Finite Group Databasebeta

← #14453465

Subgroups — #14453465

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
1C2×#91797C211yesmaximal, characteristic, complemented
2C22×#6706C211yesmaximal, characteristic, complemented
3#11756311C211yesmaximal, characteristic, complemented
4D4×D60C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6#11751235C211yesmaximal, characteristic, complemented
7#11751216C211yesmaximal, characteristic, complemented
8#11750949C211yesmaximal, characteristic, complemented
9#11750945C211yesmaximal, characteristic, complemented
10#11750839C211yesmaximal, characteristic, complemented
11#11750835C211yesmaximal, characteristic, complemented
12#11750833C211yesmaximal, characteristic, complemented
13#11750832C211yesmaximal, characteristic, complemented
14#11750813C211yesmaximal, characteristic, complemented
15#11750811C211yesmaximal, characteristic, complemented
16#10611225—31nomaximal, Hall
17C2×D4×D15—21no—
18C2×#6817C2211yescharacteristic, complemented
19C22×D60C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C2×C3×C5×M16C2211yescharacteristic, complemented
23C22×C3×C5×C8C2211yescharacteristic, complemented
24C3×C4×C5×D4C2211yescharacteristic
25#91828—21no—
26#91819C2211yescharacteristic
27#91819C2211yescharacteristic
28#91819C2211yescharacteristic, complemented
29#91813C2211yescharacteristic, complemented
30#91797—24no—
31C2×D120C2211yescharacteristic
32C2×D120C2211yescharacteristic, complemented
33C2×D120C2211yescharacteristic, complemented
34C2×#6706—24no—
35C2×#6706C2211yescharacteristic
36C2×#6706C2211yescharacteristic
37C2×#6706C2211yescharacteristic, complemented
38C2×#6706C2211yescharacteristic, complemented
39C2×#6706C2211yescharacteristic, complemented
40C2×#6706C2211yescharacteristic, complemented
41#91785—21no—
42#91784—21no—
43#91774—21no—
44#91771—21no—
45#91771—21no—
46#91770—21no—
47#91764C2211yescharacteristic, complemented
48#91763C2211yescharacteristic
49C4×D60C2211yescharacteristic
50C4×Dic30C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55#91105C2211yescharacteristic
56#91105C2211yescharacteristic, complemented
57#91105C2211yescharacteristic, complemented
58#91105C2211yescharacteristic, complemented
59#91102C2211yescharacteristic, complemented
60#91100C2211yescharacteristic, complemented
61#91100C2211yescharacteristic, complemented
62#79494—51nomaximal, Hall
63C2×#4054—31no—
64C22×#677—31no—
65#65886—31no—
66D4×D20—31no—
67C5×#435D311yescharacteristic, complemented
68#65423—31no—
69#65404—31no—
70#65137—31no—
71#65133—31no—
72#65027—31no—
73#65023—31no—
74#65021—31no—
75#65020—31no—
76#65001—31no—
77#64999—31no—
78C23×D15—21no—
79C23×D15—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—21no—
85C2×#1220—21no—
86C2×#1220—21no—
87C22×Dic15—21no—
88D4×D15—44no—
89#6817—22no—
90#6817—41no—
91C2×D60—22no—
92C2×D60—22no—
93C2×D60—21no—
94C2×D60—21no—
95C2×D60—21no—
96C2×D60—21no—
97C2×D60—41no—
98C2×D60—41no—
99C2×D60C2311yescharacteristic
100C2×D60C2311yescharacteristic
101C2×D60C2311yescharacteristic
102C2×D60C2311yescharacteristic
103C2×C4×D15—21no—
104C2×C4×D15—21no—
105C2×Dic30—22no—
106C2×Dic30—21no—
107C2×Dic30—41no—
108C2×Dic30C2311yescharacteristic
109C2×Dic30C2311yescharacteristic
110C3×C5×M16—22no—
111C2×C3×C5×C8—22no—
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C2×C3×C5×C8C2311yescharacteristic
116C3×C5×C4⋊C4D411yescharacteristic
117C3×C5×C22⋊C4D411yescharacteristic
118C3×C5×C22⋊C4D411yescharacteristic
119C3×C42×C5C2311yescharacteristic
120#6719—21no—
121#6714—21no—
122#6714—21no—
123#6714—21no—
124#6714—21no—
125#6714—21no—
126#6714—21no—
127C4⋊Dic15C2311yescharacteristic
128C4⋊Dic15C2311yescharacteristic
129#6712—21no—
130#6712—21no—
131C4×Dic15—21no—
132D120—22no—
133D120—22no—
134D120—41no—
135#6706—22no—
136#6706—22no—
137#6706—22no—
138#6706—22no—
139#6706—41no—
140#6706D414yescomplemented
141C2×#908—51no—
142C22×#204—51no—
143#5552—51no—
144D4×D12—51no—
145C3×#435D511yescharacteristic, complemented
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×D4×D5—61no—
157C2×#709—31no—
158C22×D20—31no—
159C22×D20—31no—
160C22×Dic10—31no—
161C2×C5×M16C2×D311yescharacteristic, complemented
162C22×C5×C8C2×D311yescharacteristic, complemented
163C4×C5×D4C2×D311yescharacteristic
164#4085—61no—
165#4076—31no—
166#4076—31no—
167#4076—31no—
168#4070—31no—
169#4054—64no—
170C2×D40—31no—
171C2×D40—31no—
172C2×D40—31no—
173C2×#677—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179C2×#677—64no—
180#4042—61no—
181#4041—61no—
182#4031—61no—
183#4028—61no—
184#4028—61no—
185#4027—61no—
186#4021—31no—
187#4020—31no—
188C4×D20—31no—
189C4×Dic10—31no—
190C5×C4⋊C8C2×D311yescharacteristic, complemented
191C5×C22⋊C8C2×D311yescharacteristic, complemented
192C5×C22⋊C8C2×D311yescharacteristic, complemented
193C5×#97C2×D311yescharacteristic, complemented
194#3953—31no—
195#3953—31no—
196#3953—31no—
197#3953—31no—
198#3950—31no—
199#3948—31no—
200#3948—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—21no—
208C22×D15—42no—
209C22×D15—42no—
210C22×D15—42no—
211C22×D15—42no—
212C22×D15—81no—
213C22×D15—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—
226#1220—42no—
227#1220—42no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—42no—
233D60—21no—
234D60—21no—
235D60—21no—
236D60—21no—
237D60—21no—
238D60—21no—
239D60—21no—
240D60—42no—
241D60—42no—
242D60—42no—
243D60—81no—
244D60C2×D412yes—
245C4×D15—42no—
246C4×D15—42no—
247Dic30—21no—
248Dic30—21no—
249Dic30—21no—
250Dic30—42no—
251Dic30C2×D412yescomplemented
252C3×C5×C8—21no—
253C3×C5×C8—21no—
254C3×C5×C8—21no—
255C3×C5×C8C2×D412yescomplemented
256C2×D3×D4—101no—
257C2×#235—51no—
258C22×D12—51no—
259C22×D12—51no—
260C22×Dic6—51no—
261C2×C3×M16C2×D511yescharacteristic, complemented
262C22×C3×C8C2×D511yescharacteristic, complemented
263C3×C4×D4C2×D511yescharacteristic
264#939—101no—
265#930—51no—
266#930—51no—
267#930—51no—
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—101no—
282#885—101no—
283#882—101no—
284#882—101no—
285#67⋊C4—101no—
286#875—51no—
287#874—51no—
288C4×D12—51no—
289C4×Dic6—51no—
290C3×C4⋊C8C2×D511yescharacteristic, complemented
291C3×C22⋊C8C2×D511yescharacteristic, complemented
292C3×C22⋊C8C2×D511yescharacteristic, complemented
293C3×#97C2×D511yescharacteristic, complemented
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—
303C2×C5×D4D1211yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C2×C22⋊D5—61no—
307C2×C22⋊D5—61no—
308C2×C22⋊D5—61no—
309C2×C22⋊D5—61no—
310C22×Dic5—61no—
311D4×D5—124no—
312#709—62no—
313#709—121no—
314C2×D20—31no—
315C2×D20—31no—
316C2×D20—31no—
317C2×D20—31no—
318C2×D20—62no—
319C2×D20—62no—
320C2×D20—61no—
321C2×D20—61no—
322C2×D20—61no—
323C2×D20—61no—
324C2×D20—121no—
325C2×D20—121no—
326C2×C4×D5—61no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—31no—
330C2×Dic10—62no—
331C2×Dic10—61no—
332C2×Dic10—121no—
333C5×M16—22no—
334C2×C5×C8—22no—
335C2×C5×C8C22×D311yescharacteristic
336C2×C5×C8C22×D311yescharacteristic
337C2×C5×C8C22×D311yescharacteristic
338C2×C5×C8C22×D311yescharacteristic
339C5×C4⋊C4D1211yescharacteristic
340C5×C22⋊C4D1211yescharacteristic
341C5×C22⋊C4D1211yescharacteristic
342C42×C5C22×D311yescharacteristic
343C22⋊Dic5—61no—
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348#685—61no—
349#685—61no—
350C4⋊Dic5—31no—
351C4⋊Dic5—31no—
352#683—61no—
353#683—61no—
354C4×Dic5—61no—
355D40—62no—
356D40—62no—
357D40—121no—
358#677—34no—
359#677—62no—
360#677—62no—
361#677—62no—
362#677—62no—
363#677—121no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—151no—
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#435D1511yescharacteristic, complemented
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—41no—
396C2×D15—41no—
397C2×D15—41no—
398C2×D15—84no—
399C2×D15—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—
409Dic15—41no—
410C23×D3—101no—
411C23×D3—101no—
412C2×C3×D4D2011yescharacteristic
413C22×C3×C4C22×D511yescharacteristic
414C22×C3×C4C22×D511yescharacteristic
415C2×#67—101no—
416C2×#67—101no—
417C2×#67—101no—
418C2×#67—101no—
419C22×Dic3—101no—
420D3×D4—204no—
421#235—102no—
422#235—201no—
423C2×D12—51no—
424C2×D12—51no—
425C2×D12—51no—
426C2×D12—51no—
427C2×D12—102no—
428C2×D12—102no—
429C2×D12—101no—
430C2×D12—101no—
431C2×D12—101no—
432C2×D12—101no—
433C2×D12—201no—
434C2×D12—201no—
435C2×C4×D3—101no—
436C2×C4×D3—101no—
437C2×Dic6—51no—
438C2×Dic6—51no—
439C2×Dic6—102no—
440C2×Dic6—101no—
441C2×Dic6—201no—
442C3×M16—22no—
443C2×C3×C8—22no—
444C2×C3×C8C22×D511yescharacteristic
445C2×C3×C8C22×D511yescharacteristic
446C2×C3×C8C22×D511yescharacteristic
447C2×C3×C8C22×D511yescharacteristic
448C3×C4⋊C4D2011yescharacteristic
449C3×C22⋊C4D2011yescharacteristic
450C3×C22⋊C4D2011yescharacteristic
451C3×C42C22×D511yescharacteristic
452#217—101no—
453(C2×D3)⋊C4—101no—
454(C2×D3)⋊C4—101no—
455(C2×D3)⋊C4—101no—
456(C2×D3)⋊C4—101no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459C4⋊Dic3—51no—
460C4⋊Dic3—51no—
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×C5C2×D1211yescharacteristic
474C23×C5C2×D1211yescharacteristic
475C22×D5—61no—
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×D4—22no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5C2×D1211yescharacteristic
491C2×C4×C5C2×D1211yescharacteristic
492C2×C4×C5C2×D1211yescharacteristic
493C2×C4×C5C2×D1211yescharacteristic
494C2×C4×C5C23×D311yescharacteristic
495C22⋊D5—122no—
496C22⋊D5—122no—
497C22⋊D5—122no—
498C22⋊D5—122no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C2×Dic5—61no—
502C2×Dic5—61no—
503C2×Dic5—122no—
504D20—32no—
505D20—61no—
506D20—61no—
507D20—61no—
508D20—61no—
509D20—61no—
510D20—61no—
511D20—61no—
512D20—122no—
513D20—122no—
514D20—122no—
515D20—241no—
516C4×D5—122no—
517C4×D5—122no—
518Dic10—32no—
519Dic10—61no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523C5×C8—21no—
524C5×C8—21no—
525C5×C8—21no—
526C5×C8D3×D412yescomplemented
527C2×#41—151no—
528C22×Q8—151no—
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×M16C2×D1511yescharacteristic, complemented
544C22×C8C2×D1511yescharacteristic, complemented
545#127—151no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—151no—
551#121—151no—
552#121—151no—
553#121—301no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—151no—
558C4×D4—151no—
559C4×D4—301no—
560C4×D4C2×D1511yescharacteristic
561#107—151no—
562C4⋊C8C2×D1511yescharacteristic, complemented
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8C2×D1511yescharacteristic, complemented
570C22⋊C8C2×D1511yescharacteristic, complemented
571#97C2×D1511yescharacteristic, complemented
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—
580D15—81no—
581C23×C3C2×D2011yescharacteristic
582C23×C3C2×D2011yescharacteristic
583C22×D3—101no—
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×D2011yescharacteristic
599C2×C3×C4C2×D2011yescharacteristic
600C2×C3×C4C2×D2011yescharacteristic
601C2×C3×C4C2×D2011yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603#67—202no—
604#67—202no—
605#67—202no—
606#67—202no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—202no—
612D12—52no—
613D12—101no—
614D12—101no—
615D12—101no—
616D12—101no—
617D12—101no—
618D12—101no—
619D12—101no—
620D12—202no—
621D12—202no—
622D12—202no—
623D12—401no—
624C4×D3—202no—
625C4×D3—202no—
626Dic6—52no—
627Dic6—101no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8D4×D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5#90812yescomplemented
641C22×C5C22×D1211yescharacteristic
642C2×D5—62no—
643C2×D5—121no—
644C2×D5—121no—
645C2×D5—121no—
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×C5C2×D3×D411yescharacteristic
661C4×C5#100911yescharacteristic
662Dic5—62no—
663Dic5—121no—
664Dic5—121no—
665Dic5—121no—
666C24—301no—
667C24—301no—
668#41—302no—
669#41—601no—
670C2×Q8—151no—
671C2×Q8—151no—
672C2×Q8—302no—
673C2×Q8—301no—
674C2×Q8—601no—
675C2×D4—151no—
676C2×D4—151no—
677C2×D4—151no—
678C2×D4—151no—
679C2×D4—302no—
680C2×D4—302no—
681C2×D4—301no—
682C2×D4—301no—
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×D4D6011yescharacteristic
693C22×C4—301no—
694C22×C4—301no—
695C22×C4—301no—
696C22×C4C22×D1511yescharacteristic
697C22×C4C22×D1511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—22no—
708C2×C8—22no—
709C2×C8C22×D1511yescharacteristic
710C2×C8C22×D1511yescharacteristic
711C2×C8C22×D1511yescharacteristic
712C2×C8C22×D1511yescharacteristic
713C4⋊C4—151no—
714C4⋊C4—151no—
715C4⋊C4—301no—
716C4⋊C4—301no—
717C4⋊C4D6011yescharacteristic
718C22⋊C4—301no—
719C22⋊C4—301no—
720C22⋊C4—301no—
721C22⋊C4—301no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4D6011yescharacteristic
726C22⋊C4D6011yescharacteristic
727C42—301no—
728C42C22×D1511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3#405412yescomplemented
736C22×C3C22×D2011yescharacteristic
737C2×D3—102no—
738C2×D3—201no—
739C2×D3—201no—
740C2×D3—201no—
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#414911yescharacteristic
757Dic3—102no—
758Dic3—201no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5D4×D1211yescharacteristic
764C2×C5C2×#90811yescharacteristic
765C2×C5#575111yescharacteristic
766D5—122no—
767D5—241no—
768D5—241no—
769D5—241no—
770C23—301no—
771C23—301no—
772C23—301no—
773C23—301no—
774C23—602no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—1201no—
779C23—1201no—
780C23C2×D6011yescharacteristic
781C23C2×D6011yescharacteristic
782Q8—152no—
783Q8—301no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—22no—
788D4—152no—
789D4—301no—
790D4—301no—
791D4—301no—
792D4—301no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—602no—
797D4—602no—
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—301no—
809C2×C4—301no—
810C2×C4—301no—
811C2×C4—301no—
812C2×C4—602no—
813C2×C4—602no—
814C2×C4—602no—
815C2×C4C2×D6011yescharacteristic
816C2×C4C2×D6011yescharacteristic
817C2×C4C2×D6011yescharacteristic
818C2×C4C2×D6011yescharacteristic
819C2×C4C23×D1511yescharacteristic
820C8—21no—
821C8—21no—
822C8—21no—
823C8D4×D1512yescomplemented
824C2×C3—22no—
825C2×C3—41no—
826C2×C3D4×D2011yescharacteristic
827C2×C3C2×#405411yescharacteristic
828C2×C3#6608511yescharacteristic
829D3—202no—
830D3—401no—
831D3—401no—
832D3—401no—
833C5#7949411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—302no—
840C22—601no—
841C22—601no—
842C22—601no—
843C22—601no—
844C22—601no—
845C22—601no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9179712yescomplemented
854C22C22×D6011yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—302no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4C2×D4×D1511yescharacteristic
864C4#9210011yescharacteristic
865C3#1061122511yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—602no—
869C2—1201no—
870C2—1201no—
871C2—1201no—
872C2D4×D6011yescharacteristic
873C2C2×#9179711yescharacteristic
874C2#1175651011yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
hypercenter#435D15
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#91797C2semidirect
2. C22×#6706C2semidirect
3. #11756311C2semidirect
4. D4×D60C2semidirect
5. C3×C5×#435C2semidirect
6. #11751235C2semidirect
7. #11751216C2semidirect
8. #11750949C2semidirect
9. #11750945C2semidirect
10. #11750839C2semidirect
11. #11750835C2semidirect
12. #11750833C2semidirect
13. #11750832C2semidirect
14. #11750813C2semidirect
15. #11750811C2semidirect
18. C2×#6817C22semidirect
21. C22×Dic30C22semidirect
22. C2×C3×C5×M16C22semidirect
23. C22×C3×C5×C8C22semidirect
28. #91819C22semidirect
29. #91813C22semidirect
32. C2×D120C22semidirect
33. C2×D120C22semidirect
37. C2×#6706C22semidirect
38. C2×#6706C22semidirect
39. C2×#6706C22semidirect
40. C2×#6706C22semidirect
47. #91764C22semidirect
50. C4×Dic30C22semidirect
51. C3×C5×C4⋊C8C22semidirect
52. C3×C5×C22⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
56. #91105C22semidirect
57. #91105C22semidirect
58. #91105C22semidirect
59. #91102C22semidirect
60. #91100C22semidirect
61. #91100C22semidirect
67. C5×#435D3semidirect
140. #6706D4semidirect
145. C3×#435D5semidirect
161. C2×C5×M16C2×D3semidirect
162. C22×C5×C8C2×D3semidirect
190. C5×C4⋊C8C2×D3semidirect
191. C5×C22⋊C8C2×D3semidirect
192. C5×C22⋊C8C2×D3semidirect
193. C5×#97C2×D3semidirect
251. Dic30C2×D4semidirect
255. C3×C5×C8C2×D4semidirect
261. C2×C3×M16C2×D5semidirect
262. C22×C3×C8C2×D5semidirect
290. C3×C4⋊C8C2×D5semidirect
291. C3×C22⋊C8C2×D5semidirect
292. C3×C22⋊C8C2×D5semidirect
293. C3×#97C2×D5semidirect
378. #435D15semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
526. C5×C8D3×D4semidirect
543. C2×M16C2×D15semidirect
544. C22×C8C2×D15semidirect
562. C4⋊C8C2×D15semidirect
569. C22⋊C8C2×D15semidirect
570. C22⋊C8C2×D15semidirect
571. #97C2×D15semidirect
634. C3×C8D4×D5semidirect
640. C22×C5#908semidirect
729. C3×C5#3265semidirect
735. C22×C3#4054semidirect
823. C8D4×D15semidirect
833. C5#79494semidirect
853. C22#91797semidirect
865. C3#10611225semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
C22×#67062
#117563112
D4×D602
C3×C5×#4352
#117512352
#117512162
#117509492
#117509452
#117508392
#117508352
#117508332
#117508322
#117508132
#117508112
#106112253
#794945