Finite Group Databasebeta

← #14453432

Subgroups — #14453432

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×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11756590C211yesmaximal, characteristic, complemented
3D4×#1220C211yesmaximal, characteristic, complemented
4C2×SD16×D15C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11751319C211yesmaximal, characteristic, complemented
7#11751271C211yesmaximal, characteristic, complemented
8#11751265C211yesmaximal, characteristic, complemented
9#11751264C211yesmaximal, characteristic, complemented
10#11751258C211yesmaximal, characteristic, complemented
11#11751257C211yesmaximal, characteristic, complemented
12#11751255C211yesmaximal, characteristic, complemented
13#11751254C211yesmaximal, characteristic, complemented
14#11751235C211yesmaximal, characteristic, complemented
15#11751228C211yesmaximal, characteristic, complemented
16#10615684—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220—21no—
20C2×Q8×D15C2211yescharacteristic, complemented
21C2×D4×D15C2211yescharacteristic
22C3×C5×AGL(1,ℤ/8)—24no—
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×SD16C2211yescharacteristic, complemented
25C2×C3×C5×D8C2211yescharacteristic
26C2×C3×C5×D8C2211yescharacteristic, complemented
27C2×C3×C5×M16C2211yescharacteristic, complemented
28#91842—21no—
29Q8×Dic15C2211yescharacteristic, complemented
30C2×#6717C2211yescharacteristic, complemented
31#91829C2211yescharacteristic
32#91828—21no—
33#91827—21no—
34#91827C2211yescharacteristic
35#91827C2211yescharacteristic, complemented
36#91826—21no—
37#91825—21no—
38#91825C2211yescharacteristic, complemented
39D4×Dic15C2211yescharacteristic
40C2×#6716C2211yescharacteristic
41C2×#6716C2211yescharacteristic, complemented
42C2×#6715C2211yescharacteristic, complemented
43#91819C2211yescharacteristic
44C4×#1220—21no—
45C4×#1220C2211yescharacteristic
46#91813—21no—
47#91813C2211yescharacteristic, complemented
48SD16×D15—24no—
49C2×#6706C2211yescharacteristic, complemented
50C2×C8×D15C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic
53#91116C2211yescharacteristic, complemented
54#91116C2211yescharacteristic, complemented
55#91114C2211yescharacteristic, complemented
56#91105C2211yescharacteristic, complemented
57#91104C2211yescharacteristic, complemented
58#91102C2211yescharacteristic, complemented
59#91100C2211yescharacteristic, complemented
60#91099C2211yescharacteristic, complemented
61#91098C2211yescharacteristic, complemented
62#83953—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)D311yescharacteristic, complemented
64#66165—31no—
65D4×C22⋊D5—31no—
66C2×D5×SD16—31no—
67#65527—31no—
68#65507—31no—
69#65459—31no—
70#65453—31no—
71#65452—31no—
72#65446—31no—
73#65445—31no—
74#65443—31no—
75#65442—31no—
76#65423—31no—
77#65416—31no—
78C24×C3×C5—21no—
79C23×D15—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—22no—
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4—41no—
87C2×C3×C5×D4C2311yescharacteristic
88C2×C3×C5×D4C2311yescharacteristic
89C2×C3×C5×D4C2311yescharacteristic
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—21no—
93C2×#1220—21no—
94C2×#1220—21no—
95C2×#1220—21no—
96C2×#1220—21no—
97C2×#1220—21no—
98C2×#1220—44no—
99C2×#1220D411yescharacteristic
100C22×Dic15—21no—
101Q8×D15—22no—
102Q8×D15—41no—
103D4×D15—22no—
104D4×D15—41no—
105C2×D60C2311yescharacteristic
106C2×C4×D15—21no—
107C2×C4×D15C2311yescharacteristic
108C2×Dic30—21no—
109C2×Dic30C2311yescharacteristic
110C3×C5×SD16—22no—
111C3×C5×SD16D414yescomplemented
112C3×C5×D8—22no—
113C3×C5×D8—22no—
114C3×C5×M16—22no—
115C2×C3×C5×C8C2311yescharacteristic
116C2×C3×C5×C8C2311yescharacteristic
117#6719—21no—
118#6719—21no—
119#6719—21no—
120#6719—21no—
121#6719—21no—
122#6719—21no—
123#6719D411yescharacteristic
124#6717—22no—
125#6716—22no—
126#6716—41no—
127#6715—41no—
128#6714—21no—
129#6714D411yescharacteristic
130C4⋊Dic15—21no—
131C4⋊Dic15C2311yescharacteristic
132C4⋊Dic15C2311yescharacteristic
133#6712—21no—
134#6712D411yescharacteristic
135C4×Dic15—21no—
136C4×Dic15C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139#6706—22no—
140C8×D15—22no—
141C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
142#5831—51no—
143D4×#67—51no—
144C2×D3×SD16—51no—
145#5238—51no—
146#5218—51no—
147#5170—51no—
148#5164—51no—
149#5163—51no—
150#5157—51no—
151#5156—51no—
152#5154—51no—
153#5153—51no—
154#5134—51no—
155#5127—51no—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×D4C2×D311yescharacteristic
158C22×C22⋊D5—61no—
159C2×Q8×D5—31no—
160C2×D4×D5—31no—
161C5×AGL(1,ℤ/8)—24no—
162C2×C5×SD16C2×D311yescharacteristic
163C2×C5×SD16C2×D311yescharacteristic, complemented
164C2×C5×D8C2×D311yescharacteristic
165C2×C5×D8C2×D311yescharacteristic, complemented
166C2×C5×M16C2×D311yescharacteristic, complemented
167#4099—61no—
168Q8×Dic5—31no—
169C2×#688—31no—
170#4086—31no—
171#4085—61no—
172#4084—31no—
173#4084—31no—
174#4084—61no—
175#4083—61no—
176#4082—31no—
177#4082—61no—
178D4×Dic5—31no—
179C2×#687—31no—
180C2×#687—31no—
181C2×#686—31no—
182#4076—31no—
183C4×C22⋊D5—31no—
184C4×C22⋊D5—61no—
185#4070—31no—
186#4070—61no—
187D5×SD16—64no—
188C2×#677—31no—
189C2×C8×D5—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193#3964—31no—
194C22⋊#168—31no—
195#3953—31no—
196#3952—31no—
197#3950—31no—
198#3948—31no—
199#3947—31no—
200#3946—31no—
201#3265—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—42no—
211C22×D15—42no—
212C22×D15—81no—
213C22×D15C2×D411yescharacteristic
214C3×C5×Q8—21no—
215C3×C5×Q8C2×D412yescomplemented
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4—42no—
223C3×C5×D4C2×D412yes—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—42no—
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2411yescharacteristic
230#1220—22no—
231#1220—42no—
232#1220—42no—
233#1220—42no—
234#1220—42no—
235#1220—42no—
236#1220—81no—
237C2×Dic15—21no—
238C2×Dic15—21no—
239C2×Dic15—21no—
240C2×Dic15—42no—
241C2×Dic15C2×D411yescharacteristic
242C2×Dic15C2×D411yescharacteristic
243C2×Dic15C2×D411yescharacteristic
244D60—21no—
245D60—21no—
246C4×D15—21no—
247C4×D15—21no—
248C4×D15—42no—
249Dic30—21no—
250Dic30—21no—
251Dic30—42no—
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C3⋊#168—21no—
255C3⋊#168—21no—
256C2×C3×#41C2×D511yescharacteristic, complemented
257C22×C3×D4C2×D511yescharacteristic
258C22×#67—101no—
259C2×D3×Q8—51no—
260C2×D3×D4—51no—
261C3×AGL(1,ℤ/8)—24no—
262C2×C3×SD16C2×D511yescharacteristic
263C2×C3×SD16C2×D511yescharacteristic, complemented
264C2×C3×D8C2×D511yescharacteristic
265C2×C3×D8C2×D511yescharacteristic, complemented
266C2×C3×M16C2×D511yescharacteristic, complemented
267#953—101no—
268Q8×Dic3—51no—
269C2×#215—51no—
270#940—51no—
271#939—101no—
272#938—51no—
273#938—51no—
274#938—101no—
275#937—101no—
276#936—51no—
277#936—101no—
278D4×Dic3—51no—
279C2×#214—51no—
280C2×#214—51no—
281C2×#213—51no—
282#930—51no—
283C4×#67—51no—
284C4×#67—101no—
285#924—51no—
286#924—101no—
287D3×SD16—104no—
288C2×#204—51no—
289C2×D3×C8—51no—
290#835—51no—
291#832—51no—
292#832—51no—
293#832—51no—
294#830—51no—
295#821—51no—
296(C2×D3)⋊C8—51no—
297#818—51no—
298#816—51no—
299#815—51no—
300Dic3⋊C8—51no—
301C24×C5—21no—
302C23×D5—61no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8C22×D311yescharacteristic
306C2×C5×D4—22no—
307C2×C5×D4—21no—
308C2×C5×D4—21no—
309C2×C5×D4—41no—
310C2×C5×D4C22×D311yescharacteristic
311C2×C5×D4C22×D311yescharacteristic
312C2×C5×D4C22×D311yescharacteristic
313C22×C4×C5—21no—
314C22×C4×C5C22×D311yescharacteristic
315C2×C22⋊D5—31no—
316C2×C22⋊D5—61no—
317C2×C22⋊D5—61no—
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320C2×C22⋊D5—61no—
321C2×C22⋊D5—61no—
322C2×C22⋊D5—124no—
323C22×Dic5—61no—
324Q8×D5—62no—
325Q8×D5—121no—
326D4×D5—62no—
327D4×D5—121no—
328C2×D20—31no—
329C2×C4×D5—31no—
330C2×C4×D5—61no—
331C2×Dic10—31no—
332C2×Dic10—61no—
333C5×SD16—22no—
334C5×SD16#6714yescomplemented
335C5×D8—22no—
336C5×D8—22no—
337C5×M16—22no—
338C2×C5×C8C22×D311yescharacteristic
339C2×C5×C8C22×D311yescharacteristic
340C22⋊Dic5—31no—
341C22⋊Dic5—61no—
342C22⋊Dic5—61no—
343C22⋊Dic5—61no—
344C22⋊Dic5—61no—
345C22⋊Dic5—61no—
346C22⋊Dic5—61no—
347#688—62no—
348#687—62no—
349#687—121no—
350#686—121no—
351#685—31no—
352#685—61no—
353C4⋊Dic5—31no—
354C4⋊Dic5—31no—
355C4⋊Dic5—61no—
356#683—31no—
357#683—61no—
358C4×Dic5—31no—
359C4×Dic5—61no—
360C2×#168—31no—
361C2×#168—31no—
362#677—62no—
363C8×D5—62no—
364C2×AGL(1,ℤ/8)D1511yescharacteristic, complemented
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#435—151no—
379C22×C3×C5—22no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5—84no—
392C22×C3×C5C22×D411yescharacteristic
393C2×D15—21no—
394C2×D15—21no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15—41no—
398C2×D15—84no—
399C2×D15AGL(1,ℤ/8)12yescomplemented
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404Dic15—21no—
405Dic15—21no—
406Dic15—21no—
407Dic15—41no—
408Dic15—41no—
409Dic15—41no—
410C24×C3—21no—
411C23×D3—101no—
412C3×#41—22no—
413C3×#41—41no—
414C2×C3×Q8C22×D511yescharacteristic
415C2×C3×D4—22no—
416C2×C3×D4—21no—
417C2×C3×D4—21no—
418C2×C3×D4—41no—
419C2×C3×D4C22×D511yescharacteristic
420C2×C3×D4C22×D511yescharacteristic
421C2×C3×D4C22×D511yescharacteristic
422C22×C3×C4—21no—
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—51no—
425C2×#67—101no—
426C2×#67—101no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—101no—
431C2×#67—204no—
432C22×Dic3—101no—
433D3×Q8—102no—
434D3×Q8—201no—
435D3×D4—102no—
436D3×D4—201no—
437C2×D12—51no—
438C2×C4×D3—51no—
439C2×C4×D3—101no—
440C2×Dic6—51no—
441C2×Dic6—101no—
442C3×SD16—22no—
443C3×SD16C22⋊D514yescomplemented
444C3×D8—22no—
445C3×D8—22no—
446C3×M16—22no—
447C2×C3×C8C22×D511yescharacteristic
448C2×C3×C8C22×D511yescharacteristic
449#217—51no—
450#217—101no—
451#217—101no—
452#217—101no—
453#217—101no—
454#217—101no—
455#217—101no—
456#215—102no—
457#214—102no—
458#214—201no—
459#213—201no—
460(C2×D3)⋊C4—51no—
461(C2×D3)⋊C4—101no—
462C4⋊Dic3—51no—
463C4⋊Dic3—51no—
464C4⋊Dic3—101no—
465Dic3⋊C4—51no—
466Dic3⋊C4—101no—
467C4×Dic3—51no—
468C4×Dic3—101no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471#204—102no—
472D3×C8—102no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—81no—
479C23×C5D3×D411yescharacteristic
480C22×D5—31no—
481C22×D5—61no—
482C22×D5—122no—
483C22×D5—122no—
484C22×D5—241no—
485C5×Q8—21no—
486C5×Q8C2×#6712yescomplemented
487C5×D4—21no—
488C5×D4—21no—
489C5×D4—21no—
490C5×D4—21no—
491C5×D4—21no—
492C5×D4—42no—
493C5×D4—42no—
494C5×D4C2×#6712yes—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—42no—
499C2×C4×C5D3×D411yescharacteristic
500C2×C4×C5C23×D311yescharacteristic
501C22⋊D5—62no—
502C22⋊D5—122no—
503C22⋊D5—122no—
504C22⋊D5—122no—
505C22⋊D5—122no—
506C22⋊D5—122no—
507C22⋊D5—241no—
508C2×Dic5—31no—
509C2×Dic5—31no—
510C2×Dic5—31no—
511C2×Dic5—61no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—61no—
516D20—61no—
517C4×D5—61no—
518C4×D5—61no—
519C4×D5—122no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523C5×C8—21no—
524C5×C8C2×#6712yescomplemented
525#168—61no—
526#168—61no—
527C2×#41C2×D1511yescharacteristic, complemented
528C22×Q8—151no—
529C22×D4—151no—
530C22×D4—301no—
531C22×D4C2×D1511yescharacteristic
532AGL(1,ℤ/8)—24no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—304no—
538C2×SD16C2×D1511yescharacteristic
539C2×SD16C2×D1511yescharacteristic, complemented
540C2×D8—151no—
541C2×D8C2×D1511yescharacteristic
542C2×D8C2×D1511yescharacteristic, complemented
543C2×M16C2×D1511yescharacteristic, complemented
544C22×C8—151no—
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—151no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—42no—
573C2×C3×C5—41no—
574C2×C3×C5—81no—
575C2×C3×C5—81no—
576C2×C3×C5D4211yescharacteristic
577C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
578C2×C3×C5#57711yescharacteristic
579D15—22no—
580D15—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—42no—
585C23×C3—42no—
586C23×C3—81no—
587C23×C3D4×D511yescharacteristic
588C22×D3—51no—
589C22×D3—101no—
590C22×D3—202no—
591C22×D3—202no—
592C22×D3—401no—
593C3×Q8—21no—
594C3×Q8C2×C22⋊D512yescomplemented
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—42no—
601C3×D4—42no—
602C3×D4C2×C22⋊D512yes—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—42no—
607C2×C3×C4D4×D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609#67—102no—
610#67—202no—
611#67—202no—
612#67—202no—
613#67—202no—
614#67—202no—
615#67—401no—
616C2×Dic3—51no—
617C2×Dic3—51no—
618C2×Dic3—51no—
619C2×Dic3—101no—
620C2×Dic3—101no—
621C2×Dic3—101no—
622C2×Dic3—202no—
623D12—101no—
624D12—101no—
625C4×D3—101no—
626C4×D3—101no—
627C4×D3—202no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—21no—
632C3×C8C2×C22⋊D512yescomplemented
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—22no—
638C22×C5—21no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—41no—
644C22×C5—41no—
645C22×C5—41no—
646C22×C5—41no—
647C22×C5—84no—
648C22×C5C2×D3×D411yescharacteristic
649C2×D5—32no—
650C2×D5—61no—
651C2×D5—61no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—244no—
656C4×C5—22no—
657C4×C5—21no—
658C4×C5#100411yescharacteristic
659C4×C5C22×#6711yescharacteristic
660Dic5—61no—
661Dic5—61no—
662Dic5—61no—
663Dic5—121no—
664Dic5—121no—
665Dic5—121no—
666C24—21no—
667C24—301no—
668#41—22no—
669#41—41no—
670C2×Q8—151no—
671C2×Q8—301no—
672C2×Q8—302no—
673C2×Q8—601no—
674C2×Q8C22×D1511yescharacteristic
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—151no—
680C2×D4—151no—
681C2×D4—301no—
682C2×D4—301no—
683C2×D4—301no—
684C2×D4—302no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—601no—
689C2×D4—604no—
690C2×D4C22×D1511yescharacteristic
691C2×D4C22×D1511yescharacteristic
692C2×D4C22×D1511yescharacteristic
693C22×C4—21no—
694C22×C4—151no—
695C22×C4—301no—
696C22×C4—301no—
697C22×C4C22×D1511yescharacteristic
698SD16—22no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—601no—
703SD16#122014yescomplemented
704D8—22no—
705D8—22no—
706D8—601no—
707M16—22no—
708C2×C8—151no—
709C2×C8—151no—
710C2×C8—302no—
711C2×C8C22×D1511yescharacteristic
712C2×C8C22×D1511yescharacteristic
713C4⋊C4—151no—
714C4⋊C4—151no—
715C4⋊C4—151no—
716C4⋊C4—301no—
717C4⋊C4—301no—
718C22⋊C4—151no—
719C22⋊C4—151no—
720C22⋊C4—301no—
721C22⋊C4—301no—
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—22no—
733C22×C3—21no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—84no—
743C22×C3C2×D4×D511yescharacteristic
744C2×D3—52no—
745C2×D3—101no—
746C2×D3—101no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—404no—
751C3×C4—22no—
752C3×C4—21no—
753C3×C4#414411yescharacteristic
754C3×C4C22×C22⋊D511yescharacteristic
755Dic3—101no—
756Dic3—101no—
757Dic3—101no—
758Dic3—201no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—42no—
762C2×C5—41no—
763C2×C5—81no—
764C2×C5—81no—
765C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
766C2×C5#577511yescharacteristic
767C2×C5D4×#6711yescharacteristic
768D5—62no—
769D5—241no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—42no—
774C23—42no—
775C23—81no—
776C23—151no—
777C23—301no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23D4×D1511yescharacteristic
782Q8—21no—
783Q8—301no—
784Q8—301no—
785Q8—602no—
786Q8C2×#122012yescomplemented
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—42no—
793D4—42no—
794D4—302no—
795D4—301no—
796D4—301no—
797D4—602no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—1201no—
803D4C2×#122012yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—42no—
808C2×C4—151no—
809C2×C4—151no—
810C2×C4—151no—
811C2×C4—301no—
812C2×C4—301no—
813C2×C4—301no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—602no—
817C2×C4—602no—
818C2×C4D4×D1511yescharacteristic
819C2×C4C23×D1511yescharacteristic
820C8—21no—
821C8—301no—
822C8—301no—
823C8C2×#122012yescomplemented
824C2×C3—42no—
825C2×C3—41no—
826C2×C3—81no—
827C2×C3—81no—
828C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
829C2×C3#6610911yescharacteristic
830C2×C3D4×C22⋊D511yescharacteristic
831D3—102no—
832D3—401no—
833C5#8395311yescharacteristic, complemented, Sylow
834C22—21no—
835C22—22no—
836C22—21no—
837C22—21no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—84no—
847C22—152no—
848C22—301no—
849C22—301no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22—1204no—
854C22C2×D4×D1511yescharacteristic
855C4—21no—
856C4—22no—
857C4—301no—
858C4—301no—
859C4—301no—
860C4—601no—
861C4—601no—
862C4—601no—
863C4#9209511yescharacteristic
864C4C22×#122011yescharacteristic
865C3#1061568411yescharacteristic, complemented, Sylow
866C2—41no—
867C2—42no—
868C2—81no—
869C2—81no—
870C2—302no—
871C2—1201no—
872C2D15×AGL(1,ℤ/8)11yescharacteristic
873C2#1175653411yescharacteristic
874C2D4×#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#3265
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. #11756590C2semidirect
3. D4×#1220C2semidirect
4. C2×SD16×D15C2semidirect
5. #11751339C2semidirect
6. #11751319C2semidirect
7. #11751271C2semidirect
8. #11751265C2semidirect
9. #11751264C2semidirect
10. #11751258C2semidirect
11. #11751257C2semidirect
12. #11751255C2semidirect
13. #11751254C2semidirect
14. #11751235C2semidirect
15. #11751228C2semidirect
17. C2×C3×C5×#41C22semidirect
20. C2×Q8×D15C22semidirect
24. C2×C3×C5×SD16C22semidirect
26. C2×C3×C5×D8C22semidirect
27. C2×C3×C5×M16C22semidirect
29. Q8×Dic15C22semidirect
30. C2×#6717C22semidirect
35. #91827C22semidirect
38. #91825C22semidirect
41. C2×#6716C22semidirect
42. C2×#6715C22semidirect
47. #91813C22semidirect
49. C2×#6706C22semidirect
50. C2×C8×D15C22semidirect
51. #91119C22semidirect
53. #91116C22semidirect
54. #91116C22semidirect
55. #91114C22semidirect
56. #91105C22semidirect
57. #91104C22semidirect
58. #91102C22semidirect
59. #91100C22semidirect
60. #91099C22semidirect
61. #91098C22semidirect
63. C2×C5×AGL(1,ℤ/8)D3semidirect
111. C3×C5×SD16D4semidirect
141. C2×C3×AGL(1,ℤ/8)D5semidirect
156. C2×C5×#41C2×D3semidirect
163. C2×C5×SD16C2×D3semidirect
165. C2×C5×D8C2×D3semidirect
166. C2×C5×M16C2×D3semidirect
215. C3×C5×Q8C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
256. C2×C3×#41C2×D5semidirect
263. C2×C3×SD16C2×D5semidirect
265. C2×C3×D8C2×D5semidirect
266. C2×C3×M16C2×D5semidirect
334. C5×SD16#67semidirect
364. C2×AGL(1,ℤ/8)D15semidirect
399. C2×D15AGL(1,ℤ/8)semidirect
443. C3×SD16C22⋊D5semidirect
486. C5×Q8C2×#67semidirect
524. C5×C8C2×#67semidirect
527. C2×#41C2×D15semidirect
539. C2×SD16C2×D15semidirect
542. C2×D8C2×D15semidirect
543. C2×M16C2×D15semidirect
594. C3×Q8C2×C22⋊D5semidirect
632. C3×C8C2×C22⋊D5semidirect
703. SD16#1220semidirect
729. C3×C5#3265semidirect
786. Q8C2×#1220semidirect
823. C8C2×#1220semidirect
833. C5#83953semidirect
865. C3#10615684semidirect

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
#117565902
D4×#12202
C2×SD16×D152
#117513392
#117513192
#117512712
#117512652
#117512642
#117512582
#117512572
#117512552
#117512542
#117512352
#117512282
#106156843
#839535