Finite Group Databasebeta

← #14453441

Subgroups — #14453441

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×#91800C211yesmaximal, characteristic, complemented
2C22×#6706C211yesmaximal, characteristic, complemented
3#11756368C211yesmaximal, characteristic, complemented
4#11756357C211yesmaximal, characteristic, complemented
5C3×C5×#466C211yesmaximal, characteristic, complemented
6#11751255C211yesmaximal, characteristic, complemented
7#11751212C211yesmaximal, characteristic, complemented
8#11751141C211yesmaximal, characteristic, complemented
9#11751137C211yesmaximal, characteristic, complemented
10#11750990C211yesmaximal, characteristic, complemented
11#11750987C211yesmaximal, characteristic, complemented
12#11750888C211yesmaximal, characteristic, complemented
13#11750882C211yesmaximal, characteristic, complemented
14#11750877C211yesmaximal, characteristic, complemented
15#11750863C211yesmaximal, characteristic, complemented
16#10612458—31nomaximal, Hall
17C2×#6819C2211yescharacteristic, complemented
18C2×D4×D15—21no—
19C2×D4×D15C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C2×C3×C5×D8C2211yescharacteristic, complemented
23C22×C3×C5×C8C2211yescharacteristic, complemented
24C3×C5×#121C2211yescharacteristic
25C3×C5×#121C2211yescharacteristic, complemented
26#91829C2211yescharacteristic
27#91828—21no—
28#91826—21no—
29#91825C2211yescharacteristic, complemented
30D4×Dic15—21no—
31C2×#6716C2211yescharacteristic, complemented
32C2×#6716C2211yescharacteristic, complemented
33C2×#6715C2211yescharacteristic
34C2×#6715C2211yescharacteristic, complemented
35C4×#1220C2211yescharacteristic
36#91800—24no—
37C2×#6706—24no—
38C2×#6706C2211yescharacteristic
39C2×#6706C2211yescharacteristic
40C2×#6706C2211yescharacteristic, complemented
41C2×#6706C2211yescharacteristic, complemented
42C2×#6705C2211yescharacteristic, complemented
43#91786C2211yescharacteristic, complemented
44#91784C2211yescharacteristic
45#91782C2211yescharacteristic
46#91776C2211yescharacteristic, complemented
47#91774—21no—
48#91773—21no—
49#91771—21no—
50#91767—21no—
51C3×C5×#107C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×#102C2211yescharacteristic, complemented
54#91114C2211yescharacteristic, complemented
55#91104C2211yescharacteristic, complemented
56#91099C2211yescharacteristic, complemented
57#91098C2211yescharacteristic, complemented
58#91094C2211yescharacteristic, complemented
59#91094C2211yescharacteristic, complemented
60#91093C2211yescharacteristic
61#91093C2211yescharacteristic, complemented
62#80727—51nomaximal, Hall
63C2×#4057—31no—
64C22×#677—31no—
65#65943—31no—
66#65932—31no—
67C5×#466D311yescharacteristic, complemented
68#65443—31no—
69#65400—31no—
70#65329—31no—
71#65325—31no—
72#65178—31no—
73#65175—31no—
74#65076—31no—
75#65070—31no—
76#65065—31no—
77#65051—31no—
78C23×D15—21no—
79C23×D15—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—21no—
86C2×#1220—21no—
87C2×#1220—21no—
88C2×#1220—21no—
89C2×#1220D411yescharacteristic
90C22×Dic15—21no—
91C22×Dic15—21no—
92#6819—22no—
93#6819—41no—
94D4×D15—22no—
95D4×D15—41no—
96D4×D15—44no—
97C2×D60—22no—
98C2×D60—21no—
99C2×D60—21no—
100C2×D60—41no—
101C2×D60C2311yescharacteristic
102C2×D60C2311yescharacteristic
103C2×C4×D15—21no—
104C2×C4×D15C2311yescharacteristic
105C2×Dic30—22no—
106C2×Dic30—21no—
107C2×Dic30—41no—
108C2×Dic30C2311yescharacteristic
109C2×Dic30C2311yescharacteristic
110C3×C5×D8—22no—
111C2×C3×C5×C8—22no—
112C2×C3×C5×C8C2311yescharacteristic
113C2×C3×C5×C8C2311yescharacteristic
114C3×C5×C4⋊C4C2311yescharacteristic
115C3×C5×C4⋊C4C2311yescharacteristic
116C3×C5×C22⋊C4—21no—
117C3×C5×C22⋊C4—21no—
118#6719—21no—
119#6719—21no—
120#6719D411yescharacteristic
121#6716—22no—
122#6716—41no—
123#6715—22no—
124#6715—41no—
125#6714—21no—
126#6714—21no—
127#6714—21no—
128#6714D411yescharacteristic
129C4⋊Dic15—21no—
130#6712—21no—
131#6712D411yescharacteristic
132C4×Dic15—21no—
133C4×Dic15C2311yescharacteristic
134C2×C3⋊#168C2311yescharacteristic
135C2×C3⋊#168C2311yescharacteristic
136#6706—22no—
137#6706—22no—
138#6706—22no—
139#6706D414yescomplemented
140#6705—22no—
141C2×#911—51no—
142C22×#204—51no—
143#5609—51no—
144#5598—51no—
145C3×#466D511yescharacteristic, complemented
146#5154—51no—
147#5111—51no—
148#5040—51no—
149#5036—51no—
150#4889—51no—
151#4886—51no—
152#4787—51no—
153#4781—51no—
154#4776—51no—
155#4762—51no—
156C2×#711—31no—
157C2×D4×D5—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×Dic10—31no—
161C2×C5×D8C2×D311yescharacteristic, complemented
162C22×C5×C8C2×D311yescharacteristic, complemented
163C5×#121C2×D311yescharacteristic
164C5×#121C2×D311yescharacteristic, complemented
165#4086—31no—
166#4085—61no—
167#4083—61no—
168#4082—31no—
169D4×Dic5—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#686—31no—
173C2×#686—31no—
174C4×C22⋊D5—31no—
175#4057—64no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179C2×#677—31no—
180C2×#677—64no—
181C2×#676—31no—
182#4043—31no—
183#4041—31no—
184#4039—31no—
185#4033—31no—
186#4031—61no—
187#4030—61no—
188#4028—61no—
189#4024—61no—
190C5×#107C2×D311yescharacteristic, complemented
191C5×#102C2×D311yescharacteristic, complemented
192C5×#102C2×D311yescharacteristic, complemented
193C22⋊#168—31no—
194#3952—31no—
195#3947—31no—
196#3946—31no—
197#3942—31no—
198#3942—31no—
199#3941—31no—
200#3941—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5C2×D411yescharacteristic
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×D15C2×D411yescharacteristic
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—42no—
219C3×C5×D4—42no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226#1220—22no—
227#1220—42no—
228#1220—42no—
229#1220—42no—
230#1220—81no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—42no—
234C2×Dic15—42no—
235C2×Dic15C2×D411yescharacteristic
236C2×Dic15C2×D411yescharacteristic
237C2×Dic15C2×D411yescharacteristic
238D60—21no—
239D60—21no—
240D60—21no—
241D60—42no—
242D60—42no—
243D60C2×D412yes—
244C4×D15—21no—
245C4×D15—21no—
246C4×D15—42no—
247Dic30—21no—
248Dic30—21no—
249Dic30—21no—
250Dic30—42no—
251Dic30C2×D412yescomplemented
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C3⋊#168—21no—
255C3⋊#168—21no—
256C2×#237—51no—
257C2×D3×D4—51no—
258C2×D3×D4—101no—
259C22×D12—51no—
260C22×Dic6—51no—
261C2×C3×D8C2×D511yescharacteristic, complemented
262C22×C3×C8C2×D511yescharacteristic, complemented
263C3×#121C2×D511yescharacteristic
264C3×#121C2×D511yescharacteristic, complemented
265#940—51no—
266#939—101no—
267#937—101no—
268#936—51no—
269D4×Dic3—101no—
270C2×#214—51no—
271C2×#214—51no—
272C2×#213—51no—
273C2×#213—51no—
274C4×#67—51no—
275#911—104no—
276C2×#204—51no—
277C2×#204—51no—
278C2×#204—51no—
279C2×#204—51no—
280C2×#204—104no—
281C2×ΓL(1,𝔽25)—51no—
282#897—51no—
283#895—51no—
284#893—51no—
285#887—51no—
286#885—101no—
287#884—101no—
288#882—101no—
289#878—101no—
290C3×#107C2×D511yescharacteristic, complemented
291C3×#102C2×D511yescharacteristic, complemented
292C3×#102C2×D511yescharacteristic, complemented
293#830—51no—
294(C2×D3)⋊C8—51no—
295#815—51no—
296Dic3⋊C8—51no—
297#810—51no—
298#810—51no—
299#809—51no—
300#809—51no—
301C23×D5—61no—
302C23×D5—61no—
303C2×C5×D4—21no—
304C2×C5×D4—21no—
305C2×C5×D4C22×D311yescharacteristic
306C2×C5×D4C22×D311yescharacteristic
307C22×C4×C5C22×D311yescharacteristic
308C2×C22⋊D5—31no—
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313C22×Dic5—61no—
314C22×Dic5—61no—
315#711—62no—
316#711—121no—
317D4×D5—62no—
318D4×D5—121no—
319D4×D5—124no—
320C2×D20—31no—
321C2×D20—31no—
322C2×D20—62no—
323C2×D20—61no—
324C2×D20—61no—
325C2×D20—121no—
326C2×C4×D5—31no—
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—31no—
330C2×Dic10—62no—
331C2×Dic10—61no—
332C2×Dic10—121no—
333C5×D8—22no—
334C2×C5×C8—22no—
335C2×C5×C8C22×D311yescharacteristic
336C2×C5×C8C22×D311yescharacteristic
337C5×C4⋊C4C22×D311yescharacteristic
338C5×C4⋊C4C22×D311yescharacteristic
339C5×C22⋊C4—21no—
340C5×C22⋊C4—21no—
341C22⋊Dic5—31no—
342C22⋊Dic5—61no—
343C22⋊Dic5—61no—
344#687—62no—
345#687—121no—
346#686—62no—
347#686—121no—
348#685—31no—
349#685—61no—
350#685—61no—
351#685—61no—
352C4⋊Dic5—61no—
353#683—31no—
354#683—61no—
355C4×Dic5—31no—
356C4×Dic5—61no—
357C2×#168—31no—
358C2×#168—31no—
359#677—34no—
360#677—62no—
361#677—62no—
362#677—62no—
363#676—62no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—151no—
367D42—151no—
368#496—151no—
369#468—151no—
370#466D1511yescharacteristic, complemented
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5AGL(1,ℤ/8)12yescomplemented
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—21no—
390C2×D15—22no—
391C2×D15—21no—
392C2×D15—21no—
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—41no—
402C3×C4×C5—41no—
403C3×C4×C5C22×D411yescharacteristic
404C3×C4×C5H(5,𝔽2)11yescharacteristic
405Dic15—22no—
406Dic15—21no—
407Dic15—21no—
408Dic15—21no—
409Dic15—41no—
410C23×D3—101no—
411C23×D3—101no—
412C2×C3×D4—21no—
413C2×C3×D4—21no—
414C2×C3×D4C22×D511yescharacteristic
415C2×C3×D4C22×D511yescharacteristic
416C22×C3×C4C22×D511yescharacteristic
417C2×#67—51no—
418C2×#67—101no—
419C2×#67—101no—
420C2×#67—101no—
421C2×#67—101no—
422C22×Dic3—101no—
423C22×Dic3—101no—
424#237—102no—
425#237—201no—
426D3×D4—102no—
427D3×D4—201no—
428D3×D4—204no—
429C2×D12—51no—
430C2×D12—51no—
431C2×D12—102no—
432C2×D12—101no—
433C2×D12—101no—
434C2×D12—201no—
435C2×C4×D3—51no—
436C2×C4×D3—101no—
437C2×Dic6—51no—
438C2×Dic6—51no—
439C2×Dic6—102no—
440C2×Dic6—101no—
441C2×Dic6—201no—
442C3×D8—22no—
443C2×C3×C8—22no—
444C2×C3×C8C22×D511yescharacteristic
445C2×C3×C8C22×D511yescharacteristic
446C3×C4⋊C4C22×D511yescharacteristic
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C22⋊C4—21no—
449C3×C22⋊C4—21no—
450#217—51no—
451#217—101no—
452#217—101no—
453#214—102no—
454#214—201no—
455#213—102no—
456#213—201no—
457(C2×D3)⋊C4—51no—
458(C2×D3)⋊C4—101no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461C4⋊Dic3—101no—
462Dic3⋊C4—51no—
463Dic3⋊C4—101no—
464C4×Dic3—51no—
465C4×Dic3—101no—
466C2×C3⋊C8—51no—
467C2×C3⋊C8—51no—
468#204—54no—
469#204—102no—
470#204—102no—
471#204—102no—
472ΓL(1,𝔽25)—102no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5D3×D411yescharacteristic
476C22×D5—31no—
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—21no—
486C5×D4—21no—
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—42no—
490C5×D4—42no—
491C2×C4×C5—21no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5D3×D411yescharacteristic
496C2×C4×C5C23×D311yescharacteristic
497C22⋊D5—62no—
498C22⋊D5—122no—
499C22⋊D5—122no—
500C22⋊D5—122no—
501C22⋊D5—241no—
502C2×Dic5—31no—
503C2×Dic5—31no—
504C2×Dic5—31no—
505C2×Dic5—61no—
506C2×Dic5—61no—
507C2×Dic5—122no—
508C2×Dic5—122no—
509D20—32no—
510D20—61no—
511D20—61no—
512D20—61no—
513D20—122no—
514D20—122no—
515C4×D5—61no—
516C4×D5—61no—
517C4×D5—122no—
518Dic10—32no—
519Dic10—61no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523C5×C8—21no—
524C5×C8D3×D412yescomplemented
525#168—61no—
526#168—61no—
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×D8C2×D1511yescharacteristic, complemented
543C2×M16—151no—
544C22×C8C2×D1511yescharacteristic, complemented
545#127—151no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—151no—
551#121—301no—
552#121—301no—
553#121C2×D1511yescharacteristic
554#121C2×D1511yescharacteristic, complemented
555#120—301no—
556#120—301no—
557C4×Q8—151no—
558C4×D4—151no—
559C4×D4—151no—
560C4×D4—301no—
561#107C2×D1511yescharacteristic, complemented
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102C2×D1511yescharacteristic, complemented
568#102C2×D1511yescharacteristic, complemented
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—81no—
574C2×C3×C5—81no—
575C2×C3×C5D4211yescharacteristic
576C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
577C2×C3×C5#57711yescharacteristic
578D15—41no—
579D15—42no—
580D15—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3D4×D511yescharacteristic
584C22×D3—51no—
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—21no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—42no—
598C3×D4—42no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4D4×D511yescharacteristic
604C2×C3×C4C23×D511yescharacteristic
605#67—102no—
606#67—202no—
607#67—202no—
608#67—202no—
609#67—401no—
610C2×Dic3—51no—
611C2×Dic3—51no—
612C2×Dic3—51no—
613C2×Dic3—101no—
614C2×Dic3—101no—
615C2×Dic3—202no—
616C2×Dic3—202no—
617D12—52no—
618D12—101no—
619D12—101no—
620D12—101no—
621D12—202no—
622D12—202no—
623C4×D3—101no—
624C4×D3—101no—
625C4×D3—202no—
626Dic6—52no—
627Dic6—101no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—21no—
632C3×C8D4×D512yescomplemented
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5#91112yescomplemented
644C22×C5C2×D3×D411yescharacteristic
645C2×D5—61no—
646C2×D5—61no—
647C2×D5—61no—
648C2×D5—62no—
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—41no—
658C4×C5—41no—
659C4×C5C2×D3×D411yescharacteristic
660C4×C5#100911yescharacteristic
661Dic5—61no—
662Dic5—61no—
663Dic5—62no—
664Dic5—61no—
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—21no—
676C2×D4—21no—
677C2×D4—151no—
678C2×D4—151no—
679C2×D4—151no—
680C2×D4—302no—
681C2×D4—301no—
682C2×D4—301no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—302no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—601no—
689C2×D4—601no—
690C2×D4—604no—
691C2×D4C22×D1511yescharacteristic
692C2×D4C22×D1511yescharacteristic
693C22×C4—151no—
694C22×C4—301no—
695C22×C4—301no—
696C22×C4—301no—
697C22×C4C22×D1511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—22no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—22no—
709C2×C8—151no—
710C2×C8—151no—
711C2×C8C22×D1511yescharacteristic
712C2×C8C22×D1511yescharacteristic
713C4⋊C4—151no—
714C4⋊C4—301no—
715C4⋊C4—301no—
716C4⋊C4C22×D1511yescharacteristic
717C4⋊C4C22×D1511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—151no—
721C22⋊C4—151no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—151no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3#405712yescomplemented
739C22×C3C2×D4×D511yescharacteristic
740C2×D3—101no—
741C2×D3—101no—
742C2×D3—101no—
743C2×D3—102no—
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—41no—
753C3×C4—41no—
754C3×C4C2×D4×D511yescharacteristic
755C3×C4#414911yescharacteristic
756Dic3—101no—
757Dic3—101no—
758Dic3—102no—
759Dic3—101no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—81no—
763C2×C5—81no—
764C2×C5#560911yescharacteristic
765C2×C5C2×#91111yescharacteristic
766C2×C5#577011yescharacteristic
767D5—121no—
768D5—122no—
769D5—241no—
770C23—21no—
771C23—21no—
772C23—151no—
773C23—301no—
774C23—301no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—602no—
779C23—1201no—
780C23—1201no—
781C23D4×D1511yescharacteristic
782Q8—152no—
783Q8—301no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—42no—
792D4—42no—
793D4—152no—
794D4—302no—
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—151no—
809C2×C4—151no—
810C2×C4—151no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—602no—
816C2×C4—602no—
817C2×C4—602no—
818C2×C4D4×D1511yescharacteristic
819C2×C4C23×D1511yescharacteristic
820C8—21no—
821C8—301no—
822C8—301no—
823C8D4×D1512yescomplemented
824C2×C3—22no—
825C2×C3—81no—
826C2×C3—81no—
827C2×C3#6594311yescharacteristic
828C2×C3C2×#405711yescharacteristic
829C2×C3#6610411yescharacteristic
830D3—201no—
831D3—202no—
832D3—401no—
833C5#8072711yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—301no—
843C22—302no—
844C22—301no—
845C22—301no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9180012yescomplemented
854C22C2×D4×D1511yescharacteristic
855C4—21no—
856C4—41no—
857C4—41no—
858C4—301no—
859C4—302no—
860C4—301no—
861C4—301no—
862C4—601no—
863C4C2×D4×D1511yescharacteristic
864C4#9210011yescharacteristic
865C3#1061245811yescharacteristic, complemented, Sylow
866C2—22no—
867C2—81no—
868C2—81no—
869C2—601no—
870C2—602no—
871C2—1201no—
872C2#1175636811yescharacteristic
873C2C2×#9180011yescharacteristic
874C2#1175652911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#466C2
socleC22×C3×C5C22×D4
hypercenter#466D15
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#91800C2semidirect
2. C22×#6706C2semidirect
3. #11756368C2semidirect
4. #11756357C2semidirect
5. C3×C5×#466C2semidirect
6. #11751255C2semidirect
7. #11751212C2semidirect
8. #11751141C2semidirect
9. #11751137C2semidirect
10. #11750990C2semidirect
11. #11750987C2semidirect
12. #11750888C2semidirect
13. #11750882C2semidirect
14. #11750877C2semidirect
15. #11750863C2semidirect
17. C2×#6819C22semidirect
21. C22×Dic30C22semidirect
22. C2×C3×C5×D8C22semidirect
23. C22×C3×C5×C8C22semidirect
25. C3×C5×#121C22semidirect
29. #91825C22semidirect
31. C2×#6716C22semidirect
32. C2×#6716C22semidirect
34. C2×#6715C22semidirect
40. C2×#6706C22semidirect
41. C2×#6706C22semidirect
42. C2×#6705C22semidirect
43. #91786C22semidirect
46. #91776C22semidirect
51. C3×C5×#107C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×#102C22semidirect
54. #91114C22semidirect
55. #91104C22semidirect
56. #91099C22semidirect
57. #91098C22semidirect
58. #91094C22semidirect
59. #91094C22semidirect
61. #91093C22semidirect
67. C5×#466D3semidirect
139. #6706D4semidirect
145. C3×#466D5semidirect
161. C2×C5×D8C2×D3semidirect
162. C22×C5×C8C2×D3semidirect
164. C5×#121C2×D3semidirect
190. C5×#107C2×D3semidirect
191. C5×#102C2×D3semidirect
192. C5×#102C2×D3semidirect
251. Dic30C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
261. C2×C3×D8C2×D5semidirect
262. C22×C3×C8C2×D5semidirect
264. C3×#121C2×D5semidirect
290. C3×#107C2×D5semidirect
291. C3×#102C2×D5semidirect
292. C3×#102C2×D5semidirect
370. #466D15semidirect
387. C22×C3×C5AGL(1,ℤ/8)semidirect
524. C5×C8D3×D4semidirect
542. C2×D8C2×D15semidirect
544. C22×C8C2×D15semidirect
554. #121C2×D15semidirect
561. #107C2×D15semidirect
567. #102C2×D15semidirect
568. #102C2×D15semidirect
632. C3×C8D4×D5semidirect
643. C22×C5#911semidirect
729. C3×C5#3265semidirect
738. C22×C3#4057semidirect
823. C8D4×D15semidirect
833. C5#80727semidirect
853. C22#91800semidirect
865. C3#10612458semidirect

Maximal subgroups

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

subgroupindex
C2×#918002
C22×#67062
#117563682
#117563572
C3×C5×#4662
#117512552
#117512122
#117511412
#117511372
#117509902
#117509872
#117508882
#117508822
#117508772
#117508632
#106124583
#807275