Finite Group Databasebeta

← #14427819

Subgroups — #14427819

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5606C211yesmaximal, characteristic, complemented
2C2×#91493C211yesmaximal, characteristic, complemented
3#11754341C211yesmaximal, characteristic, complemented
4C22×D3×#168C211yesmaximal, characteristic, complemented
5#11751142C211yesmaximal, characteristic, complemented
6C3×#65327C211yesmaximal, characteristic, complemented
7#11749055C211yesmaximal, characteristic, complemented
8#11749028C211yesmaximal, characteristic, complemented
9#11748965C211yesmaximal, characteristic, complemented
10#11748557C211yesmaximal, characteristic, complemented
11#11748545C211yesmaximal, characteristic, complemented
12#11747502C211yesmaximal, characteristic, complemented
13#11747447C211yesmaximal, characteristic, complemented
14#11747435C211yesmaximal, characteristic, complemented
15#11747321C211yesmaximal, characteristic, complemented
16#10614653—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C2×#6765C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C2×#6716C2211yescharacteristic, complemented
22#91813C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#938C2211yescharacteristic
25C5×#937—21no—
26C5×D4×Dic3—21no—
27C5×#924C2211yescharacteristic
28C5×#897C2211yescharacteristic
29C5×#892C2211yescharacteristic
30C5×#883—21no—
31C5×#67⋊C4—21no—
32C2×C3×#686C2211yescharacteristic, complemented
33C3×#4076C2211yescharacteristic
34C22×C3×#168C2211yescharacteristic
35#91568—21no—
36Dic3×C22⋊D5—21no—
37#91493—24no—
38#91456C2211yescharacteristic
39#91452—21no—
40#91441—21no—
41#91365C2211yescharacteristic
42#91338C2211yescharacteristic
43C2×#6663C2211yescharacteristic, complemented
44C2×#6655C2211yescharacteristic, complemented
45C2×D3×#168—24no—
46C2×D3×#168C2211yescharacteristic
47C2×D3×#168C2211yescharacteristic
48C2×D3×#168C2211yescharacteristic
49C2×D3×#168C2211yescharacteristic
50#91116C2211yescharacteristic, complemented
51#91094C2211yescharacteristic, complemented
52#91092C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×#3941C2211yescharacteristic, complemented
55C3×#3939C2211yescharacteristic, complemented
56#90988C2211yescharacteristic, complemented
57#90986C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90972C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#80714—51nomaximal, Hall
63C5×#525—31no—
64C2×#4096—31no—
65#66125—31no—
66C23×#168—31no—
67#65522—31no—
68#65340—31no—
69#65340—31no—
70#65337—31no—
71#65337—31no—
72#65330—31no—
73#65330—31no—
74#65327—31no—
75#65327D311yescharacteristic, complemented
76#65291—31no—
77#65287—31no—
78C23×C5×D3D411yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×#67—21no—
85C22×C5×Dic3—21no—
86C22×C5×Dic3D411yescharacteristic
87C5×#237—22no—
88C5×#237—22no—
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3D411yescharacteristic
92C2×C4×C5×D3D411yescharacteristic
93C2×C4×C5×D3C2311yescharacteristic
94C2×C4×C5×D3C2311yescharacteristic
95C2×C5×Dic6C2311yescharacteristic
96C2×C3×C22⋊D5—21no—
97C2×C3×D20C2311yescharacteristic
98C2×#1201—21no—
99C2×#1201—21no—
100C2×D5×Dic3—21no—
101#6765—22no—
102#6765—22no—
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105#6719—21no—
106#6716—22no—
107C4⋊Dic15C2311yescharacteristic
108#6712—21no—
109C2×C3⋊#168—22no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217—21no—
113C5×#217—21no—
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×C4⋊Dic3—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C4×C5×Dic3—21no—
120C3×#686—22no—
121C3×#685—21no—
122C3×C4⋊Dic5C2311yescharacteristic
123C2×C3×#168—22no—
124C2×C3×#168C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126#6668—21no—
127(C2×D3)⋊Dic5—21no—
128(C2×D3)⋊Dic5—21no—
129#6665—21no—
130Dic3×Dic5—21no—
131#6663—22no—
132#6655—22no—
133D3×#168—22no—
134D3×#168—22no—
135D3×#168—22no—
136D3×#168D414yescomplemented
137C2×#912—51no—
138C22×D3×C8—51no—
139#5606—51no—
140#5606D511yescharacteristic, complemented
141C3×#466—51no—
142#5157—51no—
143#5116—51no—
144#5041—51no—
145#5041—51no—
146#4887—51no—
147#4880—51no—
148#4778—51no—
149#4778—51no—
150#4772—51no—
151#4772—51no—
152C2×C5×#41—31no—
153C23×C4×C5—31no—
154C2×#709—31no—
155C5×#123—61no—
156C5×C22⋊Q8—31no—
157C5×C22⋊Q8—31no—
158C5×#121—31no—
159C5×#121C2×D311yescharacteristic
160C5×#120—61no—
161C4×C5×D4—61no—
162C4×C5×D4—61no—
163C5×#117—31no—
164#4099—61no—
165#4096—64no—
166C2×#689—31no—
167C2×#688—31no—
168C2×#687—31no—
169C2×#686C2×D311yescharacteristic, complemented
170#4076—31no—
171#4076C2×D311yescharacteristic
172#4075—61no—
173C4×C22⋊D5—61no—
174C4×C22⋊D5—61no—
175#4072—31no—
176#4070—31no—
177#4070—31no—
178C22×#168—31no—
179C22×#168—31no—
180C22×#168—31no—
181C22×#168—31no—
182C22×#168—31no—
183C22×#168—64no—
184C22×#168C2×D311yescharacteristic
185#3967—31no—
186#3967—31no—
187#3964—31no—
188#3964C2×D311yescharacteristic, complemented
189#3942—31no—
190#3942—31no—
191#3941—31no—
192#3941C2×D311yescharacteristic, complemented
193#3940—31no—
194#3940—31no—
195#3939—31no—
196#3939C2×D311yescharacteristic, complemented
197#3050—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×C5×D3—22no—
201C22×C5×D3—22no—
202C22×C5×D3—22no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
206C3×C5×D4—21no—
207C3×C5×D4—21no—
208C3×C5×D4—42no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2411yescharacteristic
214C2×Dic15—21no—
215C2×Dic15—21no—
216Dic30—21no—
217Dic30—21no—
218C5×#67—42no—
219C5×#67—42no—
220C2×C5×Dic3—22no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—42no—
224C2×C5×Dic3C2×D411yescharacteristic
225C2×C5×Dic3C2×D411yescharacteristic
226C4×C5×D3—22no—
227C4×C5×D3—21no—
228C4×C5×D3—21no—
229C4×C5×D3—22no—
230C4×C5×D3C2×D412yes—
231C4×C5×D3#4112yes—
232C5×Dic6—21no—
233C5×Dic6—21no—
234C3×C22⋊D5—42no—
235C2×C3×Dic5—21no—
236C3×D20—21no—
237C3×D20—21no—
238#1201—42no—
239#1201—42no—
240D5×Dic3—42no—
241C3⋊#168—21no—
242C3⋊#168C2×D412yes—
243C3×#168—21no—
244C3×#168C2×D412yes—
245C2×#237—51no—
246C2×#237C2×D511yescharacteristic
247C22×C4×D3C2×D511yescharacteristic
248C2×C3×D8—51no—
249C22×C3×C8—51no—
250C3×#121—51no—
251C3×#121C2×D511yescharacteristic
252#938—51no—
253#938C2×D511yescharacteristic
254#937—21no—
255#937—101no—
256D4×Dic3—21no—
257D4×Dic3—101no—
258C2×#214—51no—
259C2×#214—51no—
260#924—51no—
261#924C2×D511yescharacteristic
262C22×C3⋊C8—51no—
263#912—104no—
264C2×Dic12—51no—
265C2×D3×C8—51no—
266C2×D3×C8—51no—
267C2×D3×C8—51no—
268C2×D3×C8—51no—
269C2×D3×C8—104no—
270#897—51no—
271#897C2×D511yescharacteristic
272#892—51no—
273#892C2×D511yescharacteristic
274#883—21no—
275#883—101no—
276#67⋊C4—21no—
277#67⋊C4—101no—
278C3×#107—51no—
279C3×#102—51no—
280C3×#102—51no—
281#832—51no—
282#832—51no—
283#818—51no—
284#816—51no—
285#816—51no—
286#810—51no—
287#810—51no—
288#808—51no—
289#808—51no—
290C24×C5—31no—
291C5×#41—62no—
292C5×#41—62no—
293C2×C5×Q8—31no—
294C2×C5×D4—21no—
295C2×C5×D4—61no—
296C2×C5×D4—61no—
297C2×C5×D4C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—31no—
300C22×C4×C5—31no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—62no—
304C22×C4×C5—62no—
305C22×C4×C5—61no—
306C22×C4×C5C22×D311yescharacteristic
307C2×C22⋊D5—21no—
308C2×C22⋊D5—61no—
309C2×C22⋊D5—61no—
310#709—62no—
311#709—62no—
312C2×D20C22×D311yescharacteristic
313C2×C4×D5—61no—
314C2×Dic10—31no—
315C5×C4⋊C4—31no—
316C5×C4⋊C4—61no—
317C5×C4⋊C4—61no—
318C5×C4⋊C4C22×D311yescharacteristic
319C5×C22⋊C4—21no—
320C5×C22⋊C4—61no—
321C5×C22⋊C4—61no—
322C5×C22⋊C4—61no—
323C5×C22⋊C4—61no—
324C42×C5—61no—
325C22⋊Dic5—61no—
326C22⋊Dic5—61no—
327C22⋊Dic5—61no—
328#689—62no—
329#688—62no—
330#687—62no—
331#686—22no—
332#685—21no—
333#685—61no—
334C4⋊Dic5—31no—
335C4⋊Dic5C22×D311yescharacteristic
336#683—61no—
337#683—61no—
338C4×Dic5—61no—
339C2×#168—22no—
340C2×#168—31no—
341C2×#168—34no—
342C2×#168—31no—
343C2×#168—62no—
344C2×#168—62no—
345C2×#168—62no—
346C2×#168—62no—
347C2×#168C22×D311yescharacteristic
348C2×#168C22×D311yescharacteristic
349C2×#135—151no—
350C23×C8—151no—
351#525—31no—
352#525—151no—
353#467—151no—
354#467—151no—
355#466—51no—
356#466—151no—
357#465—151no—
358#465—151no—
359#465—151no—
360#465—151no—
361#427—151no—
362#416—151no—
363#416—151no—
364C22×C3×C5—21no—
365C22×C3×C5—21no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5—41no—
369C22×C3×C5#13512yescomplemented
370C22×C3×C5C22×D411yescharacteristic
371C2×C5×D3—28no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3#12112yes—
377C2×C5×D3#13512yescomplemented
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C3×C4×C5—21no—
382C3×C4×C5—41no—
383C3×C4×C5C22×D411yescharacteristic
384C3×C4×C5C2×#4111yescharacteristic
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—41no—
388C5×Dic3—21no—
389C5×Dic3—41no—
390C5×Dic3—41no—
391C5×Dic3#12112yes—
392C23×D3C22⋊D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C2×C3×D4C22×D511yescharacteristic
397C22×C3×C4C22×D511yescharacteristic
398C2×#67—21no—
399C2×#67—21no—
400C2×#67—101no—
401C2×#67—101no—
402C22×Dic3—21no—
403C22×Dic3—101no—
404C22×Dic3C22⋊D511yescharacteristic
405#237—22no—
406#237—22no—
407#237—102no—
408#237—102no—
409C2×C4×D3—22no—
410C2×C4×D3—22no—
411C2×C4×D3C22⋊D511yescharacteristic
412C2×C4×D3C22⋊D511yescharacteristic
413C2×C4×D3C22×D511yescharacteristic
414C2×C4×D3C22×D511yescharacteristic
415C2×Dic6—51no—
416C2×Dic6C22×D511yescharacteristic
417C3×D8—102no—
418C2×C3×C8—51no—
419C2×C3×C8—51no—
420C2×C3×C8—102no—
421C3×C4⋊C4—51no—
422C3×C4⋊C4C22×D511yescharacteristic
423C3×C22⋊C4—21no—
424C3×C22⋊C4—101no—
425#217—21no—
426#217—21no—
427#217—101no—
428#217—101no—
429#214—102no—
430#214—102no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—101no—
434(C2×D3)⋊C4—101no—
435C4⋊Dic3—21no—
436C4⋊Dic3—51no—
437C4⋊Dic3—101no—
438C4⋊Dic3C22×D511yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—101no—
441C4×Dic3—21no—
442C4×Dic3—101no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446Dic12—102no—
447D3×C8—54no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—21no—
452C23×C5—31no—
453C23×C5—31no—
454C23×C5—62no—
455C23×C5—62no—
456C23×C5—62no—
457C23×C5D3×D411yescharacteristic
458C22×D5—21no—
459C5×Q8—61no—
460C5×Q8—61no—
461C5×D4—21no—
462C5×D4—21no—
463C5×D4—42no—
464C5×D4—122no—
465C5×D4—122no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—31no—
470C2×C4×C5—32no—
471C2×C4×C5—32no—
472C2×C4×C5—31no—
473C2×C4×C5—62no—
474C2×C4×C5—62no—
475C2×C4×C5—62no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—122no—
481C2×C4×C5D3×D411yescharacteristic
482C2×C4×C5C23×D311yescharacteristic
483C22⋊D5—42no—
484C22⋊D5—122no—
485C22⋊D5—122no—
486C2×Dic5—21no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489D20—21no—
490D20—21no—
491C4×D5—122no—
492Dic10—61no—
493Dic10—61no—
494#168—21no—
495#168—32no—
496#168—61no—
497#168D3×D412yes—
498C2×#41—31no—
499C2×#41—151no—
500C23×C4—31no—
501#135—304no—
502C2×Q16—151no—
503C2×SD16—151no—
504C2×SD16—151no—
505C2×D8—51no—
506C22×C8—51no—
507C22×C8—151no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—304no—
513#123—61no—
514#123—301no—
515C22⋊Q8—31no—
516C22⋊Q8—31no—
517C22⋊Q8—151no—
518C22⋊Q8—151no—
519#121—31no—
520#121—51no—
521#121—151no—
522#121D3×D511yescharacteristic
523#120—61no—
524#120—301no—
525C4×D4—61no—
526C4×D4—61no—
527C4×D4—301no—
528C4×D4—301no—
529#117—31no—
530#117—151no—
531#107—51no—
532#107—151no—
533#106—151no—
534#106—151no—
535#103—151no—
536#103—151no—
537#103—151no—
538#103—151no—
539#102—51no—
540#102—51no—
541#102—151no—
542#102—151no—
543C2×C3×C5—22no—
544C2×C3×C5—81no—
545C2×C3×C5C2×#12111yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547C2×C3×C5C2×#13511yescharacteristic
548C3×D5—81no—
549C5×D3—22no—
550C5×D3—22no—
551C23×C3—21no—
552C23×C3—101no—
553C23×C3C2×C22⋊D511yescharacteristic
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3C2×C22⋊D511yescharacteristic
558C22×D3C2×C22⋊D511yescharacteristic
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—42no—
562C3×D4—101no—
563C3×D4—101no—
564C3×D4—202no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—101no—
569C2×C3×C4C2×C22⋊D511yescharacteristic
570C2×C3×C4C23×D511yescharacteristic
571#67—42no—
572#67—42no—
573#67—202no—
574#67—202no—
575C2×Dic3—22no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—42no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—202no—
582C2×Dic3C2×C22⋊D511yescharacteristic
583C2×Dic3C2×C22⋊D511yescharacteristic
584C4×D3—22no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—22no—
588C4×D3D4×D512yes—
589C4×D3#71112yes—
590Dic6—21no—
591Dic6—21no—
592Dic6—101no—
593Dic6—101no—
594C3×C8—52no—
595C3×C8—101no—
596C3⋊C8—52no—
597C3⋊C8—101no—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—32no—
601C22×C5—32no—
602C22×C5—41no—
603C22×C5—41no—
604C22×C5—41no—
605C22×C5—68no—
606C22×C5—61no—
607C22×C5—61no—
608C22×C5—61no—
609C22×C5—61no—
610C22×C5#91212yescomplemented
611C22×C5C2×D3×D411yescharacteristic
612C2×D5—41no—
613C2×D5—41no—
614C2×D5—41no—
615C4×C5—21no—
616C4×C5—32no—
617C4×C5—41no—
618C4×C5—61no—
619C4×C5—121no—
620C4×C5—121no—
621C4×C5C2×D3×D411yescharacteristic
622C4×C5D3×#4111yescharacteristic
623Dic5—41no—
624Dic5—121no—
625Dic5—121no—
626C24—31no—
627#41—62no—
628#41—62no—
629#41—302no—
630#41—302no—
631C2×Q8—31no—
632C2×Q8—151no—
633C2×D4—21no—
634C2×D4—51no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—101no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4C2×D3×D511yescharacteristic
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—61no—
649C22×C4—301no—
650C22×C4C2×D3×D511yescharacteristic
651Q16—302no—
652SD16—302no—
653SD16—302no—
654D8—102no—
655C2×C8—51no—
656C2×C8—51no—
657C2×C8—102no—
658C2×C8—154no—
659C2×C8—151no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8—302no—
665C4⋊C4—31no—
666C4⋊C4—51no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—151no—
670C4⋊C4—301no—
671C4⋊C4—301no—
672C4⋊C4C2×D3×D511yescharacteristic
673C22⋊C4—21no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—101no—
679C22⋊C4—301no—
680C22⋊C4—301no—
681C22⋊C4—301no—
682C22⋊C4—301no—
683C42—61no—
684C42—301no—
685C3×C5#305011yescharacteristic, complemented, Hall
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—201no—
692C22×C3—201no—
693C22×C3—201no—
694C22×C3#409612yescomplemented
695C22×C3C22×C22⋊D511yescharacteristic
696C2×D3—28no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3#408512yes—
702C2×D3#409612yescomplemented
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—201no—
706C3×C4C2×D4×D511yescharacteristic
707C3×C4C2×#71111yescharacteristic
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—201no—
712Dic3—201no—
713Dic3#408512yes—
714C2×C5—22no—
715C2×C5—62no—
716C2×C5—62no—
717C2×C5—81no—
718C2×C5D3×#12111yescharacteristic
719C2×C5C2×#91211yescharacteristic
720C2×C5D3×#13511yescharacteristic
721D5—81no—
722C23—21no—
723C23—31no—
724C23—31no—
725C23—62no—
726C23—62no—
727C23—62no—
728C23—101no—
729C23D3×C22⋊D511yescharacteristic
730Q8—61no—
731Q8—61no—
732Q8—301no—
733Q8—301no—
734D4—21no—
735D4—21no—
736D4—42no—
737D4—101no—
738D4—101no—
739D4—122no—
740D4—122no—
741D4—202no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—31no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—31no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—101no—
759C2×C4—122no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—602no—
763C2×C4D3×C22⋊D511yescharacteristic
764C2×C4C22×D3×D511yescharacteristic
765C8—52no—
766C8—101no—
767C8—152no—
768C8—301no—
769C2×C3—22no—
770C2×C3—81no—
771C2×C3—401no—
772C2×C3C2×#408511yescharacteristic
773C2×C3C2×#409611yescharacteristic
774C2×C3C2×#409611yescharacteristic
775D3—22no—
776D3—22no—
777C5#8071411yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—32no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—68no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—201no—
791C22—201no—
792C22—201no—
793C22#9149312yescomplemented
794C22C2×D3×C22⋊D511yescharacteristic
795C4—21no—
796C4—32no—
797C4—41no—
798C4—61no—
799C4—121no—
800C4—121no—
801C4—201no—
802C4—601no—
803C4—601no—
804C4D3×D4×D511yescharacteristic
805C4D3×#71111yescharacteristic
806C3#1061465311yescharacteristic, complemented, Sylow
807C2—22no—
808C2—62no—
809C2—62no—
810C2—81no—
811C2—401no—
812C2C2×#9149311yescharacteristic
813C2D3×#408511yescharacteristic
814C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C5×#5606C2semidirect
2. C2×#91493C2semidirect
3. #11754341C2semidirect
4. C22×D3×#168C2semidirect
5. #11751142C2semidirect
6. C3×#65327C2semidirect
7. #11749055C2semidirect
8. #11749028C2semidirect
9. #11748965C2semidirect
10. #11748557C2semidirect
11. #11748545C2semidirect
12. #11747502C2semidirect
13. #11747447C2semidirect
14. #11747435C2semidirect
15. #11747321C2semidirect
21. C2×#6716C22semidirect
32. C2×C3×#686C22semidirect
43. C2×#6663C22semidirect
44. C2×#6655C22semidirect
50. #91116C22semidirect
51. #91094C22semidirect
52. #91092C22semidirect
53. C3×#3964C22semidirect
54. C3×#3941C22semidirect
55. C3×#3939C22semidirect
56. #90988C22semidirect
57. #90986C22semidirect
58. #90975C22semidirect
59. #90973C22semidirect
60. #90972C22semidirect
61. #90964C22semidirect
75. #65327D3semidirect
136. D3×#168D4semidirect
140. #5606D5semidirect
169. C2×#686C2×D3semidirect
188. #3964C2×D3semidirect
192. #3941C2×D3semidirect
196. #3939C2×D3semidirect
369. C22×C3×C5#135semidirect
377. C2×C5×D3#135semidirect
610. C22×C5#912semidirect
685. C3×C5#3050semidirect
694. C22×C3#4096semidirect
702. C2×D3#4096semidirect
777. C5#80714semidirect
793. C22#91493semidirect
806. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C5×#56062
C2×#914932
#117543412
C22×D3×#1682
#117511422
C3×#653272
#117490552
#117490282
#117489652
#117485572
#117485452
#117475022
#117474472
#117474352
#117473212
#106146533
#807145