Finite Group Databasebeta

← #14453515

Subgroups — #14453515

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D60C211yesmaximal, characteristic, complemented
2C5×#5552C211yesmaximal, characteristic, complemented
3C22×#6660C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5C3×#65300C211yesmaximal, characteristic, complemented
6#11748554C211yesmaximal, characteristic, complemented
7#11748544C211yesmaximal, characteristic, complemented
8#11748525C211yesmaximal, characteristic, complemented
9#11748521C211yesmaximal, characteristic, complemented
10#11748514C211yesmaximal, characteristic, complemented
11#11748456C211yesmaximal, characteristic, complemented
12#11747078C211yesmaximal, characteristic, complemented
13#11747058C211yesmaximal, characteristic, complemented
14#11747046C211yesmaximal, characteristic, complemented
15#11747032C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C2×D4×D15—21no—
18C22×D60C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C2×C5×#235C2211yescharacteristic, complemented
21C22×C5×Dic6C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23#91819C2211yescharacteristic
24#91819C2211yescharacteristic
25#91784—21no—
26#91771—21no—
27#91771—21no—
28#91763C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C5×#939—21no—
31C5×#930C2211yescharacteristic, complemented
32C5×#924C2211yescharacteristic, complemented
33C5×#896—21no—
34C5×#885—21no—
35C5×#67⋊C4—21no—
36C5×#875C2211yescharacteristic, complemented
37C4×C5×Dic6C2211yescharacteristic, complemented
38C2×C3×#681C2211yescharacteristic, complemented
39C22×C3×#168C2211yescharacteristic, complemented
40C2×#6660—24no—
41C2×#6660C2211yescharacteristic
42C2×#6660C2211yescharacteristic
43C2×#6660C2211yescharacteristic, complemented
44C2×#6660C2211yescharacteristic, complemented
45C2×#6660C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic, complemented
47#91305—24no—
48C2×#6654C2211yescharacteristic
49C2×#6654C2211yescharacteristic, complemented
50C2×#6654C2211yescharacteristic, complemented
51C3×C22⋊#168C2211yescharacteristic, complemented
52C3×C22⋊#168C2211yescharacteristic, complemented
53C3×C4⋊#168C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90973C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90969C2211yescharacteristic, complemented
60#90969C2211yescharacteristic, complemented
61#90967C2211yescharacteristic, complemented
62#79494—51nomaximal, Hall
63C5×#548—31no—
64C2×#4095—31no—
65C22×#688—31no—
66D4×D20—31no—
67#65527—31no—
68#65516—31no—
69#65347—31no—
70#65346—31no—
71#65338—31no—
72#65335—31no—
73#65327—31no—
74#65325—31no—
75#65316—31no—
76#65315—31no—
77#65300D311yescharacteristic, complemented
78C23×D15—21no—
79C23×D15—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—21no—
85D4×D15—44no—
86C2×D60—22no—
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—21no—
90C2×D60—21no—
91C2×D60—21no—
92C2×D60—41no—
93C2×D60—41no—
94C2×D60C2311yescharacteristic
95C2×D60C2311yescharacteristic
96C2×D60C2311yescharacteristic
97C2×C4×D15—21no—
98C2×C5×#67—21no—
99C2×C5×#67—21no—
100C22×C5×Dic3—21no—
101C5×#235—22no—
102C5×#235—41no—
103C2×C5×D12C2311yescharacteristic
104C2×C4×C5×D3—21no—
105C2×C5×Dic6—22no—
106C2×C5×Dic6—21no—
107C2×C5×Dic6—41no—
108C2×C5×Dic6C2311yescharacteristic
109C2×C5×Dic6C2311yescharacteristic
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C22⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C42×C5C2311yescharacteristic
114#6714—21no—
115#6714—21no—
116#6714—21no—
117C4⋊Dic15C2311yescharacteristic
118C5×#217—21no—
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×C4⋊Dic3C2311yescharacteristic
123C5×Dic3⋊C4—21no—
124C5×Dic3⋊C4—21no—
125C4×C5×Dic3—21no—
126C3×#681—22no—
127C2×C3×#168—22no—
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131C2×C3×#168C2311yescharacteristic
132#6660—22no—
133#6660—22no—
134#6660—22no—
135#6660—22no—
136#6660—41no—
137#6660D414yescomplemented
138#6654—22no—
139#6654—22no—
140#6654—41no—
141C2×#908—51no—
142C22×#204—51no—
143#5552D511yescharacteristic, complemented
144D4×D12—51no—
145C3×#435—51no—
146#5134—51no—
147#5115—51no—
148#4848—51no—
149#4844—51no—
150#4738—51no—
151#4734—51no—
152#4732—51no—
153#4731—51no—
154#4712—51no—
155#4710—51no—
156C2×C5×#41—31no—
157C22×C5×Q8—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124—31no—
162C5×#124—61no—
163C5×C22⋊Q8—31no—
164C5×C22⋊Q8—61no—
165C5×#121—31no—
166C5×#121—61no—
167C4×C5×Q8—31no—
168C4×C5×D4—61no—
169C4×C5×D4C2×D311yescharacteristic
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4076—31no—
183C2×#681C2×D311yescharacteristic, complemented
184C22×#168C2×D311yescharacteristic, complemented
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020—31no—
189C4×D20—31no—
190#3967—31no—
191#3967—31no—
192#3964—31no—
193C22⋊#168C2×D311yescharacteristic, complemented
194C22⋊#168C2×D311yescharacteristic, complemented
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168C2×D311yescharacteristic, complemented
200#3935C2×D311yescharacteristic, complemented
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—42no—
208C22×D15—42no—
209C22×D15—42no—
210C22×D15—42no—
211C22×D15—81no—
212C22×D15—81no—
213C22×C5×D3—21no—
214C3×C5×D4—22no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224#1220—42no—
225#1220—42no—
226C2×Dic15—21no—
227D60—21no—
228D60—21no—
229D60—21no—
230D60—21no—
231D60—21no—
232D60—42no—
233D60—42no—
234D60—42no—
235D60—81no—
236D60C2×D412yes—
237C4×D15—42no—
238C5×#67—42no—
239C5×#67—42no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3—42no—
244C5×D12—21no—
245C5×D12—21no—
246C4×C5×D3—42no—
247C5×Dic6—21no—
248C5×Dic6—21no—
249C5×Dic6—21no—
250C5×Dic6—42no—
251C5×Dic6C2×D412yescomplemented
252C3×#168—21no—
253C3×#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×D3×D4—101no—
257C2×#235C2×D511yescharacteristic, complemented
258C22×D12—51no—
259C22×D12—51no—
260C22×Dic6C2×D511yescharacteristic, complemented
261C2×C3×M16—51no—
262C22×C3×C8—51no—
263C3×C4×D4C2×D511yescharacteristic
264#939—21no—
265#930—51no—
266#930—51no—
267#930C2×D511yescharacteristic, complemented
268#924C2×D511yescharacteristic, complemented
269#908—104no—
270C2×D24—51no—
271C2×D24—51no—
272C2×D24—51no—
273C2×#204—51no—
274C2×#204—51no—
275C2×#204—51no—
276C2×#204—51no—
277C2×#204—51no—
278C2×#204—51no—
279C2×#204—104no—
280#896—21no—
281#895—101no—
282#885—21no—
283#882—101no—
284#882—101no—
285#67⋊C4—21no—
286#875C2×D511yescharacteristic, complemented
287#874—51no—
288C4×D12—51no—
289C4×Dic6C2×D511yescharacteristic, complemented
290C3×C4⋊C8—51no—
291C3×C22⋊C8—51no—
292C3×C22⋊C8—51no—
293C3×#97—51no—
294#821—51no—
295#821—51no—
296#821—51no—
297#821—51no—
298#818—51no—
299#816—51no—
300#816—51no—
301C23×D5—61no—
302C23×D5—61no—
303C5×#41—62no—
304C5×#41—121no—
305C2×C5×Q8—31no—
306C2×C5×Q8—31no—
307C2×C5×Q8—62no—
308C2×C5×Q8—61no—
309C2×C5×Q8—121no—
310C2×C5×D4—31no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4D1211yescharacteristic
314C22×C4×C5—61no—
315C22×C4×C5—61no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320D4×D5—124no—
321C2×D20—31no—
322C2×D20—31no—
323C2×D20—31no—
324C2×D20—62no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—61no—
329C2×D20—61no—
330C2×D20—121no—
331C2×D20—121no—
332C2×C4×D5—61no—
333C5×C4⋊C4—31no—
334C5×C4⋊C4—61no—
335C5×C4⋊C4—61no—
336C5×C4⋊C4D1211yescharacteristic
337C5×C22⋊C4—61no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C5×C22⋊C4—61no—
341C5×C22⋊C4D1211yescharacteristic
342C5×C22⋊C4D1211yescharacteristic
343C42×C5—61no—
344C42×C5C22×D311yescharacteristic
345#688—34no—
346#688—62no—
347#688—62no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—62no—
352#686—62no—
353#686—121no—
354#685—61no—
355#685—61no—
356#685—61no—
357C4⋊Dic5—31no—
358#681—22no—
359C2×#168—22no—
360C2×#168C22×D311yescharacteristic
361C2×#168C22×D311yescharacteristic
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—31no—
367D42—151no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—51no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5AGL(1,ℤ/8)12yescomplemented
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—84no—
396C2×D15—84no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406Dic15—41no—
407C5×Dic3—22no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C23×D3—101no—
411C23×D3—101no—
412C2×C3×D4C22⋊D511yescharacteristic
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C2×#67—21no—
416C2×#67—21no—
417C2×#67—101no—
418C2×#67—101no—
419C22×Dic3—21no—
420D3×D4—204no—
421#235—22no—
422#235—41no—
423C2×D12—51no—
424C2×D12—51no—
425C2×D12—51no—
426C2×D12—102no—
427C2×D12—102no—
428C2×D12—101no—
429C2×D12—101no—
430C2×D12—101no—
431C2×D12—101no—
432C2×D12—201no—
433C2×D12—201no—
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—101no—
437C2×Dic6—22no—
438C2×Dic6—21no—
439C2×Dic6—41no—
440C2×Dic6C22×D511yescharacteristic
441C2×Dic6C22×D511yescharacteristic
442C3×M16—102no—
443C2×C3×C8—51no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C2×C3×C8—51no—
447C2×C3×C8—102no—
448C3×C4⋊C4C22⋊D511yescharacteristic
449C3×C22⋊C4C22⋊D511yescharacteristic
450C3×C22⋊C4C22⋊D511yescharacteristic
451C3×C42C22×D511yescharacteristic
452#217—21no—
453(C2×D3)⋊C4—21no—
454(C2×D3)⋊C4—21no—
455(C2×D3)⋊C4—21no—
456(C2×D3)⋊C4—101no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459C4⋊Dic3—51no—
460C4⋊Dic3C22×D511yescharacteristic
461Dic3⋊C4—21no—
462Dic3⋊C4—21no—
463C4×Dic3—21no—
464D24—102no—
465D24—102no—
466D24—201no—
467#204—54no—
468#204—102no—
469#204—102no—
470#204—102no—
471#204—102no—
472#204—201no—
473C23×C5—61no—
474C23×C5C2×D1211yescharacteristic
475C23×C5C2×D1211yescharacteristic
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—122no—
480C22×D5—122no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5—241no—
485C5×Q8—32no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—61no—
489C5×Q8—122no—
490C5×D4—22no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—122no—
494C5×D4—122no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5—122no—
503C2×C4×C5—122no—
504C2×C4×C5C2×D1211yescharacteristic
505C2×C4×C5C2×D1211yescharacteristic
506C2×C4×C5C2×D1211yescharacteristic
507C2×C4×C5C2×D1211yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—61no—
512D20—32no—
513D20—61no—
514D20—61no—
515D20—61no—
516D20—61no—
517D20—61no—
518D20—122no—
519D20—122no—
520D20—122no—
521D20—241no—
522C4×D5—122no—
523#168—21no—
524#168—21no—
525#168—21no—
526#168D3×D412yescomplemented
527C2×#41—31no—
528C22×Q8—31no—
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—51no—
544C22×C8—51no—
545#127—151no—
546#124—31no—
547#124—61no—
548C22⋊Q8—31no—
549C22⋊Q8—61no—
550#121—31no—
551#121—61no—
552#121—151no—
553#121—151no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—31no—
558C4×D4—61no—
559C4×D4—151no—
560C4×D4D3×D511yescharacteristic
561#107—151no—
562C4⋊C8—51no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577D15—42no—
578D15—81no—
579D15—81no—
580C5×D3—81no—
581C23×C3C2×C22⋊D511yescharacteristic
582C23×C3C2×C22⋊D511yescharacteristic
583C22×D3—21no—
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3—401no—
593C3×D4—22no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4C2×C22⋊D511yescharacteristic
599C2×C3×C4C2×C22⋊D511yescharacteristic
600C2×C3×C4C2×C22⋊D511yescharacteristic
601C2×C3×C4C2×C22⋊D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603#67—42no—
604#67—42no—
605#67—202no—
606#67—202no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—42no—
611C2×Dic3—101no—
612D12—21no—
613D12—21no—
614D12—52no—
615D12—101no—
616D12—101no—
617D12—101no—
618D12—101no—
619D12—101no—
620D12—202no—
621D12—202no—
622D12—202no—
623D12—401no—
624C4×D3—42no—
625C4×D3—202no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630Dic6D4×D512yescomplemented
631C3×C8—52no—
632C3×C8—101no—
633C3×C8—101no—
634C3×C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5—121no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5#90812yescomplemented
644C22×C5C22×D1211yescharacteristic
645C2×D5—62no—
646C2×D5—121no—
647C2×D5—121no—
648C2×D5—121no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—62no—
661C4×C5—121no—
662C4×C5—121no—
663C4×C5C2×D3×D411yescharacteristic
664C4×C5#100911yescharacteristic
665Dic5—121no—
666C24—301no—
667C24—301no—
668#41—62no—
669#41—121no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×Q8—62no—
673C2×Q8—61no—
674C2×Q8—121no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—151no—
679C2×D4—151no—
680C2×D4—151no—
681C2×D4—302no—
682C2×D4—302no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—301no—
689C2×D4—601no—
690C2×D4—601no—
691C2×D4—604no—
692C2×D4#120311yescharacteristic
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—301no—
696C22×C4C2×D3×D511yescharacteristic
697C22×C4C2×D3×D511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—102no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—51no—
711C2×C8—51no—
712C2×C8—102no—
713C4⋊C4—31no—
714C4⋊C4—61no—
715C4⋊C4—61no—
716C4⋊C4—151no—
717C4⋊C4#120311yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4#120311yescharacteristic
726C22⋊C4#120311yescharacteristic
727C42—61no—
728C42C2×D3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3#409512yescomplemented
736C22×C3C22×C22⋊D511yescharacteristic
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—102no—
741C2×D3—201no—
742C2×D3—201no—
743C2×D3—201no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—404no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4C2×D4×D511yescharacteristic
756C3×C4#414411yescharacteristic
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—241no—
764C2×C5D4×D1211yescharacteristic
765C2×C5C2×#90811yescharacteristic
766C2×C5#575111yescharacteristic
767D5—122no—
768D5—241no—
769D5—241no—
770C23—61no—
771C23—301no—
772C23—301no—
773C23—301no—
774C23—602no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—1201no—
779C23—1201no—
780C23C2×#120311yescharacteristic
781C23C2×#120311yescharacteristic
782Q8—32no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—122no—
787D4—22no—
788D4—61no—
789D4—61no—
790D4—122no—
791D4—122no—
792D4—152no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—301no—
797D4—301no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—301no—
814C2×C4—602no—
815C2×C4C2×#120311yescharacteristic
816C2×C4C2×#120311yescharacteristic
817C2×C4C2×#120311yescharacteristic
818C2×C4C2×#120311yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—101no—
823C8—101no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3D4×C22⋊D511yescharacteristic
827C2×C3C2×#409511yescharacteristic
828C2×C3#6617111yescharacteristic
829D3—81no—
830D3—202no—
831D3—401no—
832D3—401no—
833C5#7949411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—302no—
843C22—601no—
844C22—601no—
845C22—601no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9130512yescomplemented
854C22C22×#120311yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—62no—
860C4—121no—
861C4—121no—
862C4—601no—
863C4D3×D4×D511yescharacteristic
864C4#9202711yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—241no—
869C2—602no—
870C2—1201no—
871C2—1201no—
872C2C2×#9130511yescharacteristic
873C2D4×#120311yescharacteristic
874C2#1175530811yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×D60C2semidirect
2. C5×#5552C2semidirect
3. C22×#6660C2semidirect
4. C2×#91305C2semidirect
5. C3×#65300C2semidirect
6. #11748554C2semidirect
7. #11748544C2semidirect
8. #11748525C2semidirect
9. #11748521C2semidirect
10. #11748514C2semidirect
11. #11748456C2semidirect
12. #11747078C2semidirect
13. #11747058C2semidirect
14. #11747046C2semidirect
15. #11747032C2semidirect
20. C2×C5×#235C22semidirect
21. C22×C5×Dic6C22semidirect
31. C5×#930C22semidirect
32. C5×#924C22semidirect
36. C5×#875C22semidirect
37. C4×C5×Dic6C22semidirect
38. C2×C3×#681C22semidirect
39. C22×C3×#168C22semidirect
43. C2×#6660C22semidirect
44. C2×#6660C22semidirect
45. C2×#6660C22semidirect
46. C2×#6660C22semidirect
49. C2×#6654C22semidirect
50. C2×#6654C22semidirect
51. C3×C22⋊#168C22semidirect
52. C3×C22⋊#168C22semidirect
53. C3×C4⋊#168C22semidirect
54. C3×#3935C22semidirect
55. #90988C22semidirect
56. #90973C22semidirect
57. #90973C22semidirect
59. #90969C22semidirect
60. #90969C22semidirect
61. #90967C22semidirect
77. #65300D3semidirect
137. #6660D4semidirect
143. #5552D5semidirect
183. C2×#681C2×D3semidirect
184. C22×#168C2×D3semidirect
193. C22⋊#168C2×D3semidirect
194. C22⋊#168C2×D3semidirect
199. C4⋊#168C2×D3semidirect
200. #3935C2×D3semidirect
251. C5×Dic6C2×D4semidirect
255. C3×#168C2×D4semidirect
257. C2×#235C2×D5semidirect
260. C22×Dic6C2×D5semidirect
267. #930C2×D5semidirect
268. #924C2×D5semidirect
286. #875C2×D5semidirect
289. C4×Dic6C2×D5semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
526. #168D3×D4semidirect
630. Dic6D4×D5semidirect
643. C22×C5#908semidirect
729. C3×C5#3265semidirect
735. C22×C3#4095semidirect
833. C5#79494semidirect
853. C22#91305semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
D4×D602
C5×#55522
C22×#66602
C2×#913052
C3×#653002
#117485542
#117485442
#117485252
#117485212
#117485142
#117484562
#117470782
#117470582
#117470462
#117470322
#106152733
#794945