Finite Group Databasebeta

← #14427827

Subgroups — #14427827

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×#5627C211yesmaximal, characteristic, complemented
2C2×#91517C211yesmaximal, characteristic, complemented
3#11754341C211yesmaximal, characteristic, complemented
4C22×D3×#168C211yesmaximal, characteristic, complemented
5#11751152C211yesmaximal, characteristic, complemented
6C3×#65337C211yesmaximal, characteristic, complemented
7#11749301C211yesmaximal, characteristic, complemented
8#11749274C211yesmaximal, characteristic, complemented
9#11749211C211yesmaximal, characteristic, complemented
10#11748533C211yesmaximal, characteristic, complemented
11#11748522C211yesmaximal, characteristic, complemented
12#11747502C211yesmaximal, characteristic, complemented
13#11747448C211yesmaximal, characteristic, complemented
14#11747437C211yesmaximal, characteristic, complemented
15#11747319C211yesmaximal, characteristic, complemented
16#10614653—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C22×C4×C5×D3C2211yescharacteristic
19C2×#6765C2211yescharacteristic
20C3×C5×C22⋊Q8C2211yescharacteristic
21C2×#6718C2211yescharacteristic, complemented
22#91813C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C5×#946C2211yescharacteristic
25C5×#930C2211yescharacteristic
26C5×#895C2211yescharacteristic
27C5×#894—21no—
28C5×#893—21no—
29C5×#892C2211yescharacteristic
30C5×#882—21no—
31C5×#67⋊C4—21no—
32C2×C3×#688C2211yescharacteristic, complemented
33C3×#4076C2211yescharacteristic
34C22×C3×#168C2211yescharacteristic
35#91568—21no—
36Dic3×C22⋊D5—21no—
37#91517—24no—
38#91456C2211yescharacteristic
39#91452—21no—
40#91441—21no—
41#91365C2211yescharacteristic
42#91338C2211yescharacteristic
43C2×#6659C2211yescharacteristic, complemented
44C2×#6652C2211yescharacteristic, complemented
45C2×D3×#168—24no—
46C2×D3×#168C2211yescharacteristic
47C2×D3×#168C2211yescharacteristic
48C2×D3×#168C2211yescharacteristic
49C2×D3×#168C2211yescharacteristic
50#91119C2211yescharacteristic, complemented
51#91094C2211yescharacteristic, complemented
52#91091C2211yescharacteristic, complemented
53C3×#3967C2211yescharacteristic, complemented
54C3×#3941C2211yescharacteristic, complemented
55C3×#3940C2211yescharacteristic, complemented
56#90989C2211yescharacteristic, complemented
57#90985C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60#90966C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#80656—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#65337D311yescharacteristic, complemented
72#65330—31no—
73#65330—31no—
74#65327—31no—
75#65327—31no—
76#65291—31no—
77#65287—31no—
78C23×C5×D3D411yescharacteristic
79C2×C3×C5×Q8C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C22×C5×Dic3D411yescharacteristic
84C5×#239—22no—
85C5×#239—22no—
86C2×C5×D12—21no—
87C2×C5×D12—21no—
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—22no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3D411yescharacteristic
93C2×C4×C5×D3D411yescharacteristic
94C2×C4×C5×D3C2311yescharacteristic
95C2×C4×C5×D3C2311yescharacteristic
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⋊C4—21no—
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106#6719—21no—
107#6718—22no—
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110C2×C3⋊#168—22no—
111C2×C3⋊#168C2311yescharacteristic
112C2×C3⋊#168C2311yescharacteristic
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C4×C5×Dic3—21no—
120C3×#688—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#6659—22no—
132#6652—22no—
133D3×#168—22no—
134D3×#168—22no—
135D3×#168—22no—
136D3×#168D414yescomplemented
137C2×#916—51no—
138C22×D3×C8—51no—
139#5627D511yescharacteristic, complemented
140#5606—51no—
141C3×#465—51no—
142#5171—51no—
143#5114—51no—
144#5051—51no—
145#5038—51no—
146#4864—51no—
147#4860—51no—
148#4813—51no—
149#4804—51no—
150#4775—51no—
151#4772—51no—
152C2×C5×#41—31no—
153C23×C4×C5—31no—
154C2×#709—31no—
155C5×#123—61no—
156C5×C22⋊Q8—31no—
157C5×C22⋊Q8C2×D311yescharacteristic
158C5×#121—31no—
159C5×#121—31no—
160C5×#120—61no—
161C4×C5×D4—61no—
162C4×C5×D4—61no—
163C5×#117—31no—
164#4099—61no—
165#4096—64no—
166C2×#689—31no—
167C2×#688C2×D311yescharacteristic, complemented
168C2×#687—31no—
169C2×#686—31no—
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#3967C2×D311yescharacteristic, complemented
187#3964—31no—
188#3964—31no—
189#3942—31no—
190#3942—31no—
191#3941—31no—
192#3941C2×D311yescharacteristic, complemented
193#3940—31no—
194#3940C2×D311yescharacteristic, complemented
195#3939—31no—
196#3939—31no—
197#3050—151noSylow
198C23×C3×C5C2×D411yescharacteristic
199C22×C5×D3—22no—
200C22×C5×D3—22no—
201C22×C5×D3—22no—
202C22×C5×D3—21no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
206C3×C5×Q8—21no—
207C3×C5×Q8—21no—
208C2×C3×C4×C5—21no—
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—
219C2×C5×Dic3—22no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C2×D411yescharacteristic
222C2×C5×Dic3C2×D411yescharacteristic
223C5×D12—21no—
224C5×D12—21no—
225C5×D12—42no—
226C5×D12—42no—
227C4×C5×D3—22no—
228C4×C5×D3—21no—
229C4×C5×D3—21no—
230C4×C5×D3—22no—
231C4×C5×D3—42no—
232C4×C5×D3C2×D412yes—
233C4×C5×D3#4112yes—
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×#239C2×D511yescharacteristic
246C2×#237—51no—
247C22×C4×D3C2×D511yescharacteristic
248C2×C3×SD16—51no—
249C22×C3×C8—51no—
250C3×C22⋊Q8C2×D511yescharacteristic
251C3×#121—51no—
252#946C2×D511yescharacteristic
253C2×#216—51no—
254#938—51no—
255#937—101no—
256D4×Dic3—101no—
257C2×#213—51no—
258#930C2×D511yescharacteristic
259#924—51no—
260C22×C3⋊C8—51no—
261#916—104no—
262C2×#204—51no—
263C2×D3×C8—51no—
264C2×D3×C8—51no—
265C2×D3×C8—51no—
266C2×D3×C8—51no—
267C2×D3×C8—104no—
268#897—51no—
269#895C2×D511yescharacteristic
270#894—21no—
271#893—21no—
272#892—51no—
273#892C2×D511yescharacteristic
274#883—101no—
275#882—21no—
276#67⋊C4—21no—
277#67⋊C4—101no—
278C3×#106—51no—
279C3×#103—51no—
280C3×#102—51no—
281#835—51no—
282#832—51no—
283#821—51no—
284#817—51no—
285#816—51no—
286#810—51no—
287#809—51no—
288#807—51no—
289#807—51no—
290C24×C5—31no—
291C5×#41—62no—
292C5×#41—62no—
293C2×C5×Q8C22×D311yescharacteristic
294C2×C5×D4—31no—
295C2×C5×D4—61no—
296C2×C5×D4—61no—
297C2×C5×D4—61no—
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—21no—
316C5×C4⋊C4—31no—
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—22no—
330#687—62no—
331#686—62no—
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—151no—
356#466—151no—
357#465—51no—
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#13512yescomplemented
367C22×C3×C5C22×D411yescharacteristic
368C2×C5×D3—28no—
369C2×C5×D3—21no—
370C2×C5×D3—21no—
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3—41no—
374C2×C5×D3—41no—
375C2×C5×D3—41no—
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×C5—41no—
384C3×C4×C5C22×D411yescharacteristic
385C3×C4×C5C2×#4111yescharacteristic
386Dic15—41no—
387Dic15—41no—
388C3×Dic5—41no—
389C5×Dic3—21no—
390C5×Dic3—41no—
391C5×Dic3#12112yes—
392C23×D3C22⋊D511yescharacteristic
393C2×C3×Q8C22×D511yescharacteristic
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C22×C3×C4C22×D511yescharacteristic
397C2×#67—21no—
398C2×#67—101no—
399C2×#67—101no—
400C22×Dic3—101no—
401C22×Dic3C22⋊D511yescharacteristic
402#239—22no—
403#239—22no—
404#237—102no—
405#237—102no—
406C2×D12—21no—
407C2×D12—21no—
408C2×D12C22×D511yescharacteristic
409C2×C4×D3—22no—
410C2×C4×D3—22no—
411C2×C4×D3—21no—
412C2×C4×D3C22⋊D511yescharacteristic
413C2×C4×D3C22⋊D511yescharacteristic
414C2×C4×D3C22×D511yescharacteristic
415C2×C4×D3C22×D511yescharacteristic
416C2×Dic6—51no—
417C3×SD16—102no—
418C2×C3×C8—51no—
419C2×C3×C8—51no—
420C2×C3×C8—102no—
421C3×C4⋊C4—21no—
422C3×C4⋊C4—51no—
423C3×C4⋊C4C22×D511yescharacteristic
424C3×C22⋊C4—21no—
425C3×C22⋊C4—101no—
426#217—101no—
427#217—101no—
428#216—102no—
429#213—102no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
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—
446#204—102no—
447D3×C8—54no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—31no—
452C23×C5—31no—
453C23×C5—62no—
454C23×C5—62no—
455C23×C5—62no—
456C23×C5—61no—
457C23×C5D3×D411yescharacteristic
458C22×D5—21no—
459C5×Q8—21no—
460C5×Q8—21no—
461C5×D4—61no—
462C5×D4—61no—
463C5×D4—122no—
464C5×D4—122no—
465C5×D4—122no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—31no—
471C2×C4×C5—32no—
472C2×C4×C5—32no—
473C2×C4×C5—31no—
474C2×C4×C5—62no—
475C2×C4×C5—62no—
476C2×C4×C5—62no—
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—51no—
504C2×SD16—151no—
505C2×D8—151no—
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—151no—
517C22⋊Q8—151no—
518C22⋊Q8D3×D511yescharacteristic
519#121—31no—
520#121—31no—
521#121—51no—
522#121—151no—
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—151no—
532#107—151no—
533#106—51no—
534#106—151no—
535#103—51no—
536#103—151no—
537#103—151no—
538#103—151no—
539#102—51no—
540#102—151no—
541#102—151no—
542#102—151no—
543C2×C3×C5—22no—
544C2×C3×C5C2×#12111yescharacteristic
545C2×C3×C5C2×#13511yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547C3×D5—81no—
548C5×D3—22no—
549C5×D3—22no—
550C5×D3—81no—
551C23×C3—101no—
552C23×C3C2×C22⋊D511yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—21no—
557C22×D3C2×C22⋊D511yescharacteristic
558C22×D3C2×C22⋊D511yescharacteristic
559C3×Q8—21no—
560C3×Q8—21no—
561C3×D4—101no—
562C3×D4—101no—
563C3×D4—202no—
564C2×C3×C4—21no—
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—202no—
573#67—202no—
574C2×Dic3—22no—
575C2×Dic3—21no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—202no—
579C2×Dic3C2×C22⋊D511yescharacteristic
580C2×Dic3C2×C22⋊D511yescharacteristic
581D12—21no—
582D12—21no—
583D12—42no—
584D12—42no—
585C4×D3—22no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—22no—
589C4×D3—42no—
590C4×D3D4×D512yes—
591C4×D3#71112yes—
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—68no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5—61no—
607C22×C5—121no—
608C22×C5—121no—
609C22×C5—121no—
610C22×C5#91612yescomplemented
611C22×C5C2×D3×D411yescharacteristic
612C2×D5—41no—
613C2×D5—41no—
614C2×D5—41no—
615C4×C5—21no—
616C4×C5—32no—
617C4×C5—41no—
618C4×C5—41no—
619C4×C5—61no—
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—151no—
632C2×Q8C2×D3×D511yescharacteristic
633C2×D4—31no—
634C2×D4—51no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—101no—
639C2×D4—301no—
640C2×D4—301no—
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—102no—
653SD16—302no—
654D8—302no—
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—21no—
666C4⋊C4—31no—
667C4⋊C4—51no—
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—201no—
689C22×C3—201no—
690C22×C3—201no—
691C22×C3#409612yescomplemented
692C22×C3C22×C22⋊D511yescharacteristic
693C2×D3—28no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3#408512yes—
702C2×D3#409612yescomplemented
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—201no—
707C3×C4C2×D4×D511yescharacteristic
708C3×C4C2×#71111yescharacteristic
709Dic3—21no—
710Dic3—41no—
711Dic3—201no—
712Dic3—201no—
713Dic3#408512yes—
714C2×C5—22no—
715C2×C5—62no—
716C2×C5—62no—
717C2×C5—241no—
718C2×C5D3×#12111yescharacteristic
719C2×C5C2×#91611yescharacteristic
720C2×C5D3×#13511yescharacteristic
721D5—81no—
722C23—31no—
723C23—31no—
724C23—62no—
725C23—62no—
726C23—62no—
727C23—61no—
728C23—101no—
729C23D3×C22⋊D511yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—301no—
733Q8—301no—
734D4—61no—
735D4—61no—
736D4—101no—
737D4—101no—
738D4—122no—
739D4—122no—
740D4—122no—
741D4—202no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—31no—
749C2×C4—32no—
750C2×C4—32no—
751C2×C4—31no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
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—401no—
771C2×C3C2×#408511yescharacteristic
772C2×C3C2×#409611yescharacteristic
773C2×C3C2×#409611yescharacteristic
774D3—22no—
775D3—22no—
776D3—81no—
777C5#8065611yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—32no—
782C22—68no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—201no—
791C22—201no—
792C22—201no—
793C22#9151712yescomplemented
794C22C2×D3×C22⋊D511yescharacteristic
795C4—21no—
796C4—32no—
797C4—41no—
798C4—41no—
799C4—61no—
800C4—121no—
801C4—201no—
802C4—601no—
803C4—601no—
804C4D3×D4×D511yescharacteristic
805C4D3×#71111yescharacteristic
806C3#1061465311yescharacteristic, complemented, Sylow
807C2—22no—
808C2—62no—
809C2—62no—
810C2—241no—
811C2—401no—
812C2D3×#408511yescharacteristic
813C2C2×#9151711yescharacteristic
814C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3050
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×#5627C2semidirect
2. C2×#91517C2semidirect
3. #11754341C2semidirect
4. C22×D3×#168C2semidirect
5. #11751152C2semidirect
6. C3×#65337C2semidirect
7. #11749301C2semidirect
8. #11749274C2semidirect
9. #11749211C2semidirect
10. #11748533C2semidirect
11. #11748522C2semidirect
12. #11747502C2semidirect
13. #11747448C2semidirect
14. #11747437C2semidirect
15. #11747319C2semidirect
21. C2×#6718C22semidirect
32. C2×C3×#688C22semidirect
43. C2×#6659C22semidirect
44. C2×#6652C22semidirect
50. #91119C22semidirect
51. #91094C22semidirect
52. #91091C22semidirect
53. C3×#3967C22semidirect
54. C3×#3941C22semidirect
55. C3×#3940C22semidirect
56. #90989C22semidirect
57. #90985C22semidirect
58. #90975C22semidirect
59. #90967C22semidirect
60. #90966C22semidirect
61. #90964C22semidirect
71. #65337D3semidirect
136. D3×#168D4semidirect
139. #5627D5semidirect
167. C2×#688C2×D3semidirect
186. #3967C2×D3semidirect
192. #3941C2×D3semidirect
194. #3940C2×D3semidirect
366. C22×C3×C5#135semidirect
377. C2×C5×D3#135semidirect
610. C22×C5#916semidirect
685. C3×C5#3050semidirect
691. C22×C3#4096semidirect
702. C2×D3#4096semidirect
777. C5#80656semidirect
793. C22#91517semidirect
806. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C5×#56272
C2×#915172
#117543412
C22×D3×#1682
#117511522
C3×#653372
#117493012
#117492742
#117492112
#117485332
#117485222
#117475022
#117474482
#117474372
#117473192
#106146533
#806565