Finite Group Databasebeta

← #14453799

Subgroups — #14453799

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
1C5×#5806C211yesmaximal, characteristic
2C22×C3×#687C211yesmaximal, characteristic, complemented
3C2×#91486C211yesmaximal, characteristic, complemented
4#67×Dic10C211yesmaximal, characteristic, complemented
5#11751319C211yesmaximal, characteristic, complemented
6#11749155C211yesmaximal, characteristic, complemented
7#11749114C211yesmaximal, characteristic, complemented
8#11749110C211yesmaximal, characteristic, complemented
9#11749059C211yesmaximal, characteristic, complemented
10#11749051C211yesmaximal, characteristic, complemented
11#11749010C211yesmaximal, characteristic, complemented
12#11749006C211yesmaximal, characteristic, complemented
13#11748557C211yesmaximal, characteristic, complemented
14#11748555C211yesmaximal, characteristic, complemented
15#11748500C211yesmaximal, characteristic, complemented
16#10615237—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C5×#237C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C2×D3×Dic10C2211yescharacteristic, complemented
21C2×#6716C2211yescharacteristic
22C2×#6716C2211yescharacteristic
23#91813C2211yescharacteristic
24C5×#953—21no—
25C2×C5×#217—21no—
26C5×#939—21no—
27C5×#938C2211yescharacteristic
28C5×#936C2211yescharacteristic
29C5×#935—21no—
30C5×D4×Dic3C2211yescharacteristic
31C4×C5×#67C2211yescharacteristic
32C5×#924C2211yescharacteristic
33C2×C3×#687—24no—
34C2×C3×#687C2211yescharacteristic
35C2×C3×#687C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic
37C2×C3×#687C2211yescharacteristic
38C22×C3×#168C2211yescharacteristic
39#91574—21no—
40Dic5×#67—21no—
41#91486—24no—
42#91410—21no—
43#91389C2211yescharacteristic, complemented
44#91369C2211yescharacteristic, complemented
45Dic3×Dic10C2211yescharacteristic, complemented
46#91327—21no—
47C2×#6663C2211yescharacteristic, complemented
48C2×#6661C2211yescharacteristic, complemented
49C2×#6661C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51#91116C2211yescharacteristic
52#91116C2211yescharacteristic
53#91114C2211yescharacteristic
54#90988C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90970C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#83866—51nomaximal, Hall
63C5×#546—31no—
64C2×#4097—31no—
65C22×#687D311yescharacteristic, complemented
66D4×Dic10—31no—
67#65528—31no—
68#65507—31no—
69#65349—31no—
70#65343—31no—
71#65340—31no—
72#65339—31no—
73#65331—31no—
74#65329—31no—
75#65308—31no—
76#65307—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C2×C3×C5×D4—22no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4—41no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C2×Dic30C2311yescharacteristic
86C2×C5×#67—21no—
87C2×C5×#67—21no—
88C2×C5×#67D411yescharacteristic
89C22×C5×Dic3—21no—
90C22×C5×Dic3—21no—
91C5×#237—22no—
92C5×#237—41no—
93C2×C4×C5×D3C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C22×C3×Dic5—21no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10—21no—
98C2×C3×Dic10—41no—
99C2×C3×Dic10C2311yescharacteristic
100C2×C3×Dic10C2311yescharacteristic
101C2×#1204—21no—
102C2×D3×Dic5—21no—
103D3×Dic10—22no—
104D3×Dic10—41no—
105#6719—21no—
106#6716—22no—
107#6716—41no—
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217—21no—
113C5×#217—21no—
114C5×#217—21no—
115C5×#217—21no—
116C5×#217—21no—
117C5×#217D411yescharacteristic
118C5×(C2×D3)⋊C4D411yescharacteristic
119C5×C4⋊Dic3C2311yescharacteristic
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4D411yescharacteristic
122C4×C5×Dic3C2311yescharacteristic
123C3×#687—22no—
124C3×#687—22no—
125C3×#687—22no—
126C3×#687D414yescomplemented
127C2×C3×#168—22no—
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130Dic3⋊Dic5—21no—
131Dic3⋊Dic5—21no—
132#6669—21no—
133#6668—21no—
134(C2×D3)⋊Dic5—21no—
135Dic3×Dic5—21no—
136#6663—22no—
137#6661—22no—
138#6661—41no—
139#6650—22no—
140C22×C3×SD16—51no—
141Q8×#67—51no—
142#5806D511yescharacteristic
143C2×#915—51no—
144#5228—51no—
145#5218—51no—
146#5174—51no—
147#5173—51no—
148#5170—51no—
149#5167—51no—
150#5166—51no—
151#5164—51no—
152#5162—51no—
153#5116—51no—
154#5111—51no—
155C2×C5×#41—31no—
156C22×C5×D4C2×D311yescharacteristic
157C22×Dic10—31no—
158C22×Dic10C2×D311yescharacteristic
159C5×#124—31no—
160C5×#123—61no—
161C5×C22⋊Q8—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#120—61no—
165C4×C5×D4—31no—
166C4×C5×D4—31no—
167C2×C5×C22⋊C4—61no—
168#4097—64no—
169C2×#689—31no—
170C2×#689—31no—
171C2×#689—31no—
172D4×Dic5—61no—
173C2×#687—24no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687C2×D311yescharacteristic
177C2×#687C2×D311yescharacteristic
178C2×#687C2×D311yescharacteristic
179C2×#687C2×D311yescharacteristic
180#4070—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168C2×D311yescharacteristic
184#4034—61no—
185#4024—61no—
186#4024—61no—
187#4015—31no—
188C4×Dic10—31no—
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3942—31no—
196#3942—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—42no—
204C23×C3×C5—42no—
205C23×C3×C5—81no—
206C23×C3×C5C2×D411yescharacteristic
207C22×C5×D3C2×D411yescharacteristic
208C3×C5×D4—21no—
209C3×C5×D4—21no—
210C3×C5×D4—21no—
211C3×C5×D4—42no—
212C3×C5×D4C2×D412yes—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2411yescharacteristic
217C2×Dic15—21no—
218C2×Dic15—21no—
219Dic30—21no—
220Dic30—21no—
221C5×#67—22no—
222C5×#67—42no—
223C5×#67—81no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—42no—
227C2×C5×Dic3—81no—
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C2×C5×Dic3C2×D411yescharacteristic
231C4×C5×D3—21no—
232C4×C5×D3—21no—
233C5×Dic6—21no—
234C5×Dic6—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—42no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—42no—
242C3×Dic10C2×D412yes—
243#1204—42no—
244D3×Dic5—42no—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C22×C3×Q8—51no—
250C22×C3×D4C2×D511yescharacteristic
251C2×D3×Q8—51no—
252C2×#237C2×D511yescharacteristic
253C2×C3×SD16—51no—
254C2×C3×SD16—51no—
255C2×C3×SD16—51no—
256C2×C3×SD16—51no—
257C2×C3×SD16—104no—
258C22×C3×C8—51no—
259#953—21no—
260C2×#217—21no—
261#946—51no—
262#946—101no—
263Q8×Dic3—51no—
264#944—51no—
265#944—101no—
266C2×#216—51no—
267C2×#216—51no—
268#939—21no—
269#938C2×D511yescharacteristic
270#936C2×D511yescharacteristic
271#935—21no—
272D4×Dic3C2×D511yescharacteristic
273C2×#214—51no—
274C2×#214—51no—
275C4×#67—101no—
276C4×#67C2×D511yescharacteristic
277#924—51no—
278#924—101no—
279#924C2×D511yescharacteristic
280#915—104no—
281C2×Dic12—51no—
282C2×ΓL(1,𝔽25)—51no—
283#835—51no—
284#835—51no—
285#832—51no—
286#832—51no—
287#830—51no—
288(C2×D3)⋊C8—51no—
289#818—51no—
290#816—51no—
291#816—51no—
292#815—51no—
293Dic3⋊C8—51no—
294C24×C5—21no—
295C5×#41—62no—
296C5×#41—121no—
297C2×C5×Q8—31no—
298C2×C5×D4—22no—
299C2×C5×D4—21no—
300C2×C5×D4—31no—
301C2×C5×D4—41no—
302C2×C5×D4—61no—
303C2×C5×D4—61no—
304C2×C5×D4C22×D311yescharacteristic
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—31no—
307C22×C4×C5—61no—
308C22×C4×C5—61no—
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—21no—
311C22×Dic5—61no—
312C2×Dic10—22no—
313C2×Dic10—21no—
314C2×Dic10—31no—
315C2×Dic10—41no—
316C2×Dic10—62no—
317C2×Dic10—61no—
318C2×Dic10—121no—
319C2×Dic10C22×D311yescharacteristic
320C2×Dic10C22×D311yescharacteristic
321C5×C4⋊C4—31no—
322C5×C4⋊C4—31no—
323C5×C4⋊C4—61no—
324C5×C22⋊C4—31no—
325C5×C22⋊C4—31no—
326C5×C22⋊C4—61no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C5×C22⋊C4—61no—
330C5×C22⋊C4—61no—
331C42×C5—31no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#689—62no—
335#689—62no—
336#689—121no—
337#687—22no—
338#687—22no—
339#687—22no—
340#687—62no—
341#687—121no—
342#687#6714yescomplemented
343C4⋊Dic5—31no—
344C4⋊Dic5—61no—
345C4⋊Dic5—61no—
346#683—61no—
347#683—61no—
348#683—61no—
349C4×Dic5—61no—
350#681—62no—
351C2×#168—22no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—151no—
357C22×SD16—51no—
358D4×Q8—151no—
359#546—31no—
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—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—22no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—84no—
380C22×C3×C5#13712yescomplemented
381C22×C3×C5C22×D411yescharacteristic
382C2×C5×D3—21no—
383C2×C5×D3—21no—
384C2×C5×D3—21no—
385C3×C4×C5—21no—
386C3×C4×C5C22×D411yescharacteristic
387C3×C4×C5H(5,𝔽2)11yescharacteristic
388Dic15—41no—
389Dic15—41no—
390C3×Dic5—22no—
391C3×Dic5—41no—
392C5×Dic3—21no—
393C5×Dic3—21no—
394C5×Dic3—21no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C24×C3—21no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×Q8—102no—
401C2×C3×Q8—101no—
402C2×C3×Q8—201no—
403C2×C3×D4—22no—
404C2×C3×D4—21no—
405C2×C3×D4—41no—
406C2×C3×D4C22×D511yescharacteristic
407C2×C3×D4C22×D511yescharacteristic
408C22×C3×C4—101no—
409C22×C3×C4C22×D511yescharacteristic
410C2×#67—21no—
411C2×#67—21no—
412C2×#67C22⋊D511yescharacteristic
413C22×Dic3—21no—
414C22×Dic3—21no—
415D3×Q8—102no—
416D3×Q8—201no—
417#237—22no—
418#237—41no—
419C2×C4×D3—101no—
420C2×C4×D3C22×D511yescharacteristic
421C2×Dic6—51no—
422C2×Dic6—101no—
423C2×Dic6C22×D511yescharacteristic
424C3×SD16—54no—
425C3×SD16—102no—
426C3×SD16—102no—
427C3×SD16—102no—
428C2×C3×C8—51no—
429C2×C3×C8—51no—
430C2×C3×C8—102no—
431#217—21no—
432#217—21no—
433#217—21no—
434#217—21no—
435#217—21no—
436#217—101no—
437#217C22⋊D511yescharacteristic
438#216—102no—
439#216—201no—
440#214—102no—
441#214—201no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4C22⋊D511yescharacteristic
444C4⋊Dic3—51no—
445C4⋊Dic3—101no—
446C4⋊Dic3C22×D511yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452Dic3⋊C4C22⋊D511yescharacteristic
453C4×Dic3—101no—
454C4×Dic3C22×D511yescharacteristic
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
457Dic12—102no—
458ΓL(1,𝔽25)—102no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—31no—
462C23×C5—42no—
463C23×C5—42no—
464C23×C5—81no—
465C23×C5D3×D411yescharacteristic
466C5×Q8—61no—
467C5×Q8—61no—
468C5×D4—21no—
469C5×D4—21no—
470C5×D4—21no—
471C5×D4—42no—
472C5×D4—62no—
473C5×D4—122no—
474C5×D4—241no—
475C5×D4C2×#6712yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—31no—
479C2×C4×C5—31no—
480C2×C4×C5—31no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—122no—
486C2×C4×C5—241no—
487C2×C4×C5D3×D411yescharacteristic
488C2×C4×C5C23×D311yescharacteristic
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—42no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—122no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—42no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10C2×#6712yes—
503#168—21no—
504#168—61no—
505#168—61no—
506#168C2×#6712yes—
507C2×#41—31no—
508C22×Q8—51no—
509C22×Q8—151no—
510C22×D4D3×D511yescharacteristic
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—51no—
518C2×SD16—51no—
519C2×SD16—104no—
520C2×SD16—151no—
521C2×SD16—151no—
522C2×M16—151no—
523C22×C8—51no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—31no—
527#123—61no—
528C22⋊Q8—31no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—31no—
534#121—61no—
535#120—61no—
536C4×Q8—151no—
537C4×D4—31no—
538C4×D4—31no—
539C4×D4—301no—
540C2×C22⋊C4—61no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5—42no—
554C2×C3×C5—81no—
555C2×C3×C5D4211yescharacteristic
556C2×C3×C5C2×#13711yescharacteristic
557C2×C3×C5#57711yescharacteristic
558C5×D3—41no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—81no—
564C23×C3C2×C22⋊D511yescharacteristic
565C22×D3C2×C22⋊D511yescharacteristic
566C3×Q8—52no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—202no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—42no—
575C3×D4D4×D512yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—101no—
579C2×C3×C4—101no—
580C2×C3×C4—202no—
581C2×C3×C4C2×C22⋊D511yescharacteristic
582C2×C3×C4C23×D511yescharacteristic
583#67—22no—
584#67—42no—
585#67—81no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—42no—
589C2×Dic3—81no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3C2×C22⋊D511yescharacteristic
593C2×Dic3C2×C22⋊D511yescharacteristic
594C2×Dic3C2×C22⋊D511yescharacteristic
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—202no—
598Dic6—21no—
599Dic6—21no—
600Dic6—101no—
601Dic6—101no—
602Dic6—202no—
603C3×C8—52no—
604C3×C8—101no—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—22no—
610C22×C5—41no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—61no—
616C22×C5—61no—
617C22×C5—61no—
618C22×C5—84no—
619C22×C5#91512yescomplemented
620C22×C5C2×D3×D411yescharacteristic
621C4×C5—21no—
622C4×C5—61no—
623C4×C5—61no—
624C4×C5—61no—
625C4×C5—121no—
626C4×C5—121no—
627C4×C5#100411yescharacteristic
628C4×C5C22×#6711yescharacteristic
629Dic5—22no—
630Dic5—41no—
631Dic5—121no—
632Dic5—121no—
633C24—21no—
634#41—62no—
635#41—121no—
636C2×Q8—31no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—102no—
640C2×Q8—101no—
641C2×Q8—151no—
642C2×Q8—201no—
643C2×Q8—301no—
644C2×Q8—302no—
645C2×Q8—601no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—31no—
649C2×D4—41no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4C2×D3×D511yescharacteristic
653C2×D4C2×D3×D511yescharacteristic
654C22×C4—31no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—101no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—54no—
664SD16—102no—
665SD16—102no—
666SD16—102no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—102no—
673C2×C8—151no—
674C2×C8—151no—
675C4⋊C4—31no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—151no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4—301no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—31no—
694C42—301no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—84no—
705C22×C3#409712yescomplemented
706C22×C3C22×C22⋊D511yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C3×C4—21no—
711C3×C4—102no—
712C3×C4—201no—
713C3×C4C2×D4×D511yescharacteristic
714C3×C4#414411yescharacteristic
715Dic3—21no—
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—42no—
724C2×C5—81no—
725C2×C5—121no—
726C2×C5C2×#91511yescharacteristic
727C2×C5#576211yescharacteristic
728C2×C5D4×#6711yescharacteristic
729C23—21no—
730C23—21no—
731C23—31no—
732C23—42no—
733C23—42no—
734C23—81no—
735C23D3×C22⋊D511yescharacteristic
736Q8—52no—
737Q8—61no—
738Q8—61no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—202no—
743Q8—301no—
744Q8—301no—
745Q8—602no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—42no—
750D4—62no—
751D4—122no—
752D4—241no—
753D4D5×#6712yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—122no—
766C2×C4—202no—
767C2×C4—241no—
768C2×C4—301no—
769C2×C4—301no—
770C2×C4—602no—
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—301no—
776C8—301no—
777C2×C3—22no—
778C2×C3—42no—
779C2×C3—81no—
780C2×C3D4×C22⋊D511yescharacteristic
781C2×C3C2×#409711yescharacteristic
782C2×C3#6617011yescharacteristic
783D3—41no—
784C5#8386611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—61no—
794C22—61no—
795C22—61no—
796C22—84no—
797C22#9148612yescomplemented
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—102no—
804C4—121no—
805C4—121no—
806C4—201no—
807C4—601no—
808C4—601no—
809C4C2×D5×#6711yescharacteristic
810C4#9204911yescharacteristic
811C3#1061523711yescharacteristic, complemented, Sylow
812C2—22no—
813C2—42no—
814C2—81no—
815C2—121no—
816C2C2×#9148611yescharacteristic
817C2#1175471111yescharacteristic
818C2#67×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5806C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#687C2semidirect
3. C2×#91486C2semidirect
4. #67×Dic10C2semidirect
5. #11751319C2semidirect
6. #11749155C2semidirect
7. #11749114C2semidirect
8. #11749110C2semidirect
9. #11749059C2semidirect
10. #11749051C2semidirect
11. #11749010C2semidirect
12. #11749006C2semidirect
13. #11748557C2semidirect
14. #11748555C2semidirect
15. #11748500C2semidirect
20. C2×D3×Dic10C22semidirect
43. #91389C22semidirect
44. #91369C22semidirect
45. Dic3×Dic10C22semidirect
47. C2×#6663C22semidirect
48. C2×#6661C22semidirect
49. C2×#6661C22semidirect
50. C2×#6650C22semidirect
54. #90988C22semidirect
55. Dic3⋊#168C22semidirect
56. #90975C22semidirect
57. #90973C22semidirect
58. #90970C22semidirect
59. #90970C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
65. C22×#687D3semidirect
126. C3×#687D4semidirect
342. #687#67semidirect
380. C22×C3×C5#137semidirect
619. C22×C5#915semidirect
695. C3×C5#3266semidirect
705. C22×C3#4097semidirect
784. C5#83866semidirect
797. C22#91486semidirect
811. C3#10615237semidirect

Maximal subgroups

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

subgroupindex
C5×#58062
C22×C3×#6872
C2×#914862
#67×Dic102
#117513192
#117491552
#117491142
#117491102
#117490592
#117490512
#117490102
#117490062
#117485572
#117485552
#117485002
#106152373
#838665