Finite Group Databasebeta

← #14453781

Subgroups — #14453781

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×#5632C211yesmaximal, characteristic, complemented
2C2×#91518C211yesmaximal, characteristic, complemented
3#11754305C211yesmaximal, characteristic
4C22×#6655C211yesmaximal, characteristic, complemented
5#11751152C211yesmaximal, characteristic, complemented
6C3×#65335C211yesmaximal, characteristic, complemented
7#11749319C211yesmaximal, characteristic, complemented
8#11749278C211yesmaximal, characteristic, complemented
9#11749227C211yesmaximal, characteristic, complemented
10#11748561C211yesmaximal, characteristic, complemented
11#11748508C211yesmaximal, characteristic, complemented
12#11747514C211yesmaximal, characteristic, complemented
13#11747373C211yesmaximal, characteristic, complemented
14#11747323C211yesmaximal, characteristic, complemented
15#11747222C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic, complemented
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C2×#6765C2211yescharacteristic
21C3×C5×C22⋊Q8C2211yescharacteristic
22C2×#6718C2211yescharacteristic, complemented
23#91813C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25C5×#944C2211yescharacteristic, complemented
26C4×C5×#67C2211yescharacteristic
27C5×#897C2211yescharacteristic, complemented
28C5×#896—21no—
29C5×#888—21no—
30C5×#887C2211yescharacteristic, complemented
31C5×#67⋊C4—21no—
32C5×#878—21no—
33C2×C3×#688C2211yescharacteristic
34C2×C3×#688C2211yescharacteristic
35#91563—21no—
36D5×#217—21no—
37#91518—24no—
38#91456C2211yescharacteristic
39Dic3×D20C2211yescharacteristic
40#91408—21no—
41#91407—21no—
42#91364C2211yescharacteristic
43C2×#6663C2211yescharacteristic, complemented
44C2×#6663C2211yescharacteristic, complemented
45C2×#6655—24no—
46C2×#6655C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×#6655C2211yescharacteristic
49C2×#6655C2211yescharacteristic
50C2×#6650C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53#91091C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic
55C3×#3941C2211yescharacteristic
56C3×#3941C2211yescharacteristic
57Dic3⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80169—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#65335D311yescharacteristic, complemented
75#65317—31no—
76#65315—31no—
77#65300—31no—
78C23×C3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×#67D411yescharacteristic
83C22×C5×Dic3—21no—
84C5×D3×Q8—22no—
85C5×D3×Q8—41no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C2×C5×Dic6—22no—
89C2×C5×Dic6—21no—
90C2×C5×Dic6—21no—
91C2×C5×Dic6—41no—
92C2×C5×Dic6C2311yescharacteristic
93C2×C5×Dic6C2311yescharacteristic
94C2×C3×D20—22no—
95C2×C3×D20—21no—
96C2×C3×D20—41no—
97C2×C3×D20C2311yescharacteristic
98C2×C3×D20C2311yescharacteristic
99C2×#1201—21no—
100C2×#1201—21no—
101C2×D5×Dic3—21no—
102C2×D5×Dic3—21no—
103#6765—22no—
104#6765—41no—
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C5×C22⋊C4—21no—
108#6719—21no—
109#6718—22no—
110C4⋊Dic15C2311yescharacteristic
111#6712—21no—
112C2×C3⋊#168—22no—
113C2×C3⋊#168C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C5×#217D411yescharacteristic
116C5×(C2×D3)⋊C4—21no—
117C5×(C2×D3)⋊C4D411yescharacteristic
118C5×C4⋊Dic3—21no—
119C5×Dic3⋊C4—21no—
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4—21no—
122C5×Dic3⋊C4D411yescharacteristic
123C4×C5×Dic3—21no—
124C4×C5×Dic3C2311yescharacteristic
125C3×#688—22no—
126C3×#688—41no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6665—21no—
130#6665—21no—
131#6665—21no—
132#6665—21no—
133#6663—22no—
134#6663—41no—
135#6655—22no—
136#6655—22no—
137#6655—22no—
138#6655D414yescomplemented
139#6650—22no—
140#5806—51no—
141C22×#214—51no—
142C2×#915—51no—
143#5632D511yescharacteristic, complemented
144C3×#450—51no—
145#5170—51no—
146#5167—51no—
147#5162—51no—
148#5051—51no—
149#4783—51no—
150#4780—51no—
151#4767—51no—
152#4757—51no—
153#4739—51no—
154#4730—51no—
155C22×C5×Q8—31no—
156C22×C5×Q8—31no—
157C2×#709—31no—
158C22×D20C2×D311yescharacteristic
159C5×C4⋊Q8—31no—
160C5×C4⋊Q8—61no—
161C5×C22⋊Q8—31no—
162C5×C22⋊Q8—61no—
163C5×C22⋊Q8—61no—
164C5×C22⋊Q8C2×D311yescharacteristic
165C4×C5×Q8—31no—
166C4×C5×D4—31no—
167C4×C5×D4—61no—
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—64no—
177C2×#688C2×D311yescharacteristic
178C2×#688C2×D311yescharacteristic
179#4083—61no—
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
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⋊#168—31no—
193C22⋊#168C2×D311yescharacteristic
194#3942—31no—
195#3941C2×D311yescharacteristic
196#3941C2×D311yescharacteristic
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×C5×D3C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—81no—
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216C2×Dic15—21no—
217C2×Dic15—21no—
218Dic30—21no—
219Dic30—21no—
220C5×#67—22no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—42no—
224C2×C5×Dic3C2×D411yescharacteristic
225C2×C5×Dic3C2×D411yescharacteristic
226C2×C5×Dic3C2×D411yescharacteristic
227C4×C5×D3—21no—
228C4×C5×D3—21no—
229C4×C5×D3—42no—
230C5×Dic6—21no—
231C5×Dic6—21no—
232C5×Dic6—21no—
233C5×Dic6—42no—
234C5×Dic6—42no—
235C5×Dic6C2×D412yes—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×D20C2×D412yes—
241#1201—42no—
242#1201—81no—
243D5×Dic3—42no—
244D5×Dic3—81no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C22×C3×D4—51no—
250C2×D3×Q8C2×D511yescharacteristic, complemented
251C2×#237—51no—
252C22×Dic6C2×D511yescharacteristic
253C2×C3×SD16—51no—
254C2×C3×SD16—51no—
255C3×C22⋊Q8C2×D511yescharacteristic
256#953—101no—
257C2×#217—101no—
258#944C2×D511yescharacteristic, complemented
259C2×#216—51no—
260#939—101no—
261#938—51no—
262#936—51no—
263#935—101no—
264D4×Dic3—51no—
265C2×#214—51no—
266C2×#214—51no—
267C2×#214—51no—
268C2×#214—51no—
269C2×#214—104no—
270C4×#67C2×D511yescharacteristic
271#924—51no—
272C22×C3⋊C8—51no—
273#915—104no—
274C2×Dic12—51no—
275C2×Dic12—51no—
276C2×ΓL(1,𝔽25)—51no—
277#897C2×D511yescharacteristic, complemented
278#896—21no—
279#888—21no—
280#887C2×D511yescharacteristic, complemented
281#67⋊C4—21no—
282#878—21no—
283C3×#102—51no—
284C3×#102—51no—
285C3×C22⋊C8—51no—
286#835—51no—
287(C2×D3)⋊C8—51no—
288#816—51no—
289#816—51no—
290#815—51no—
291Dic3⋊C8—51no—
292#810—51no—
293#807—51no—
294C23×D5—21no—
295C2×C5×Q8—31no—
296C2×C5×Q8—31no—
297C2×C5×Q8—61no—
298C2×C5×Q8—62no—
299C2×C5×Q8—61no—
300C2×C5×Q8—62no—
301C2×C5×Q8—121no—
302C2×C5×Q8—121no—
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4—31no—
305C22×C4×C5—31no—
306C22×C4×C5—61no—
307C22×C4×C5—61no—
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311#709—62no—
312#709—121no—
313C2×D20—22no—
314C2×D20—21no—
315C2×D20—41no—
316C2×D20C22×D311yescharacteristic
317C2×D20C22×D311yescharacteristic
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×Dic10—31no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4—31no—
323C5×C4⋊C4—61no—
324C5×C4⋊C4—61no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4C22×D311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—31no—
331C5×C22⋊C4—61no—
332C42×C5—31no—
333C42×C5—61no—
334C22⋊Dic5—61no—
335#689—62no—
336#689—62no—
337#689—121no—
338#688—22no—
339#688—34no—
340#688—41no—
341#688—62no—
342#688—62no—
343#688—62no—
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5—31no—
349#683—61no—
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—62no—
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—51no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5#13712yescomplemented
374C22×C3×C5C22×D411yescharacteristic
375C2×C5×D3—21no—
376C2×C5×D3—21no—
377C2×C5×D3—21no—
378C2×C3×D5—22no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—84no—
385C3×C4×C5—21no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—41no—
391Dic15—41no—
392C5×Dic3—21no—
393C5×Dic3—22no—
394C5×Dic3—21no—
395C5×Dic3—21no—
396C5×Dic3—41no—
397C24×C3—101no—
398C2×C3×Q8C22×D511yescharacteristic
399C2×C3×D4—51no—
400C2×C3×D4—51no—
401C2×C3×D4—102no—
402C2×C3×D4—101no—
403C2×C3×D4—201no—
404C22×C3×C4C22×D511yescharacteristic
405C2×#67—101no—
406C2×#67—101no—
407C2×#67C22⋊D511yescharacteristic
408C22×Dic3—21no—
409C22×Dic3—101no—
410C22×Dic3—101no—
411D3×Q8—22no—
412D3×Q8—41no—
413#237—102no—
414#237—201no—
415C2×C4×D3—21no—
416C2×C4×D3C22×D511yescharacteristic
417C2×Dic6—22no—
418C2×Dic6—21no—
419C2×Dic6—21no—
420C2×Dic6—41no—
421C2×Dic6—51no—
422C2×Dic6C22×D511yescharacteristic
423C2×Dic6C22×D511yescharacteristic
424C3×SD16—102no—
425C3×SD16—201no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4C22×D511yescharacteristic
430C3×C22⋊C4—21no—
431#217—101no—
432#217—101no—
433#217—101no—
434#217—101no—
435#217—101no—
436#217C22⋊D511yescharacteristic
437#216—102no—
438#214—54no—
439#214—102no—
440#214—102no—
441#214—102no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4C22⋊D511yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3—51no—
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4—101no—
450Dic3⋊C4C22⋊D511yescharacteristic
451C4×Dic3—21no—
452C4×Dic3C22×D511yescharacteristic
453C2×C3⋊C8—51no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—102no—
456Dic12—102no—
457Dic12—201no—
458ΓL(1,𝔽25)—102no—
459C23×C5—31no—
460C23×C5D3×D411yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—42no—
464C22×D5—42no—
465C22×D5—81no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—32no—
469C5×Q8—61no—
470C5×Q8—61no—
471C5×Q8—61no—
472C5×Q8—122no—
473C5×Q8—122no—
474C5×D4—62no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—31no—
480C2×C4×C5—31no—
481C2×C4×C5—31no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—122no—
487C2×C4×C5—122no—
488C2×C4×C5D3×D411yescharacteristic
489C2×C4×C5C23×D311yescharacteristic
490C22⋊D5—122no—
491C22⋊D5—241no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494D20—21no—
495D20—21no—
496D20—21no—
497D20—42no—
498D20D3×D412yes—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—61no—
502Dic10—61no—
503#168—21no—
504#168—21no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—31no—
509C22×Q8—31no—
510C22×D4—51no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—31no—
525C4⋊Q8—61no—
526#124—151no—
527#123—301no—
528C22⋊Q8—31no—
529C22⋊Q8—61no—
530C22⋊Q8—61no—
531C22⋊Q8—151no—
532C22⋊Q8D3×D511yescharacteristic
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—31no—
537C4×D4—31no—
538C4×D4—61no—
539C4×D4—151no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—51no—
548#102—51no—
549C22⋊C8—51no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556C3×D5—42no—
557C3×D5—81no—
558C5×D3—41no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—202no—
562C23×C3—202no—
563C23×C3—401no—
564C23×C3C2×C22⋊D511yescharacteristic
565C22×D3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×D4—52no—
569C3×D4—101no—
570C3×D4—101no—
571C3×D4—101no—
572C3×D4—202no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4C2×C22⋊D511yescharacteristic
578C2×C3×C4C23×D511yescharacteristic
579#67—22no—
580#67—202no—
581#67—401no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—42no—
585C2×Dic3—101no—
586C2×Dic3—101no—
587C2×Dic3—202no—
588C2×Dic3—401no—
589C2×Dic3C2×C22⋊D511yescharacteristic
590C2×Dic3C2×C22⋊D511yescharacteristic
591C2×Dic3C2×C22⋊D511yescharacteristic
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—42no—
595Dic6—21no—
596Dic6—21no—
597Dic6—21no—
598Dic6—42no—
599Dic6—42no—
600Dic6—101no—
601Dic6—101no—
602Dic6D4×D512yes—
603C3×C8—101no—
604C3×C8—101no—
605C3⋊C8—52no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—61no—
610C22×C5—61no—
611C22×C5—61no—
612C22×C5#91512yescomplemented
613C22×C5C2×D3×D411yescharacteristic
614C2×D5—22no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—41no—
620C2×D5—84no—
621C4×C5—21no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5—62no—
628C4×C5—121no—
629C4×C5C2×D3×D411yescharacteristic
630C4×C5#100411yescharacteristic
631Dic5—121no—
632Dic5—121no—
633C24—101no—
634#41—302no—
635#41—601no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—61no—
639C2×Q8—62no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—121no—
643C2×Q8—121no—
644C2×Q8—151no—
645C2×Q8C2×D3×D511yescharacteristic
646C2×D4—31no—
647C2×D4—51no—
648C2×D4—51no—
649C2×D4—102no—
650C2×D4—101no—
651C2×D4—201no—
652C2×D4—301no—
653C2×D4—301no—
654C22×C4—31no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—102no—
664SD16—154no—
665SD16—201no—
666SD16—302no—
667SD16—302no—
668SD16—302no—
669M16—302no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—151no—
682C4⋊C4—301no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—31no—
686C22⋊C4—31no—
687C22⋊C4—61no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—31no—
694C42—61no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—102no—
699C22×C3—201no—
700C22×C3—201no—
701C22×C3—201no—
702C22×C3—201no—
703C22×C3—201no—
704C22×C3—404no—
705C22×C3#408812yescomplemented
706C22×C3C22×C22⋊D511yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C3×C4—21no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4C2×D4×D511yescharacteristic
714C3×C4#414411yescharacteristic
715Dic3—22no—
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—121no—
724C2×C5#559011yescharacteristic
725C2×C5C2×#91511yescharacteristic
726C2×C5#577511yescharacteristic
727D5—42no—
728D5—81no—
729C23—31no—
730C23—101no—
731C23—101no—
732C23—202no—
733C23—202no—
734C23—401no—
735C23D3×C22⋊D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—32no—
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—122no—
743Q8—122no—
744Q8—301no—
745Q8—301no—
746D4—52no—
747D4—62no—
748D4—101no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—101no—
774C8—101no—
775C8—152no—
776C8—301no—
777C2×C3—22no—
778C2×C3—202no—
779C2×C3—401no—
780C2×C3D4×C22⋊D511yescharacteristic
781C2×C3C2×#408811yescharacteristic
782C2×C3#6617111yescharacteristic
783D3—41no—
784C5#8016911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—102no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—404no—
797C22#9151812yescomplemented
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—61no—
803C4—62no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202511yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—22no—
813C2—121no—
814C2—202no—
815C2—401no—
816C2#1175503211yescharacteristic
817C2C2×#9151811yescharacteristic
818C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754305C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5632C2semidirect
2. C2×#91518C2semidirect
4. C22×#6655C2semidirect
5. #11751152C2semidirect
6. C3×#65335C2semidirect
7. #11749319C2semidirect
8. #11749278C2semidirect
9. #11749227C2semidirect
10. #11748561C2semidirect
11. #11748508C2semidirect
12. #11747514C2semidirect
13. #11747373C2semidirect
14. #11747323C2semidirect
15. #11747222C2semidirect
17. C2×C5×D3×Q8C22semidirect
22. C2×#6718C22semidirect
25. C5×#944C22semidirect
27. C5×#897C22semidirect
30. C5×#887C22semidirect
43. C2×#6663C22semidirect
44. C2×#6663C22semidirect
50. C2×#6650C22semidirect
51. #91119C22semidirect
52. #91094C22semidirect
53. #91091C22semidirect
57. Dic3⋊#168C22semidirect
58. #90973C22semidirect
59. #90973C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
74. #65335D3semidirect
138. #6655D4semidirect
143. #5632D5semidirect
250. C2×D3×Q8C2×D5semidirect
258. #944C2×D5semidirect
277. #897C2×D5semidirect
280. #887C2×D5semidirect
373. C22×C3×C5#137semidirect
612. C22×C5#915semidirect
695. C3×C5#3266semidirect
705. C22×C3#4088semidirect
784. C5#80169semidirect
797. C22#91518semidirect
811. C3#10615290semidirect

Maximal subgroups

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

subgroupindex
C5×#56322
C2×#915182
#117543052
C22×#66552
#117511522
C3×#653352
#117493192
#117492782
#117492272
#117485612
#117485082
#117475142
#117473732
#117473232
#117472222
#106152903
#801695