2×D12—51no—
409C2×D12—102no—
410C2×D12—101no—
411C2×D12—201no—
412C2×C4×D3—101no—
413C2×C4×D3—101no—
414C2×Dic6—22no—
415C2×Dic6—22no—
416C2×Dic6—21no—
417C2×Dic6—21no—
418C2×Dic6—41no—
419C2×Dic6—41no—
420C2×Dic6—51no—
421C2×Dic6C22×D511yescharacteristic
422C2×Dic6C22×D511yescharacteristic
423C2×Dic6C22×D511yescharacteristic
424C3×M16—102no—
425C2×C3×C8—51no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C2×C3×C8—51no—
429C2×C3×C8—102no—
430C3×C4⋊C4C22⋊D511yescharacteristic
431C3×C22⋊C4C22⋊D511yescharacteristic
432C3×C22⋊C4C22⋊D511yescharacteristic
433C3×C42C22×D511yescharacteristic
434#217—21no—
435#217—21no—
436#217—101no—
437(C2×D3)⋊C4—101no—
438(C2×D3)⋊C4—101no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441C4⋊Dic3—21no—
442C4⋊Dic3—21no—
443C4⋊Dic3—51no—
444C4⋊Dic3C22×D511yescharacteristic
445Dic3⋊C4—21no—
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—101no—
449C4×Dic3—21no—
450Dic12—102no—
451Dic12—102no—
452Dic12—201no—
453#204—54no—
454#204—102no—
455#204—102no—
456#204—102no—
457#204—102no—
458#204—201no—
459C23×C5C2×D1211yescharacteristic
460C23×C5C2×D1211yescharacteristic
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—32no—
467C5×Q8—61no—
468C5×Q8—61no—
469C5×Q8—61no—
470C5×Q8—61no—
471C5×Q8—61no—
472C5×Q8—122no—
473C5×Q8—122no—
474C5×D4—22no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—122no—
484C2×C4×C5—122no—
485C2×C4×C5C2×D1211yescharacteristic
486C2×C4×C5C2×D1211yescharacteristic
487C2×C4×C5C2×D1211yescharacteristic
488C2×C4×C5C2×D1211yescharacteristic
489C2×C4×C5C23×D311yescharacteristic
490C22⋊D5—122no—
491C22⋊D5—241no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494D20—32no—
495D20—61no—
496D20—61no—
497D20—61no—
498D20—122no—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—61no—
502Dic10—61no—
503#168—21no—
504#168—21no—
505#168—21no—
506#168D3×D412yes—
507C2×#41—151no—
508C22×Q8—31no—
509C22×Q8—31no—
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—31no—
525C4⋊Q8—61no—
526#124—151no—
527#123—301no—
528C22⋊Q8—31no—
529C22⋊Q8—31no—
530C22⋊Q8—61no—
531C22⋊Q8—61no—
532C22⋊Q8—151no—
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—31no—
537C4×D4—61no—
538C4×D4—151no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—51no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—51no—
550C22⋊C8—51no—
551#97—51no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557D15—42no—
558D15—81no—
559C23×C3C2×C22⋊D511yescharacteristic
560C23×C3C2×C22⋊D511yescharacteristic
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×D4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4C2×C22⋊D511yescharacteristic
572C2×C3×C4C2×C22⋊D511yescharacteristic
573C2×C3×C4C2×C22⋊D511yescharacteristic
574C2×C3×C4C2×C22⋊D511yescharacteristic
575C2×C3×C4C23×D511yescharacteristic
576#67—202no—
577#67—401no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3—101no—
585C2×Dic3—101no—
586D12—52no—
587D12—101no—
588D12—101no—
589D12—101no—
590D12—202no—
591C4×D3—202no—
592C4×D3—401no—
593Dic6—21no—
594Dic6—21no—
595Dic6—21no—
596Dic6—21no—
597Dic6—21no—
598Dic6—42no—
599Dic6—42no—
600Dic6—101no—
601Dic6—101no—
602Dic6D4×D512yes—
603C3×C8—52no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5#90912yescomplemented
613C22×C5C22×D1211yescharacteristic
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—62no—
626C4×C5—121no—
627C4×C5—121no—
628C4×C5—121no—
629C4×C5C2×D3×D411yescharacteristic
630C4×C5#100911yescharacteristic
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—31no—
639C2×Q8—62no—
640C2×Q8—62no—
641C2×Q8—61no—
642C2×Q8—61no—
643C2×Q8—121no—
644C2×Q8—121no—
645C2×Q8—151no—
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—302no—
649C2×D4—301no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—601no—
653C2×D4#120311yescharacteristic
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4C2×D3×D511yescharacteristic
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—51no—
673C2×C8—51no—
674C2×C8—102no—
675C4⋊C4—31no—
676C4⋊C4—61no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—151no—
682C4⋊C4—301no—
683C4⋊C4#120311yescharacteristic
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—301no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#120311yescharacteristic
692C22⋊C4#120311yescharacteristic
693C42—61no—
694C42C2×D3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3#408812yescomplemented
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4C2×D4×D511yescharacteristic
715C3×C4#414411yescharacteristic
716Dic3—22no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5D4×D1211yescharacteristic
725C2×C5C2×#90911yescharacteristic
726C2×C5#575111yescharacteristic
727D5—122no—
728D5—241no—
729C23—301no—
730C23—301no—
731C23—602no—
732C23—602no—
733C23—1201no—
734C23C2×#120311yescharacteristic
735C23C2×#120311yescharacteristic
736Q8—32no—
737Q8—61no—
738Q8—61no—
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—122no—
743Q8—122no—
744Q8—301no—
745Q8—301no—
746D4—22no—
747D4—152no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—602no—
767C2×C4—1201no—
768C2×C4C2×#120311yescharacteristic
769C2×C4C2×#120311yescharacteristic
770C2×C4C2×#120311yescharacteristic
771C2×C4C2×#120311yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—101no—
776C8—101no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#408811yescharacteristic
781C2×C3#6617111yescharacteristic
782D3—202no—
783D3—401no—
784C5#7949511yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—302no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9132112yescomplemented
798C22C22×#120311yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—62no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202711yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—602no—
815C2—1201no—
816C2C2×#9132111yescharacteristic
817C2D4×#120311yescharacteristic
818C2#1175530811yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756309C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×D4×Dic6C2semidirect
3. C2×#91321C2semidirect
4. C22×#6660C2semidirect
5. C3×#65300C2semidirect
6. #11748566C2semidirect
7. #11748561C2semidirect
8. #11748557C2semidirect
9. #11748554C2semidirect
10. #11748544C2semidirect
11. #11748456C2semidirect
12. #11747102C2semidirect
13. #11747097C2semidirect
14. #11747087C2semidirect
15. #11747058C2semidirect
20. C22×C5×Dic6C22semidirect
32. C5×#924C22semidirect
36. C5×#869C22semidirect
37. C4×C5×Dic6C22semidirect
38. C2×C3×#681C22semidirect
41. C2×#6663C22semidirect
42. C2×#6663C22semidirect
43. C2×#6663C22semidirect
52. C3×C22⋊#168C22semidirect
53. C3×C4⋊#168C22semidirect
54. C3×#3935C22semidirect
55. #90988C22semidirect
56. #90975C22semidirect
57. #90973C22semidirect
58. #90973C22semidirect
59. #90973C22semidirect
77. #65300D3semidirect
139. #6660D4semidirect
143. D4×Dic6D5semidirect
182. C2×#681C2×D3semidirect
193. C22⋊#168C2×D3semidirect
198. C4⋊#168C2×D3semidirect
199. #3935C2×D3semidirect
252. C22×Dic6C2×D5semidirect
261. #924C2×D5semidirect
281. #869C2×D5semidirect
282. C4×Dic6C2×D5semidirect
376. C22×C3×C5#137semidirect
612. C22×C5#909semidirect
695. C3×C5#3266semidirect
701. C22×C3#4088semidirect
784. C5#79495semidirect
797. C22#91321semidirect
811. C3#10615290semidirect

Maximal subgroups

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

subgroupindex
#117563092
C5×D4×Dic62
C2×#913212
C22×#66602
C3×#653002
#117485662
#117485612
#117485572
#117485542
#117485442
#117484562
#117471022
#117470972
#117470872
#117470582
#106152903
#794955