Finite Group Databasebeta

← #14426297

Subgroups — #14426297

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91839C211yesmaximal, characteristic, complemented
2C5×Dic3×#41C211yesmaximal, characteristic, complemented
3C2×C3×#4096C211yesmaximal, characteristic, complemented
4#11754581C211yesmaximal, characteristic, complemented
5#11749360C211yesmaximal, characteristic, complemented
6#11749345C211yesmaximal, characteristic, complemented
7#11749326C211yesmaximal, characteristic, complemented
8#11749325C211yesmaximal, characteristic, complemented
9#11749114C211yesmaximal, characteristic, complemented
10#11749099C211yesmaximal, characteristic, complemented
11#11749080C211yesmaximal, characteristic, complemented
12#11749079C211yesmaximal, characteristic, complemented
13C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
14#11748393C211yesmaximal, characteristic, complemented
15#11748364C211yesmaximal, characteristic, complemented
16#10614256—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×#6817C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20#91839—24no—
21C2×#6718C2211yescharacteristic
22C2×#6717C2211yescharacteristic
23C2×#6716C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25C22×C3⋊#168C2211yescharacteristic
26C5×Q8×Dic3C2211yescharacteristic
27C5×Q8×Dic3C2211yescharacteristic
28C5×D4×Dic3—21no—
29C5×D4×Dic3—21no—
30C5×D4×Dic3C2211yescharacteristic
31C5×D4×Dic3C2211yescharacteristic
32C5×#926—21no—
33C5×#926C2211yescharacteristic
34C2×C4×C5×Dic3—21no—
35C2×C4×C5×Dic3C2211yescharacteristic
36C3×#4096—24no—
37C2×C3×#689C2211yescharacteristic
38C2×C3×#688C2211yescharacteristic
39C2×C3×#687C2211yescharacteristic
40C2×C3×#686C2211yescharacteristic
41C22×C3×#168C2211yescharacteristic
42#91569—21no—
43#91569—21no—
44#91458C2211yescharacteristic
45C4×#1202—21no—
46C4×#1202—21no—
47#91389C2211yescharacteristic
48#91374C2211yescharacteristic
49#91364C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90975C2211yescharacteristic
56#90970C2211yescharacteristic
57#90970C2211yescharacteristic
58#90969C2211yescharacteristic
59#90969C2211yescharacteristic
60#90964C2211yescharacteristic
61#90964C2211yescharacteristic
62#83900—51nomaximal, Hall
63C4×C5×#41—31no—
64C2×#4096—31no—
65C2×#4096D311yescharacteristic, complemented
66#65811—31no—
67#65320—31no—
68#65317—31no—
69#65317—31no—
70#65316—31no—
71#65308—31no—
72#65305—31no—
73#65305—31no—
74#65304—31no—
75#65291—31no—
76#65291—31no—
77C2×C4⋊#168—31no—
78C3×C5×#41—22no—
79C3×C5×#41D414yescomplemented
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—21no—
86#6817—22no—
87#6817—22no—
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×Dic30C2311yescharacteristic
91C22×C5×Dic3—21no—
92C22×C5×Dic3—21no—
93C22×C5×Dic3D411yescharacteristic
94C22×C5×Dic3D411yescharacteristic
95C2×C3×C22⋊D5—21no—
96C3×#709—22no—
97C3×#709—22no—
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×Dic10C2311yescharacteristic
101C2×#1202—21no—
102C2×#1202—21no—
103#6718—22no—
104#6717—22no—
105#6716—22no—
106#6715—22no—
107C2×C3⋊#168—22no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#217—21no—
111C5×#217—21no—
112C5×#217—21no—
113C5×C4⋊Dic3—21no—
114C5×C4⋊Dic3—21no—
115C5×C4⋊Dic3C2311yescharacteristic
116C5×C4⋊Dic3C2311yescharacteristic
117C4×C5×Dic3—21no—
118C4×C5×Dic3—21no—
119C4×C5×Dic3—21no—
120C4×C5×Dic3D411yescharacteristic
121C4×C5×Dic3D411yescharacteristic
122C4×C5×Dic3C2311yescharacteristic
123C4×C5×Dic3C2311yescharacteristic
124C3×#689—22no—
125C3×#688—22no—
126C3×#687—22no—
127C3×#686—22no—
128C2×C3×#168—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131Dic3⋊Dic5—21no—
132Dic3⋊Dic5—21no—
133#6667—21no—
134#6667—21no—
135#6665—21no—
136#6665—21no—
137C2×C3×#135—51no—
138#5832—51no—
139Dic3×#41D511yescharacteristic, complemented
140C2×#950—51no—
141#5233—51no—
142#5185—51no—
143#5182—51no—
144#5166—51no—
145#5165—51no—
146#5163—51no—
147#5162—51no—
148#5153—51no—
149#5150—51no—
150#5113—51no—
151C2×Dic3⋊C8—51no—
152C2×C5×#41C2×D311yescharacteristic
153C2×#709—31no—
154C2×#709C2×D311yescharacteristic
155C4×C5×Q8—31no—
156C4×C5×Q8—31no—
157C4×C5×D4—31no—
158C4×C5×D4—31no—
159C4×C5×D4—61no—
160C4×C5×D4—61no—
161C5×#117—31no—
162C5×#117—61no—
163C2×C42×C5—31no—
164C2×C42×C5—61no—
165#4096—24no—
166#4096—64no—
167C2×#689—31no—
168C2×#689C2×D311yescharacteristic
169C2×#688—31no—
170C2×#688C2×D311yescharacteristic
171C2×#687—31no—
172C2×#687C2×D311yescharacteristic
173C2×#686—31no—
174C2×#686C2×D311yescharacteristic
175#4076—61no—
176#4076—61no—
177C22×#168—31no—
178C22×#168C2×D311yescharacteristic
179#4021—31no—
180#4021—31no—
181#4020—31no—
182C4×D20—61no—
183C4×D20—61no—
184#4015—31no—
185#3942—31no—
186#3942—31no—
187#3942—31no—
188#3942—31no—
189#3941—31no—
190#3941—31no—
191#3941—31no—
192#3941—31no—
193C4⋊#168—31no—
194C4⋊#168—31no—
195C4⋊#168—31no—
196C4⋊#168—31no—
197#3035—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×D15—21no—
201C22×C3×D5—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8C2×D412yes—
204C3×C5×D4—24no—
205C3×C5×D4—21no—
206C3×C5×D4C2×D412yes—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—24no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5#4112yes—
212C2×C3×C4×C5C2411yescharacteristic
213#1220—42no—
214C2×Dic15—21no—
215D60—21no—
216D60—21no—
217C4×D15—42no—
218Dic30—21no—
219Dic30—21no—
220C2×C5×Dic3—22no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—41no—
224C2×C5×Dic3—42no—
225C2×C5×Dic3—42no—
226C2×C5×Dic3C2×D411yescharacteristic
227C2×C5×Dic3C2×D411yescharacteristic
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C3×C22⋊D5—42no—
231C2×C3×Dic5—21no—
232C3×D20—21no—
233C3×D20—21no—
234C3×C4×D5—42no—
235C3×Dic10—21no—
236C3×Dic10—21no—
237#1202—42no—
238#1202—42no—
239C3⋊#168—21no—
240C3⋊#168—21no—
241C3×#168—21no—
242C3×#168—21no—
243C2×C3×#41—51no—
244C2×C3×#41C2×D511yescharacteristic
245C2×#235—51no—
246C3×#135—104no—
247C2×C3×Q16—51no—
248C2×C3×SD16—51no—
249C2×C3×SD16—51no—
250C2×C3×D8—51no—
251C22×C3×C8—51no—
252#950—104no—
253#947—51no—
254Q8×Dic3C2×D511yescharacteristic
255Q8×Dic3C2×D511yescharacteristic
256#944—51no—
257C2×#216—51no—
258C2×#215—51no—
259#940—51no—
260#939—101no—
261#939—101no—
262#936—51no—
263D4×Dic3—21no—
264D4×Dic3—21no—
265D4×Dic3C2×D511yescharacteristic
266D4×Dic3C2×D511yescharacteristic
267C2×#214—51no—
268C2×#213—51no—
269C4×#67—101no—
270C4×#67—101no—
271#926—21no—
272#926C2×D511yescharacteristic
273C2×C4×Dic3—21no—
274C2×C4×Dic3C2×D511yescharacteristic
275C22×C3⋊C8—51no—
276#835—51no—
277#835—51no—
278#832—51no—
279#832—51no—
280#821—51no—
281#821—51no—
282#816—51no—
283#816—51no—
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C5×#41—22no—
289C5×#41#6714yescomplemented
290C2×C5×Q8C22×D311yescharacteristic
291C2×C5×D4—21no—
292C2×C5×D4C22×D311yescharacteristic
293C22×C4×C5—21no—
294C22×C4×C5—31no—
295C22×C4×C5—31no—
296C22×C4×C5—61no—
297C22×C4×C5—61no—
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—21no—
300C2×C22⋊D5—61no—
301#709—22no—
302#709—22no—
303#709—62no—
304#709—62no—
305C2×D20—31no—
306C2×D20—61no—
307C2×D20—61no—
308C2×D20C22×D311yescharacteristic
309C2×C4×D5—21no—
310C2×C4×D5—61no—
311C2×Dic10—31no—
312C2×Dic10C22×D311yescharacteristic
313C5×C4⋊C4—31no—
314C5×C4⋊C4—31no—
315C5×C4⋊C4—61no—
316C5×C4⋊C4—61no—
317C5×C22⋊C4—61no—
318C5×C22⋊C4—61no—
319C5×C22⋊C4—61no—
320C42×C5—31no—
321C42×C5—31no—
322C42×C5—31no—
323C42×C5—31no—
324C42×C5—61no—
325C42×C5—61no—
326C42×C5—61no—
327#689—22no—
328#689—62no—
329#688—22no—
330#688—62no—
331#687—22no—
332#687—62no—
333#686—22no—
334#686—62no—
335#685—61no—
336#685—61no—
337#685—61no—
338#685—61no—
339C4⋊Dic5—61no—
340C4⋊Dic5—61no—
341C2×#168—22no—
342C2×#168—31no—
343C2×#168—31no—
344C2×#168—62no—
345C2×#168C22×D311yescharacteristic
346C2×#168C22×D311yescharacteristic
347C2×#135—51no—
348C2×#135—151no—
349#532—151no—
350C4×#41—31no—
351#464—151no—
352#464—151no—
353#463—151no—
354#463—151no—
355#462—151no—
356#461—151no—
357#460—151no—
358#459—151no—
359C2×C4⋊C8—151no—
360#416—151no—
361#416—151no—
362C22×C3×C5—21no—
363C22×C3×C5—21no—
364C22×C3×C5—22no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5#12112yes—
368C22×C3×C5C22×D411yescharacteristic
369C2×D15—41no—
370C2×D15—41no—
371C2×D15—41no—
372C2×C3×D5—41no—
373C2×C3×D5—41no—
374C2×C3×D5—41no—
375C3×C4×C5—22no—
376C3×C4×C5#12112yes—
377C3×C4×C5C22×D411yescharacteristic
378C3×C4×C5C2×#4111yescharacteristic
379Dic15—41no—
380C3×Dic5—41no—
381C5×Dic3—21no—
382C5×Dic3—21no—
383C5×Dic3—21no—
384C5×Dic3—41no—
385C5×Dic3—41no—
386C5×Dic3#13512yescomplemented
387C3×#41—22no—
388C3×#41—102no—
389C3×#41—102no—
390C3×#41D2014yescomplemented
391C2×C3×Q8—51no—
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C2×C3×D4C22×D511yescharacteristic
397C22×C3×C4—21no—
398C22×C3×C4—101no—
399C22×C3×C4C22×D511yescharacteristic
400C2×#67—101no—
401C2×#67—101no—
402C2×#67—101no—
403C22×Dic3—21no—
404C22×Dic3—21no—
405C22×Dic3C22⋊D511yescharacteristic
406C22×Dic3C22⋊D511yescharacteristic
407#235—102no—
408#235—102no—
409C2×D12—51no—
410C2×C4×D3—101no—
411C2×Dic6—51no—
412C3×Q16—102no—
413C3×SD16—102no—
414C3×SD16—102no—
415C3×D8—102no—
416C2×C3×C8—51no—
417C2×C3×C8—51no—
418C2×C3×C8—102no—
419#217—21no—
420#217—21no—
421#217—21no—
422#217—101no—
423#217—101no—
424#216—102no—
425#215—102no—
426#214—102no—
427#213—102no—
428(C2×D3)⋊C4—101no—
429(C2×D3)⋊C4—101no—
430C4⋊Dic3—21no—
431C4⋊Dic3—21no—
432C4⋊Dic3C22×D511yescharacteristic
433C4⋊Dic3C22×D511yescharacteristic
434Dic3⋊C4—101no—
435Dic3⋊C4—101no—
436C4×Dic3—21no—
437C4×Dic3—21no—
438C4×Dic3—21no—
439C4×Dic3C22⋊D511yescharacteristic
440C4×Dic3C22⋊D511yescharacteristic
441C4×Dic3C22×D511yescharacteristic
442C4×Dic3C22×D511yescharacteristic
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C23×C5—21no—
447C23×C5D3×D411yescharacteristic
448C22×D5—21no—
449C22×D5—61no—
450C5×Q8—21no—
451C5×Q8C2×#6712yes—
452C5×D4—24no—
453C5×D4—21no—
454C5×D4C2×#6712yes—
455C2×C4×C5—21no—
456C2×C4×C5—24no—
457C2×C4×C5—31no—
458C2×C4×C5—31no—
459C2×C4×C5—31no—
460C2×C4×C5—31no—
461C2×C4×C5—62no—
462C2×C4×C5—61no—
463C2×C4×C5—61no—
464C2×C4×C5—122no—
465C2×C4×C5—121no—
466C2×C4×C5—122no—
467C2×C4×C5D3×D411yescharacteristic
468C2×C4×C5#23712yes—
469C2×C4×C5C2×#6712yes—
470C2×C4×C5C23×D311yescharacteristic
471C22⋊D5—42no—
472C22⋊D5—122no—
473C2×Dic5—21no—
474C2×Dic5—61no—
475D20—21no—
476D20—21no—
477D20—61no—
478D20—61no—
479D20—122no—
480D20—122no—
481C4×D5—42no—
482C4×D5—122no—
483Dic10—21no—
484Dic10—21no—
485Dic10—61no—
486Dic10—61no—
487#168—21no—
488#168—21no—
489#168—61no—
490#168—61no—
491C2×#41—51no—
492C2×#41—151no—
493C2×#41D3×D511yescharacteristic
494#135—104no—
495#135—304no—
496C2×Q16—51no—
497C2×Q16—151no—
498C2×SD16—51no—
499C2×SD16—51no—
500C2×SD16—151no—
501C2×SD16—151no—
502C2×D8—51no—
503C2×D8—151no—
504C22×C8—51no—
505C22×C8—151no—
506C4⋊Q8—151no—
507#127—151no—
508#124—151no—
509#124—151no—
510#121—301no—
511#121—301no—
512C4×Q8—31no—
513C4×Q8—31no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—61no—
517C4×D4—61no—
518C4×D4—301no—
519C4×D4—301no—
520#117—31no—
521#117—61no—
522C2×C42—31no—
523C2×C42—61no—
524C4⋊C8—151no—
525C4⋊C8—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528#103—151no—
529#103—151no—
530#103—151no—
531#103—151no—
532#102—151no—
533#102—151no—
534#102—151no—
535#102—151no—
536C2×C3×C5—22no—
537C2×C3×C5—42no—
538C2×C3×C5C2×#12111yescharacteristic
539C2×C3×C5C2×#13511yescharacteristic
540C2×C3×C5#57511yescharacteristic
541D15—81no—
542C3×D5—81no—
543C23×C3—21no—
544C23×C3—101no—
545C23×C3C2×C22⋊D511yescharacteristic
546C22×D3—101no—
547C3×Q8—21no—
548C3×Q8—101no—
549C3×Q8—101no—
550C3×Q8C2×D2012yes—
551C3×D4—24no—
552C3×D4—21no—
553C3×D4—101no—
554C3×D4—101no—
555C3×D4—202no—
556C3×D4C2×D2012yes—
557C2×C3×C4—21no—
558C2×C3×C4—24no—
559C2×C3×C4—101no—
560C2×C3×C4—202no—
561C2×C3×C4C2×D2012yes—
562C2×C3×C4#70912yes—
563C2×C3×C4C2×C22⋊D511yescharacteristic
564C2×C3×C4C23×D511yescharacteristic
565#67—202no—
566#67—202no—
567#67—202no—
568C2×Dic3—22no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—41no—
572C2×Dic3—42no—
573C2×Dic3—42no—
574C2×Dic3—101no—
575C2×Dic3C2×C22⋊D511yescharacteristic
576C2×Dic3C2×C22⋊D511yescharacteristic
577C2×Dic3C2×C22⋊D511yescharacteristic
578C2×Dic3C2×C22⋊D511yescharacteristic
579D12—101no—
580D12—101no—
581C4×D3—202no—
582Dic6—101no—
583Dic6—101no—
584C3×C8—101no—
585C3×C8—101no—
586C3⋊C8—101no—
587C3⋊C8—101no—
588C22×C5—21no—
589C22×C5—21no—
590C22×C5—22no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5#93912yes—
594C22×C5C2×D3×D411yescharacteristic
595C2×D5—41no—
596C2×D5—41no—
597C2×D5—41no—
598C2×D5—121no—
599C2×D5—121no—
600C2×D5—121no—
601C4×C5—22no—
602C4×C5—32no—
603C4×C5—61no—
604C4×C5—61no—
605C4×C5—61no—
606C4×C5—121no—
607C4×C5—121no—
608C4×C5#93912yes—
609C4×C5C2×#23711yescharacteristic
610C4×C5C22×#6711yescharacteristic
611Dic5—41no—
612Dic5—121no—
613#41—22no—
614#41—102no—
615#41—102no—
616#41—302no—
617#41—302no—
618#41#120214yescomplemented
619C2×Q8—51no—
620C2×Q8—151no—
621C2×Q8C2×D3×D511yescharacteristic
622C2×D4—21no—
623C2×D4—51no—
624C2×D4—101no—
625C2×D4—151no—
626C2×D4—301no—
627C2×D4—301no—
628C2×D4—301no—
629C2×D4C2×D3×D511yescharacteristic
630C22×C4—21no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—101no—
636C22×C4—301no—
637C22×C4C2×D3×D511yescharacteristic
638Q16—102no—
639Q16—302no—
640SD16—102no—
641SD16—102no—
642SD16—302no—
643SD16—302no—
644D8—102no—
645D8—302no—
646C2×C8—51no—
647C2×C8—51no—
648C2×C8—102no—
649C2×C8—151no—
650C2×C8—151no—
651C2×C8—302no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—301no—
657C4⋊C4—301no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—301no—
662C22⋊C4—301no—
663C22⋊C4—301no—
664C22⋊C4—301no—
665C42—31no—
666C42—31no—
667C42—31no—
668C42—31no—
669C42—61no—
670C42—61no—
671C42—61no—
672C3×C5#303511yescharacteristic, complemented, Hall
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—201no—
679C22×C3—201no—
680C22×C3—201no—
681C22×C3#407612yes—
682C22×C3C22×C22⋊D511yescharacteristic
683C2×D3—201no—
684C2×D3—201no—
685C2×D3—201no—
686C3×C4—22no—
687C3×C4—201no—
688C3×C4#407612yes—
689C3×C4C22×D2011yescharacteristic
690C3×C4C2×#70911yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—201no—
697Dic3#409612yescomplemented
698C2×C5—22no—
699C2×C5—42no—
700C2×C5D3×#13511yescharacteristic
701C2×C5#576811yescharacteristic
702C2×C5C2×#93911yescharacteristic
703D5—81no—
704D5—241no—
705C23—21no—
706C23—101no—
707C23—301no—
708C23D3×C22⋊D511yescharacteristic
709Q8—21no—
710Q8—101no—
711Q8—101no—
712Q8—301no—
713Q8—301no—
714Q8C2×#120212yes—
715D4—24no—
716D4—21no—
717D4—101no—
718D4—101no—
719D4—202no—
720D4—301no—
721D4—301no—
722D4—602no—
723D4—602no—
724D4—602no—
725D4C2×#120212yes—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—101no—
736C2×C4—122no—
737C2×C4—121no—
738C2×C4—122no—
739C2×C4—202no—
740C2×C4—301no—
741C2×C4—602no—
742C2×C4#677912yes—
743C2×C4C2×#120212yes—
744C2×C4D3×C22⋊D511yescharacteristic
745C2×C4C22×D3×D511yescharacteristic
746C8—101no—
747C8—101no—
748C8—301no—
749C8—301no—
750C2×C3—22no—
751C2×C3—42no—
752C2×C3—401no—
753C2×C3C2×#407611yescharacteristic
754C2×C3C2×#409611yescharacteristic
755C2×C3#6615611yescharacteristic
756D3—401no—
757C5#8390011yescharacteristic, complemented, Sylow
758C22—21no—
759C22—21no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—601no—
767C22—601no—
768C22—601no—
769C22#9156912yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—22no—
772C4—32no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—201no—
779C4—601no—
780C4#9156912yes—
781C4C2×#677911yescharacteristic
782C4C22×#120211yescharacteristic
783C3#1061425611yescharacteristic, complemented, Sylow
784C2—22no—
785C2—42no—
786C2—401no—
787C2—1201no—
788C2D3×#409611yescharacteristic
789C2#1175532211yescharacteristic
790C2C2×#9156911yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91839C2semidirect
2. C5×Dic3×#41C2semidirect
3. C2×C3×#4096C2semidirect
4. #11754581C2semidirect
5. #11749360C2semidirect
6. #11749345C2semidirect
7. #11749326C2semidirect
8. #11749325C2semidirect
9. #11749114C2semidirect
10. #11749099C2semidirect
11. #11749080C2semidirect
12. #11749079C2semidirect
13. C2×Dic3⋊#168C2semidirect
14. #11748393C2semidirect
15. #11748364C2semidirect
65. C2×#4096D3semidirect
79. C3×C5×#41D4semidirect
139. Dic3×#41D5semidirect
289. C5×#41#67semidirect
386. C5×Dic3#135semidirect
390. C3×#41D20semidirect
618. #41#1202semidirect
672. C3×C5#3035semidirect
697. Dic3#4096semidirect
757. C5#83900semidirect
783. C3#10614256semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×Dic3×#412
C2×C3×#40962
#117545812
#117493602
#117493452
#117493262
#117493252
#117491142
#117490992
#117490802
#117490792
C2×Dic3⋊#1682
#117483932
#117483642
#106142563
#839005