Finite Group Databasebeta

← #14453517

Subgroups — #14453517

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
1#11756311C211yesmaximal, characteristic, complemented
2C5×D4×D12C211yesmaximal, characteristic, complemented
3C22×#6659C211yesmaximal, characteristic, complemented
4C2×#91304C211yesmaximal, characteristic, complemented
5C3×#65300C211yesmaximal, characteristic, complemented
6#11748553C211yesmaximal, characteristic, complemented
7#11748543C211yesmaximal, characteristic, complemented
8#11748534C211yesmaximal, characteristic, complemented
9#11748526C211yesmaximal, characteristic, complemented
10#11748520C211yesmaximal, characteristic, complemented
11#11748514C211yesmaximal, characteristic, complemented
12#11747086C211yesmaximal, characteristic, complemented
13#11747056C211yesmaximal, characteristic, complemented
14#11747038C211yesmaximal, characteristic, complemented
15#11747031C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C2×#6817C2211yescharacteristic, complemented
18C22×Dic30C2211yescharacteristic, complemented
19C2×C5×D3×D4—21no—
20C22×C5×D12C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic
23#91828—21no—
24#91819C2211yescharacteristic, complemented
25#91813C2211yescharacteristic, complemented
26#91785—21no—
27#91774—21no—
28#91770—21no—
29#91764C2211yescharacteristic, complemented
30C4×Dic30C2211yescharacteristic, complemented
31C5×#930C2211yescharacteristic
32C5×#930C2211yescharacteristic
33C5×#895—21no—
34C5×#882—21no—
35C5×#882—21no—
36C5×#874C2211yescharacteristic
37C4×C5×D12C2211yescharacteristic
38C2×C3×#681C2211yescharacteristic, complemented
39C22×C3×#168C2211yescharacteristic, complemented
40C2×#6659—24no—
41C2×#6659C2211yescharacteristic
42C2×#6659C2211yescharacteristic
43C2×#6659C2211yescharacteristic, complemented
44C2×#6659C2211yescharacteristic, complemented
45C2×#6659C2211yescharacteristic, complemented
46C2×#6659C2211yescharacteristic, complemented
47#91304—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#90975C2211yescharacteristic, complemented
57#90975C2211yescharacteristic, complemented
58#90969C2211yescharacteristic, complemented
59#90967C2211yescharacteristic
60#90967C2211yescharacteristic, complemented
61#90967C2211yescharacteristic, complemented
62#79494—51nomaximal, Hall
63C5×D42—31no—
64C22×#687—31no—
65C2×#4078—31no—
66#65886—31no—
67#65507—31no—
68#65506—31no—
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326—31no—
75#65307—31no—
76#65305—31no—
77#65300D311yescharacteristic, complemented
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—21no—
85C22×Dic15—21no—
86#6817—22no—
87#6817—41no—
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×Dic30—22no—
91C2×Dic30—21no—
92C2×Dic30—41no—
93C2×Dic30C2311yescharacteristic
94C2×Dic30C2311yescharacteristic
95C2×C5×#67—21no—
96C2×C5×#67—21no—
97C5×D3×D4—44no—
98C2×C5×D12—22no—
99C2×C5×D12—22no—
100C2×C5×D12—21no—
101C2×C5×D12—21no—
102C2×C5×D12—21no—
103C2×C5×D12—21no—
104C2×C5×D12—41no—
105C2×C5×D12—41no—
106C2×C5×D12C2311yescharacteristic
107C2×C5×D12C2311yescharacteristic
108C2×C5×D12C2311yescharacteristic
109C2×C4×C5×D3—21no—
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C22⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C42×C5C2311yescharacteristic
114#6719—21no—
115#6714—21no—
116#6714—21no—
117#6714—21no—
118C4⋊Dic15C2311yescharacteristic
119#6712—21no—
120#6712—21no—
121C4×Dic15—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4—21no—
124C5×(C2×D3)⋊C4—21no—
125C5×C4⋊Dic3C2311yescharacteristic
126C3×#681—22no—
127C2×C3×#168—22no—
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131C2×C3×#168C2311yescharacteristic
132#6659—22no—
133#6659—22no—
134#6659—22no—
135#6659—22no—
136#6659—41no—
137#6659D414yescomplemented
138#6654—22no—
139#6654—22no—
140#6654—41no—
141C2×#908—51no—
142C22×#204—51no—
143#5552—51no—
144D4×D12D511yescharacteristic, complemented
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—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709—31no—
160C22×Dic10—31no—
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4C2×D311yescharacteristic
169#4085—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—64no—
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4070—31no—
183C2×#681C2×D311yescharacteristic, complemented
184C22×#168C2×D311yescharacteristic, complemented
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168C2×D311yescharacteristic, complemented
194C22⋊#168C2×D311yescharacteristic, complemented
195#3942—31no—
196#3942—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×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3—42no—
209C22×C5×D3—42no—
210C22×C5×D3—42no—
211C22×C5×D3—42no—
212C22×C5×D3—81no—
213C22×C5×D3—81no—
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—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—42no—
230D60—21no—
231D60—21no—
232C4×D15—42no—
233Dic30—21no—
234Dic30—21no—
235Dic30—21no—
236Dic30—42no—
237Dic30C2×D412yescomplemented
238C5×#67—42no—
239C5×#67—42no—
240C2×C5×Dic3—21no—
241C5×D12—21no—
242C5×D12—21no—
243C5×D12—21no—
244C5×D12—21no—
245C5×D12—21no—
246C5×D12—42no—
247C5×D12—42no—
248C5×D12—42no—
249C5×D12—81no—
250C5×D12C2×D412yes—
251C4×C5×D3—42no—
252C3×#168—21no—
253C3×#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×D3×D4—21no—
257C2×#235—51no—
258C22×D12C2×D511yescharacteristic
259C22×D12C2×D511yescharacteristic
260C22×Dic6—51no—
261C2×C3×M16—51no—
262C22×C3×C8—51no—
263C3×C4×D4C2×D511yescharacteristic
264#939—101no—
265#930—51no—
266#930C2×D511yescharacteristic
267#930C2×D511yescharacteristic
268#924—51no—
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—101no—
281#895—21no—
282#885—101no—
283#882—21no—
284#882—21no—
285#67⋊C4—101no—
286#875—51no—
287#874C2×D511yescharacteristic
288C4×D12C2×D511yescharacteristic
289C4×Dic6—51no—
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—
301C24×C5—61no—
302C24×C5—61no—
303C2×C5×D4—31no—
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—62no—
307C2×C5×D4—62no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4—121no—
316C2×C5×D4—124no—
317C2×C5×D4D1211yescharacteristic
318C22×C4×C5—61no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C22×Dic5—61no—
324#709—62no—
325#709—121no—
326C2×D20—31no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—31no—
330C2×Dic10—62no—
331C2×Dic10—61no—
332C2×Dic10—121no—
333C5×C4⋊C4—31no—
334C5×C4⋊C4D1211yescharacteristic
335C5×C22⋊C4—61no—
336C5×C22⋊C4—61no—
337C5×C22⋊C4—61no—
338C5×C22⋊C4D1211yescharacteristic
339C5×C22⋊C4D1211yescharacteristic
340C42×C5C22×D311yescharacteristic
341C22⋊Dic5—61no—
342#687—34no—
343#687—62no—
344#687—62no—
345#687—62no—
346#687—62no—
347#687—121no—
348#686—62no—
349#686—62no—
350#686—121no—
351#685—61no—
352#685—61no—
353#685—61no—
354C4⋊Dic5—31no—
355#683—61no—
356#683—61no—
357C4×Dic5—61no—
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—151no—
367D42—31no—
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—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—22no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—84no—
399C2×C5×D3—84no—
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—22no—
407Dic15—41no—
408Dic15—41no—
409C5×Dic3—41no—
410C23×D3—21no—
411C23×D3—21no—
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—101no—
420D3×D4—44no—
421#235—102no—
422#235—201no—
423C2×D12—22no—
424C2×D12—22no—
425C2×D12—21no—
426C2×D12—21no—
427C2×D12—21no—
428C2×D12—21no—
429C2×D12—41no—
430C2×D12—41no—
431C2×D12—51no—
432C2×D12C22×D511yescharacteristic
433C2×D12C22×D511yescharacteristic
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—101no—
437C2×Dic6—51no—
438C2×Dic6—51no—
439C2×Dic6—102no—
440C2×Dic6—101no—
441C2×Dic6—201no—
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—101no—
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—101no—
462Dic3⋊C4—101no—
463C4×Dic3—101no—
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×C5—61no—
475C23×C5—61no—
476C23×C5—122no—
477C23×C5—122no—
478C23×C5—122no—
479C23×C5—122no—
480C23×C5—241no—
481C23×C5—241no—
482C23×C5C2×D1211yescharacteristic
483C23×C5C2×D1211yescharacteristic
484C22×D5—61no—
485C5×D4—22no—
486C5×D4—32no—
487C5×D4—61no—
488C5×D4—61no—
489C5×D4—61no—
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—122no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—122no—
497C5×D4—241no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—61no—
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—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—61no—
516D20—61no—
517C4×D5—122no—
518Dic10—32no—
519Dic10—61no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523#168—21no—
524#168—21no—
525#168—21no—
526#168D3×D412yescomplemented
527C2×#41—151no—
528C22×Q8—151no—
529C22×D4—31no—
530C22×D4—31no—
531C22×D4—61no—
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—31no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—31no—
551#121—31no—
552#121—61no—
553#121—151no—
554#121—301no—
555#120—61no—
556#120—61no—
557C4×Q8—151no—
558C4×D4—31no—
559C4×D4—301no—
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—81no—
578C5×D3—42no—
579C5×D3—81no—
580C5×D3—81no—
581C23×C3C2×C22⋊D511yescharacteristic
582C23×C3C2×C22⋊D511yescharacteristic
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—42no—
587C22×D3—42no—
588C22×D3—42no—
589C22×D3—42no—
590C22×D3—81no—
591C22×D3—81no—
592C22×D3—101no—
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—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—202no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—42no—
618D12—42no—
619D12—42no—
620D12—81no—
621D12—101no—
622D12—101no—
623D12D4×D512yes—
624C4×D3—42no—
625C4×D3—202no—
626Dic6—52no—
627Dic6—101no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
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—62no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5—121no—
644C22×C5—121no—
645C22×C5—121no—
646C22×C5—121no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—244no—
650C22×C5—244no—
651C22×C5#90812yescomplemented
652C22×C5C22×D1211yescharacteristic
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—121no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5—121no—
661C4×C5C2×D3×D411yescharacteristic
662C4×C5#100911yescharacteristic
663Dic5—62no—
664Dic5—121no—
665Dic5—121no—
666C24—61no—
667C24—61no—
668#41—302no—
669#41—601no—
670C2×Q8—151no—
671C2×Q8—151no—
672C2×Q8—302no—
673C2×Q8—301no—
674C2×Q8—601no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—31no—
678C2×D4—62no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—121no—
687C2×D4—121no—
688C2×D4—124no—
689C2×D4—151no—
690C2×D4—301no—
691C2×D4—301no—
692C2×D4#120311yescharacteristic
693C22×C4—61no—
694C22×C4—301no—
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—151no—
715C4⋊C4—301no—
716C4⋊C4—301no—
717C4⋊C4#120311yescharacteristic
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—301no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4#120311yescharacteristic
726C22⋊C4#120311yescharacteristic
727C42—301no—
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#407812yescomplemented
736C22×C3C22×C22⋊D511yescharacteristic
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—84no—
747C2×D3—84no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4C2×D4×D511yescharacteristic
756C3×C4#414411yescharacteristic
757Dic3—41no—
758Dic3—102no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5—122no—
764C2×C5—241no—
765C2×C5—241no—
766C2×C5D4×D1211yescharacteristic
767C2×C5C2×#90811yescharacteristic
768C2×C5#575111yescharacteristic
769D5—241no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23—122no—
774C23—122no—
775C23—122no—
776C23—122no—
777C23—241no—
778C23—241no—
779C23—301no—
780C23C2×#120311yescharacteristic
781C23C2×#120311yescharacteristic
782Q8—152no—
783Q8—301no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—22no—
788D4—32no—
789D4—61no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—61no—
794D4—122no—
795D4—122no—
796D4—122no—
797D4—122no—
798D4—122no—
799D4—241no—
800D4—301no—
801D4—301no—
802D4—602no—
803D4—602no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—61no—
809C2×C4—122no—
810C2×C4—301no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—602no—
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×C3C2×#407811yescharacteristic
827C2×C3D4×C22⋊D511yescharacteristic
828C2×C3#6617011yescharacteristic
829D3—42no—
830D3—81no—
831D3—81no—
832D3—401no—
833C5#7949411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—62no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—244no—
849C22—244no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22#9130412yescomplemented
854C22C22×#120311yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—121no—
860C4—302no—
861C4—601no—
862C4—601no—
863C4D3×D4×D511yescharacteristic
864C4#9202711yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—122no—
869C2—241no—
870C2—241no—
871C2—1201no—
872C2C2×#9130411yescharacteristic
873C2D4×#120311yescharacteristic
874C2#1175530711yescharacteristic
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. #11756311C2semidirect
2. C5×D4×D12C2semidirect
3. C22×#6659C2semidirect
4. C2×#91304C2semidirect
5. C3×#65300C2semidirect
6. #11748553C2semidirect
7. #11748543C2semidirect
8. #11748534C2semidirect
9. #11748526C2semidirect
10. #11748520C2semidirect
11. #11748514C2semidirect
12. #11747086C2semidirect
13. #11747056C2semidirect
14. #11747038C2semidirect
15. #11747031C2semidirect
17. C2×#6817C22semidirect
18. C22×Dic30C22semidirect
24. #91819C22semidirect
25. #91813C22semidirect
29. #91764C22semidirect
30. C4×Dic30C22semidirect
38. C2×C3×#681C22semidirect
39. C22×C3×#168C22semidirect
43. C2×#6659C22semidirect
44. C2×#6659C22semidirect
45. C2×#6659C22semidirect
46. C2×#6659C22semidirect
49. C2×#6654C22semidirect
50. C2×#6654C22semidirect
51. C3×C22⋊#168C22semidirect
52. C3×C22⋊#168C22semidirect
53. C3×C4⋊#168C22semidirect
54. C3×#3935C22semidirect
55. #90988C22semidirect
56. #90975C22semidirect
57. #90975C22semidirect
58. #90969C22semidirect
60. #90967C22semidirect
61. #90967C22semidirect
77. #65300D3semidirect
137. #6659D4semidirect
144. D4×D12D5semidirect
183. C2×#681C2×D3semidirect
184. C22×#168C2×D3semidirect
193. C22⋊#168C2×D3semidirect
194. C22⋊#168C2×D3semidirect
199. C4⋊#168C2×D3semidirect
200. #3935C2×D3semidirect
237. Dic30C2×D4semidirect
255. C3×#168C2×D4semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
526. #168D3×D4semidirect
651. C22×C5#908semidirect
729. C3×C5#3265semidirect
735. C22×C3#4078semidirect
833. C5#79494semidirect
853. C22#91304semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
#117563112
C5×D4×D122
C22×#66592
C2×#913042
C3×#653002
#117485532
#117485432
#117485342
#117485262
#117485202
#117485142
#117470862
#117470562
#117470382
#117470312
#106152223
#794945