Finite Group Databasebeta

← #14453177

Subgroups — #14453177

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11756588C211yesmaximal, characteristic, complemented
3D4×#1220C211yesmaximal, characteristic, complemented
4C2×D8×D15C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11751318C211yesmaximal, characteristic, complemented
7#11751277C211yesmaximal, characteristic, complemented
8#11751272C211yesmaximal, characteristic, complemented
9#11751270C211yesmaximal, characteristic, complemented
10#11751266C211yesmaximal, characteristic, complemented
11#11751257C211yesmaximal, characteristic, complemented
12#11751253C211yesmaximal, characteristic, complemented
13#11751251C211yesmaximal, characteristic, complemented
14#11751236C211yesmaximal, characteristic, complemented
15#11751228C211yesmaximal, characteristic, complemented
16#10615683—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic, complemented
19C22×#1220—21no—
20C2×D4×D15C2211yescharacteristic
21C2×D4×D15C2211yescharacteristic, complemented
22C3×C5×AGL(1,ℤ/8)—24no—
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C2×C3×C5×SD16C2211yescharacteristic, complemented
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×D8C2211yescharacteristic, complemented
27C2×C3×C5×M16C2211yescharacteristic, complemented
28#91842—21no—
29#91836C2211yescharacteristic, complemented
30#91835C2211yescharacteristic, complemented
31C2×#6717C2211yescharacteristic, complemented
32#91829C2211yescharacteristic, complemented
33#91828—21no—
34#91828—21no—
35#91827C2211yescharacteristic
36#91826—21no—
37#91826—21no—
38D4×Dic15C2211yescharacteristic, complemented
39D4×Dic15C2211yescharacteristic, complemented
40C2×#6715C2211yescharacteristic
41C2×#6715C2211yescharacteristic, complemented
42C2×#6715C2211yescharacteristic, complemented
43#91819C2211yescharacteristic, complemented
44#91819C2211yescharacteristic, complemented
45#91818—21no—
46C4×#1220C2211yescharacteristic
47C2×#6714—21no—
48D8×D15—24no—
49C2×D120C2211yescharacteristic, complemented
50C2×C8×D15C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91116C2211yescharacteristic, complemented
54#91116C2211yescharacteristic, complemented
55#91114C2211yescharacteristic, complemented
56#91105C2211yescharacteristic, complemented
57#91105C2211yescharacteristic, complemented
58#91104C2211yescharacteristic, complemented
59#91101C2211yescharacteristic, complemented
60#91099C2211yescharacteristic, complemented
61#91098C2211yescharacteristic, complemented
62#83952—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)D311yescharacteristic, complemented
64#66163—31no—
65D4×C22⋊D5—31no—
66C2×D5×D8—31no—
67#65527—31no—
68#65506—31no—
69#65465—31no—
70#65460—31no—
71#65458—31no—
72#65454—31no—
73#65445—31no—
74#65441—31no—
75#65439—31no—
76#65424—31no—
77#65416—31no—
78C24×C3×C5—21no—
79C23×D15—21no—
80C23×D15—21no—
81C3×C5×#41—22no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—21no—
87C2×C3×C5×D4—41no—
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C2×C3×C5×D4C2311yescharacteristic
91C22×C3×C4×C5—21no—
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—21no—
94C2×#1220—21no—
95C2×#1220—21no—
96C2×#1220—21no—
97C2×#1220—21no—
98C2×#1220—21no—
99C2×#1220—21no—
100C2×#1220—44no—
101C2×#1220D411yescharacteristic
102C22×Dic15—21no—
103C22×Dic15—21no—
104D4×D15—22no—
105D4×D15—22no—
106D4×D15—41no—
107D4×D15—41no—
108C2×D60C2311yescharacteristic
109C2×D60C2311yescharacteristic
110C2×C4×D15C2311yescharacteristic
111C3×C5×SD16—22no—
112C3×C5×SD16—22no—
113C3×C5×D8—22no—
114C3×C5×D8D414yescomplemented
115C3×C5×M16—22no—
116C2×C3×C5×C8C2311yescharacteristic
117C2×C3×C5×C8C2311yescharacteristic
118#6719—21no—
119#6719—21no—
120#6719—21no—
121#6719D411yescharacteristic
122#6717—41no—
123#6715—22no—
124#6715—22no—
125#6715—41no—
126#6714—21no—
127#6714—21no—
128#6714—21no—
129#6714—21no—
130#6714—21no—
131#6714D411yescharacteristic
132C4⋊Dic15C2311yescharacteristic
133C4⋊Dic15C2311yescharacteristic
134#6712—21no—
135#6712D411yescharacteristic
136C4×Dic15C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139D120—22no—
140C8×D15—22no—
141C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
142#5829—51no—
143D4×#67—51no—
144C2×D3×D8—51no—
145#5238—51no—
146#5217—51no—
147#5176—51no—
148#5171—51no—
149#5169—51no—
150#5165—51no—
151#5156—51no—
152#5152—51no—
153#5150—51no—
154#5135—51no—
155#5127—51no—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×D4C2×D311yescharacteristic, complemented
158C22×C22⋊D5—61no—
159C2×D4×D5—31no—
160C2×D4×D5—31no—
161C5×AGL(1,ℤ/8)—24no—
162C2×C5×SD16C2×D311yescharacteristic, complemented
163C2×C5×SD16C2×D311yescharacteristic, complemented
164C2×C5×D8C2×D311yescharacteristic
165C2×C5×D8C2×D311yescharacteristic, complemented
166C2×C5×M16C2×D311yescharacteristic, complemented
167#4099—61no—
168#4093—31no—
169#4092—31no—
170C2×#688—31no—
171#4086—31no—
172#4085—61no—
173#4085—61no—
174#4084—31no—
175#4083—61no—
176#4083—61no—
177D4×Dic5—31no—
178D4×Dic5—31no—
179C2×#686—31no—
180C2×#686—31no—
181C2×#686—31no—
182#4076—31no—
183#4076—31no—
184#4075—61no—
185C4×C22⋊D5—31no—
186C2×#685—61no—
187D5×D8—64no—
188C2×D40—31no—
189C2×C8×D5—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193#3964—31no—
194C22⋊#168—31no—
195#3953—31no—
196#3953—31no—
197#3952—31no—
198#3949—31no—
199#3947—31no—
200#3946—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5—42no—
206C23×C3×C5—42no—
207C23×C3×C5—81no—
208C23×C3×C5C2×D411yescharacteristic
209C22×D15—21no—
210C22×D15—21no—
211C22×D15—42no—
212C22×D15—42no—
213C22×D15—42no—
214C22×D15—42no—
215C22×D15—81no—
216C22×D15—81no—
217C22×D15C2×D411yescharacteristic
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C3×C5×D4—21no—
223C3×C5×D4—21no—
224C3×C5×D4—42no—
225C3×C5×D4—42no—
226C3×C5×D4C2×D412yes—
227C3×C5×D4C2×D412yescomplemented
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—42no—
232C2×C3×C4×C5C2×D411yescharacteristic
233C2×C3×C4×C5C2411yescharacteristic
234#1220—22no—
235#1220—42no—
236#1220—42no—
237#1220—42no—
238#1220—42no—
239#1220—42no—
240#1220—81no—
241#1220—81no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—42no—
245C2×Dic15—81no—
246C2×Dic15C2×D411yescharacteristic
247C2×Dic15C2×D411yescharacteristic
248C2×Dic15C2×D411yescharacteristic
249D60—21no—
250D60—21no—
251D60—21no—
252D60—21no—
253C4×D15—21no—
254C4×D15—21no—
255C3×C5×C8—21no—
256C3×C5×C8C2×D412yescomplemented
257C3⋊#168—21no—
258C3⋊#168—21no—
259C2×C3×#41C2×D511yescharacteristic, complemented
260C22×C3×D4C2×D511yescharacteristic, complemented
261C22×#67—101no—
262C2×D3×D4—51no—
263C2×D3×D4—51no—
264C3×AGL(1,ℤ/8)—24no—
265C2×C3×SD16C2×D511yescharacteristic, complemented
266C2×C3×SD16C2×D511yescharacteristic, complemented
267C2×C3×D8C2×D511yescharacteristic
268C2×C3×D8C2×D511yescharacteristic, complemented
269C2×C3×M16C2×D511yescharacteristic, complemented
270#953—101no—
271#947—51no—
272#946—51no—
273C2×#215—51no—
274#940—51no—
275#939—101no—
276#939—101no—
277#938—51no—
278#937—101no—
279#937—101no—
280D4×Dic3—51no—
281D4×Dic3—51no—
282C2×#213—51no—
283C2×#213—51no—
284C2×#213—51no—
285#930—51no—
286#930—51no—
287#929—101no—
288C4×#67—51no—
289C2×(C2×D3)⋊C4—101no—
290D3×D8—104no—
291C2×D24—51no—
292C2×D3×C8—51no—
293#835—51no—
294#832—51no—
295#832—51no—
296#832—51no—
297#830—51no—
298#821—51no—
299#821—51no—
300(C2×D3)⋊C8—51no—
301#817—51no—
302#815—51no—
303Dic3⋊C8—51no—
304C24×C5—21no—
305C23×D5—61no—
306C23×D5—61no—
307C5×#41—22no—
308C5×#41—41no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—22no—
311C2×C5×D4—21no—
312C2×C5×D4—21no—
313C2×C5×D4—41no—
314C2×C5×D4C22×D311yescharacteristic
315C2×C5×D4C22×D311yescharacteristic
316C2×C5×D4C22×D311yescharacteristic
317C22×C4×C5—21no—
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—31no—
320C2×C22⋊D5—61no—
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324C2×C22⋊D5—61no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5—61no—
327C2×C22⋊D5—124no—
328C22×Dic5—61no—
329C22×Dic5—61no—
330D4×D5—62no—
331D4×D5—62no—
332D4×D5—121no—
333D4×D5—121no—
334C2×D20—31no—
335C2×D20—31no—
336C2×C4×D5—31no—
337C5×SD16—22no—
338C5×SD16—22no—
339C5×D8—22no—
340C5×D8#6714yescomplemented
341C5×M16—22no—
342C2×C5×C8C22×D311yescharacteristic
343C2×C5×C8C22×D311yescharacteristic
344C22⋊Dic5—31no—
345C22⋊Dic5—61no—
346C22⋊Dic5—61no—
347C22⋊Dic5—61no—
348#688—121no—
349#686—62no—
350#686—62no—
351#686—121no—
352#685—31no—
353#685—61no—
354#685—61no—
355#685—61no—
356#685—61no—
357#685—61no—
358C4⋊Dic5—31no—
359C4⋊Dic5—31no—
360#683—31no—
361#683—61no—
362C4×Dic5—31no—
363C2×#168—31no—
364C2×#168—31no—
365D40—62no—
366C8×D5—62no—
367C2×AGL(1,ℤ/8)D1511yescharacteristic, complemented
368C22×D8—151no—
369#546—151no—
370D42—151no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—21no—
385C22×C3×C5—21no—
386C22×C3×C5—21no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—41no—
392C22×C3×C5—41no—
393C22×C3×C5—41no—
394C22×C3×C5—84no—
395C22×C3×C5C22×D411yescharacteristic
396C2×D15—21no—
397C2×D15—21no—
398C2×D15—41no—
399C2×D15—41no—
400C2×D15—41no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—41no—
404C2×D15—84no—
405C2×D15—84no—
406C2×D15AGL(1,ℤ/8)12yescomplemented
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411Dic15—21no—
412Dic15—21no—
413Dic15—21no—
414Dic15—41no—
415Dic15—41no—
416C24×C3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C3×#41—22no—
420C3×#41—41no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—22no—
423C2×C3×D4—21no—
424C2×C3×D4—21no—
425C2×C3×D4—41no—
426C2×C3×D4C22×D511yescharacteristic
427C2×C3×D4C22×D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C22×C3×C4—21no—
430C22×C3×C4C22×D511yescharacteristic
431C2×#67—51no—
432C2×#67—101no—
433C2×#67—101no—
434C2×#67—101no—
435C2×#67—101no—
436C2×#67—101no—
437C2×#67—101no—
438C2×#67—101no—
439C2×#67—204no—
440C22×Dic3—101no—
441C22×Dic3—101no—
442D3×D4—102no—
443D3×D4—102no—
444D3×D4—201no—
445D3×D4—201no—
446C2×D12—51no—
447C2×D12—51no—
448C2×C4×D3—51no—
449C3×SD16—22no—
450C3×SD16—22no—
451C3×D8—22no—
452C3×D8C22⋊D514yescomplemented
453C3×M16—22no—
454C2×C3×C8C22×D511yescharacteristic
455C2×C3×C8C22×D511yescharacteristic
456#217—51no—
457#217—101no—
458#217—101no—
459#217—101no—
460#215—201no—
461#213—102no—
462#213—102no—
463#213—201no—
464(C2×D3)⋊C4—51no—
465(C2×D3)⋊C4—101no—
466(C2×D3)⋊C4—101no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4—101no—
469(C2×D3)⋊C4—101no—
470C4⋊Dic3—51no—
471C4⋊Dic3—51no—
472Dic3⋊C4—51no—
473Dic3⋊C4—101no—
474C4×Dic3—51no—
475C2×C3⋊C8—51no—
476C2×C3⋊C8—51no—
477D24—102no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—42no—
483C23×C5—42no—
484C23×C5—81no—
485C23×C5D3×D411yescharacteristic
486C22×D5—31no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—122no—
490C22×D5—122no—
491C22×D5—122no—
492C22×D5—122no—
493C22×D5—241no—
494C22×D5—241no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—21no—
500C5×D4—21no—
501C5×D4—42no—
502C5×D4—42no—
503C5×D4C2×#6712yes—
504C5×D4C2×#6712yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—42no—
509C2×C4×C5D3×D411yescharacteristic
510C2×C4×C5C23×D311yescharacteristic
511C22⋊D5—62no—
512C22⋊D5—122no—
513C22⋊D5—122no—
514C22⋊D5—122no—
515C22⋊D5—122no—
516C22⋊D5—122no—
517C22⋊D5—241no—
518C22⋊D5—241no—
519C2×Dic5—31no—
520C2×Dic5—31no—
521C2×Dic5—31no—
522C2×Dic5—61no—
523C2×Dic5—61no—
524C2×Dic5—122no—
525C2×Dic5—241no—
526D20—61no—
527D20—61no—
528D20—61no—
529D20—61no—
530C4×D5—61no—
531C4×D5—61no—
532C5×C8—21no—
533C5×C8C2×#6712yescomplemented
534#168—61no—
535#168—61no—
536C2×#41C2×D1511yescharacteristic, complemented
537C22×D4—151no—
538C22×D4—151no—
539C22×D4—301no—
540C22×D4C2×D1511yescharacteristic, complemented
541AGL(1,ℤ/8)—24no—
542C2×SD16—151no—
543C2×SD16C2×D1511yescharacteristic, complemented
544C2×SD16C2×D1511yescharacteristic, complemented
545C2×D8—151no—
546C2×D8—151no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—304no—
550C2×D8C2×D1511yescharacteristic
551C2×D8C2×D1511yescharacteristic, complemented
552C2×M16C2×D1511yescharacteristic, complemented
553C22×C8—151no—
554#127—151no—
555#124—151no—
556#123—301no—
557C22⋊Q8—151no—
558#121—151no—
559#121—151no—
560#121—151no—
561#121—301no—
562#121—301no—
563#120—301no—
564#120—301no—
565#120—301no—
566C4×D4—151no—
567C4×D4—151no—
568C4×D4—151no—
569C2×C22⋊C4—301no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—151no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—42no—
582C2×C3×C5—42no—
583C2×C3×C5—41no—
584C2×C3×C5—81no—
585C2×C3×C5D4211yescharacteristic
586C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
587C2×C3×C5#57611yescharacteristic
588D15—22no—
589D15—81no—
590D15—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—21no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—81no—
597C23×C3D4×D511yescharacteristic
598C22×D3—51no—
599C22×D3—101no—
600C22×D3—101no—
601C22×D3—202no—
602C22×D3—202no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3—401no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—21no—
612C3×D4—21no—
613C3×D4—42no—
614C3×D4—42no—
615C3×D4C2×C22⋊D512yes—
616C3×D4C2×C22⋊D512yescomplemented
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—42no—
621C2×C3×C4D4×D511yescharacteristic
622C2×C3×C4C23×D511yescharacteristic
623#67—102no—
624#67—202no—
625#67—202no—
626#67—202no—
627#67—202no—
628#67—202no—
629#67—401no—
630#67—401no—
631C2×Dic3—51no—
632C2×Dic3—51no—
633C2×Dic3—51no—
634C2×Dic3—101no—
635C2×Dic3—101no—
636C2×Dic3—202no—
637C2×Dic3—401no—
638D12—101no—
639D12—101no—
640D12—101no—
641D12—101no—
642C4×D3—101no—
643C4×D3—101no—
644C3×C8—21no—
645C3×C8C2×C22⋊D512yescomplemented
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—21no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5—41no—
660C22×C5—84no—
661C22×C5C2×D3×D411yescharacteristic
662C2×D5—32no—
663C2×D5—61no—
664C2×D5—61no—
665C2×D5—121no—
666C2×D5—121no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—244no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—41no—
675C4×C5#100411yescharacteristic
676C4×C5C22×#6711yescharacteristic
677Dic5—61no—
678Dic5—61no—
679Dic5—61no—
680Dic5—121no—
681Dic5—121no—
682C24—21no—
683C24—301no—
684C24—301no—
685#41—22no—
686#41—41no—
687C2×Q8C22×D1511yescharacteristic
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—41no—
692C2×D4—151no—
693C2×D4—151no—
694C2×D4—151no—
695C2×D4—301no—
696C2×D4—301no—
697C2×D4—301no—
698C2×D4—301no—
699C2×D4—302no—
700C2×D4—302no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—601no—
705C2×D4—601no—
706C2×D4—604no—
707C2×D4C22×D1511yescharacteristic
708C2×D4C22×D1511yescharacteristic
709C2×D4C22×D1511yescharacteristic
710C22×C4—21no—
711C22×C4—151no—
712C22×C4—301no—
713C22×C4—301no—
714C22×C4C22×D1511yescharacteristic
715SD16—22no—
716SD16—22no—
717SD16—601no—
718D8—22no—
719D8—302no—
720D8—302no—
721D8—302no—
722D8—601no—
723D8#122014yescomplemented
724M16—22no—
725C2×C8—151no—
726C2×C8—151no—
727C2×C8—302no—
728C2×C8C22×D1511yescharacteristic
729C2×C8C22×D1511yescharacteristic
730C4⋊C4—151no—
731C4⋊C4—151no—
732C4⋊C4—151no—
733C4⋊C4—301no—
734C22⋊C4—151no—
735C22⋊C4—151no—
736C22⋊C4—301no—
737C22⋊C4—301no—
738C22⋊C4—301no—
739C22⋊C4—301no—
740C22⋊C4—301no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—151no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—84no—
759C22×C3C2×D4×D511yescharacteristic
760C2×D3—52no—
761C2×D3—101no—
762C2×D3—101no—
763C2×D3—201no—
764C2×D3—201no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3—404no—
771C3×C4—21no—
772C3×C4—41no—
773C3×C4#414411yescharacteristic
774C3×C4C22×C22⋊D511yescharacteristic
775Dic3—101no—
776Dic3—101no—
777Dic3—101no—
778Dic3—201no—
779Dic3—201no—
780C2×C5—42no—
781C2×C5—42no—
782C2×C5—41no—
783C2×C5—81no—
784C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
785C2×C5#577411yescharacteristic
786C2×C5D4×#6711yescharacteristic
787D5—62no—
788D5—241no—
789D5—241no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—42no—
794C23—42no—
795C23—81no—
796C23—151no—
797C23—301no—
798C23—301no—
799C23—602no—
800C23—602no—
801C23—602no—
802C23—602no—
803C23—1201no—
804C23—1201no—
805C23D4×D1511yescharacteristic
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—42no—
814D4—302no—
815D4—301no—
816D4—301no—
817D4—301no—
818D4—301no—
819D4—602no—
820D4—602no—
821D4—602no—
822D4—602no—
823D4—602no—
824D4—1201no—
825D4—1201no—
826D4C2×#122012yes—
827D4C2×#122012yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—42no—
832C2×C4—151no—
833C2×C4—151no—
834C2×C4—151no—
835C2×C4—301no—
836C2×C4—301no—
837C2×C4—301no—
838C2×C4—301no—
839C2×C4—602no—
840C2×C4—1201no—
841C2×C4D4×D1511yescharacteristic
842C2×C4C23×D1511yescharacteristic
843C8—21no—
844C8—301no—
845C8—301no—
846C8C2×#122012yescomplemented
847C2×C3—42no—
848C2×C3—42no—
849C2×C3—41no—
850C2×C3—81no—
851C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
852C2×C3#6610811yescharacteristic
853C2×C3D4×C22⋊D511yescharacteristic
854D3—102no—
855D3—401no—
856D3—401no—
857C5#8395211yescharacteristic, complemented, Sylow
858C22—21no—
859C22—22no—
860C22—22no—
861C22—21no—
862C22—21no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—84no—
871C22—152no—
872C22—301no—
873C22—301no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—601no—
880C22—1204no—
881C22—1204no—
882C22C2×D4×D1511yescharacteristic
883C4—21no—
884C4—41no—
885C4—301no—
886C4—301no—
887C4—301no—
888C4—601no—
889C4—601no—
890C4#9209511yescharacteristic
891C4C22×#122011yescharacteristic
892C3#1061568311yescharacteristic, complemented, Sylow
893C2—41no—
894C2—42no—
895C2—42no—
896C2—81no—
897C2—302no—
898C2—1201no—
899C2—1201no—
900C2D15×AGL(1,ℤ/8)11yescharacteristic
901C2#1175653311yescharacteristic
902C2D4×#122011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
hypercenterC2×AGL(1,ℤ/8)D15
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
2. #11756588C2semidirect
3. D4×#1220C2semidirect
4. C2×D8×D15C2semidirect
5. #11751339C2semidirect
6. #11751318C2semidirect
7. #11751277C2semidirect
8. #11751272C2semidirect
9. #11751270C2semidirect
10. #11751266C2semidirect
11. #11751257C2semidirect
12. #11751253C2semidirect
13. #11751251C2semidirect
14. #11751236C2semidirect
15. #11751228C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C3×C5×D4C22semidirect
21. C2×D4×D15C22semidirect
23. C2×C3×C5×SD16C22semidirect
24. C2×C3×C5×SD16C22semidirect
26. C2×C3×C5×D8C22semidirect
27. C2×C3×C5×M16C22semidirect
29. #91836C22semidirect
30. #91835C22semidirect
31. C2×#6717C22semidirect
32. #91829C22semidirect
38. D4×Dic15C22semidirect
39. D4×Dic15C22semidirect
41. C2×#6715C22semidirect
42. C2×#6715C22semidirect
43. #91819C22semidirect
44. #91819C22semidirect
49. C2×D120C22semidirect
50. C2×C8×D15C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91116C22semidirect
54. #91116C22semidirect
55. #91114C22semidirect
56. #91105C22semidirect
57. #91105C22semidirect
58. #91104C22semidirect
59. #91101C22semidirect
60. #91099C22semidirect
61. #91098C22semidirect
63. C2×C5×AGL(1,ℤ/8)D3semidirect
114. C3×C5×D8D4semidirect
141. C2×C3×AGL(1,ℤ/8)D5semidirect
156. C2×C5×#41C2×D3semidirect
157. C22×C5×D4C2×D3semidirect
162. C2×C5×SD16C2×D3semidirect
163. C2×C5×SD16C2×D3semidirect
165. C2×C5×D8C2×D3semidirect
166. C2×C5×M16C2×D3semidirect
227. C3×C5×D4C2×D4semidirect
256. C3×C5×C8C2×D4semidirect
259. C2×C3×#41C2×D5semidirect
260. C22×C3×D4C2×D5semidirect
265. C2×C3×SD16C2×D5semidirect
266. C2×C3×SD16C2×D5semidirect
268. C2×C3×D8C2×D5semidirect
269. C2×C3×M16C2×D5semidirect
340. C5×D8#67semidirect
367. C2×AGL(1,ℤ/8)D15semidirect
406. C2×D15AGL(1,ℤ/8)semidirect
452. C3×D8C22⋊D5semidirect
504. C5×D4C2×#67semidirect
533. C5×C8C2×#67semidirect
536. C2×#41C2×D15semidirect
540. C22×D4C2×D15semidirect
543. C2×SD16C2×D15semidirect
544. C2×SD16C2×D15semidirect
551. C2×D8C2×D15semidirect
552. C2×M16C2×D15semidirect
616. C3×D4C2×C22⋊D5semidirect
645. C3×C8C2×C22⋊D5semidirect
723. D8#1220semidirect
745. C3×C5#3264semidirect
827. D4C2×#1220semidirect
846. C8C2×#1220semidirect
857. C5#83952semidirect
892. C3#10615683semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
#117565882
D4×#12202
C2×D8×D152
#117513392
#117513182
#117512772
#117512722
#117512702
#117512662
#117512572
#117512532
#117512512
#117512362
#117512282
#106156833
#839525