Finite Group Databasebeta

← #14453207

Subgroups — #14453207

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
1D4×#1220C211yesmaximal, characteristic, complemented
2C22×#6715C211yesmaximal, characteristic, complemented
3C2×#91803C211yesmaximal, characteristic, complemented
4#11756389C211yesmaximal, characteristic, complemented
5C3×C5×#450C211yesmaximal, characteristic, complemented
6#11751277C211yesmaximal, characteristic, complemented
7#11751273C211yesmaximal, characteristic, complemented
8#11751266C211yesmaximal, characteristic, complemented
9#11751149C211yesmaximal, characteristic, complemented
10#11750887C211yesmaximal, characteristic, complemented
11#11750886C211yesmaximal, characteristic, complemented
12#11750883C211yesmaximal, characteristic, complemented
13#11750874C211yesmaximal, characteristic, complemented
14#11750833C211yesmaximal, characteristic, complemented
15#11750831C211yesmaximal, characteristic, complemented
16#10611897—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220—21no—
19C2×#6821C2211yescharacteristic, complemented
20C2×D4×D15C2211yescharacteristic, complemented
21C22×D60C2211yescharacteristic, complemented
22C2×C3×C5×SD16C2211yescharacteristic, complemented
23C2×C3×C5×SD16C2211yescharacteristic, complemented
24C3×C5×C22⋊Q8C2211yescharacteristic, complemented
25#91842—21no—
26#91836C2211yescharacteristic, complemented
27C2×#6717C2211yescharacteristic, complemented
28#91829C2211yescharacteristic, complemented
29#91828—21no—
30#91827C2211yescharacteristic, complemented
31#91826—21no—
32D4×Dic15C2211yescharacteristic, complemented
33C2×#6715—24no—
34C2×#6715C2211yescharacteristic
35C2×#6715C2211yescharacteristic
36C2×#6715C2211yescharacteristic, complemented
37C2×#6715C2211yescharacteristic, complemented
38#91819C2211yescharacteristic
39C4×#1220C2211yescharacteristic
40C22×C3⋊#168C2211yescharacteristic, complemented
41#91803—24no—
42C2×D120C2211yescharacteristic, complemented
43C2×D120C2211yescharacteristic, complemented
44C2×#6705C2211yescharacteristic, complemented
45#91784—21no—
46#91784C2211yescharacteristic, complemented
47#91783—21no—
48#91782C2211yescharacteristic, complemented
49#91771—21no—
50C22⋊C4×D15—21no—
51C3×C5×#102C2211yescharacteristic, complemented
52C3×C5×#102C2211yescharacteristic, complemented
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54#91119C2211yescharacteristic, complemented
55#91105C2211yescharacteristic, complemented
56#91105C2211yescharacteristic, complemented
57#91104C2211yescharacteristic, complemented
58#91099C2211yescharacteristic, complemented
59#91098C2211yescharacteristic, complemented
60#91093C2211yescharacteristic, complemented
61#91092C2211yescharacteristic, complemented
62#80166—51nomaximal, Hall
63D4×C22⋊D5—31no—
64C22×#686—31no—
65C2×#4060—31no—
66#65964—31no—
67C5×#450D311yescharacteristic, complemented
68#65465—31no—
69#65461—31no—
70#65454—31no—
71#65337—31no—
72#65075—31no—
73#65074—31no—
74#65071—31no—
75#65062—31no—
76#65021—31no—
77#65019—31no—
78C24×C3×C5—21no—
79C23×D15—21no—
80C23×D15—21no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4—22no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—41no—
85C2×C3×C5×D4C2311yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—21no—
89C2×#1220—21no—
90C2×#1220—21no—
91C2×#1220—21no—
92C2×#1220—21no—
93C2×#1220—44no—
94C2×#1220D411yescharacteristic
95C22×Dic15—21no—
96#6821—22no—
97#6821—41no—
98D4×D15—22no—
99D4×D15—41no—
100C2×D60—22no—
101C2×D60—21no—
102C2×D60—21no—
103C2×D60—21no—
104C2×D60—41no—
105C2×D60C2311yescharacteristic
106C2×D60C2311yescharacteristic
107C2×D60C2311yescharacteristic
108C2×C4×D15—21no—
109C2×C4×D15—21no—
110C2×C4×D15C2311yescharacteristic
111C3×C5×SD16—22no—
112C3×C5×SD16—41no—
113C2×C3×C5×C8C2311yescharacteristic
114C2×C3×C5×C8C2311yescharacteristic
115C3×C5×C4⋊C4—21no—
116C3×C5×C4⋊C4C2311yescharacteristic
117C3×C5×C22⋊C4—21no—
118#6719—21no—
119#6719—21no—
120#6719D411yescharacteristic
121#6717—22no—
122#6715—22no—
123#6715—22no—
124#6715—22no—
125#6715D414yescomplemented
126#6714—21no—
127#6714—21no—
128#6714—21no—
129#6714—21no—
130#6714—21no—
131#6714D411yescharacteristic
132C4⋊Dic15C2311yescharacteristic
133#6712D411yescharacteristic
134C4×Dic15C2311yescharacteristic
135C2×C3⋊#168—22no—
136C2×C3⋊#168C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138D120—22no—
139D120—41no—
140#6705—22no—
141D4×#67—51no—
142C22×#213—51no—
143C2×#914—51no—
144#5630—51no—
145C3×#450D511yescharacteristic, complemented
146#5176—51no—
147#5172—51no—
148#5165—51no—
149#5048—51no—
150#4786—51no—
151#4785—51no—
152#4782—51no—
153#4773—51no—
154#4732—51no—
155#4730—51no—
156C22×C5×D4C2×D311yescharacteristic
157C22×C22⋊D5—61no—
158C2×#713—31no—
159C2×D4×D5—31no—
160C22×D20—31no—
161C2×C5×SD16C2×D311yescharacteristic, complemented
162C2×C5×SD16C2×D311yescharacteristic, complemented
163C5×C22⋊Q8C2×D311yescharacteristic, complemented
164#4099—61no—
165#4093—31no—
166C2×#688—31no—
167#4086—31no—
168#4085—61no—
169#4084—31no—
170#4083—61no—
171D4×Dic5—31no—
172C2×#686—31no—
173C2×#686—31no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—64no—
177#4076—31no—
178C4×C22⋊D5—31no—
179C22×#168—31no—
180#4060—64no—
181C2×D40—31no—
182C2×D40—31no—
183C2×#676—31no—
184#4041—31no—
185#4041—61no—
186#4040—61no—
187#4039—31no—
188#4028—61no—
189D5×C22⋊C4—61no—
190C5×#102C2×D311yescharacteristic, complemented
191C5×#102C2×D311yescharacteristic, complemented
192C5×C22⋊C8C2×D311yescharacteristic, complemented
193#3967—31no—
194#3953—31no—
195#3953—31no—
196#3952—31no—
197#3947—31no—
198#3946—31no—
199#3941—31no—
200#3940—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C22×D15—21no—
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—42no—
224C3×C5×D4C2×D412yes—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2411yescharacteristic
231#1220—22no—
232#1220—42no—
233#1220—42no—
234#1220—42no—
235#1220—42no—
236#1220—81no—
237C2×Dic15—21no—
238C2×Dic15—42no—
239C2×Dic15C2×D411yescharacteristic
240C2×Dic15C2×D411yescharacteristic
241C2×Dic15C2×D411yescharacteristic
242D60—21no—
243D60—21no—
244D60—21no—
245D60—21no—
246D60—21no—
247D60—42no—
248D60—42no—
249D60—81no—
250D60C2×D412yescomplemented
251C4×D15—21no—
252C4×D15—21no—
253C4×D15—42no—
254C4×D15—81no—
255C3×C5×C8—21no—
256C3×C5×C8—21no—
257C3⋊#168—21no—
258C3⋊#168C2×D412yescomplemented
259C22×C3×D4C2×D511yescharacteristic
260C22×#67—101no—
261C2×#239—51no—
262C2×D3×D4—51no—
263C22×D12—51no—
264C2×C3×SD16C2×D511yescharacteristic, complemented
265C2×C3×SD16C2×D511yescharacteristic, complemented
266C3×C22⋊Q8C2×D511yescharacteristic, complemented
267#953—101no—
268#947—51no—
269C2×#215—51no—
270#940—51no—
271#939—101no—
272#938—51no—
273#937—101no—
274D4×Dic3—51no—
275C2×#213—51no—
276C2×#213—51no—
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—104no—
280#930—51no—
281C4×#67—51no—
282C22×C3⋊C8—51no—
283#914—104no—
284C2×D24—51no—
285C2×D24—51no—
286C2×ΓL(1,𝔽25)—51no—
287#895—51no—
288#895—101no—
289#894—101no—
290#893—51no—
291#882—101no—
292D3×C22⋊C4—101no—
293C3×#102C2×D511yescharacteristic, complemented
294C3×#102C2×D511yescharacteristic, complemented
295C3×C22⋊C8C2×D511yescharacteristic, complemented
296#835—51no—
297#821—51no—
298#821—51no—
299(C2×D3)⋊C8—51no—
300#815—51no—
301Dic3⋊C8—51no—
302#809—51no—
303#808—51no—
304C24×C5—21no—
305C23×D5—61no—
306C23×D5—61no—
307C2×C5×Q8C22×D311yescharacteristic
308C2×C5×D4—22no—
309C2×C5×D4—21no—
310C2×C5×D4—41no—
311C2×C5×D4C22×D311yescharacteristic
312C2×C5×D4C22×D311yescharacteristic
313C22×C4×C5C22×D311yescharacteristic
314C2×C22⋊D5—31no—
315C2×C22⋊D5—61no—
316C2×C22⋊D5—61no—
317C2×C22⋊D5—61no—
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320C2×C22⋊D5—124no—
321C22×Dic5—61no—
322#713—62no—
323#713—121no—
324D4×D5—62no—
325D4×D5—121no—
326C2×D20—31no—
327C2×D20—31no—
328C2×D20—31no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—121no—
334C2×C4×D5—31no—
335C2×C4×D5—61no—
336C2×C4×D5—61no—
337C5×SD16—22no—
338C5×SD16—41no—
339C2×C5×C8C22×D311yescharacteristic
340C2×C5×C8C22×D311yescharacteristic
341C5×C4⋊C4—21no—
342C5×C4⋊C4C22×D311yescharacteristic
343C5×C22⋊C4—21no—
344C22⋊Dic5—31no—
345C22⋊Dic5—61no—
346C22⋊Dic5—61no—
347#688—62no—
348#686—34no—
349#686—62no—
350#686—62no—
351#686—62no—
352#685—31no—
353#685—61no—
354#685—61no—
355#685—61no—
356#685—61no—
357#685—61no—
358C4⋊Dic5—31no—
359#683—31no—
360C4×Dic5—31no—
361C2×#168—31no—
362C2×#168—31no—
363C2×#168—62no—
364D40—62no—
365D40—121no—
366#676—62no—
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—151no—
370D42—151no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450D1511yescharacteristic, complemented
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—22no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—84no—
391C22×C3×C5AGL(1,ℤ/8)12yescomplemented
392C22×C3×C5C22×D411yescharacteristic
393C2×D15—21no—
394C2×D15—22no—
395C2×D15—21no—
396C2×D15—21no—
397C2×D15—41no—
398C2×D15—41no—
399C2×D15—41no—
400C2×D15—41no—
401C2×D15—41no—
402C2×D15—41no—
403C2×D15—41no—
404C2×D15—41no—
405C2×D15—84no—
406C2×D15—84no—
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5—41no—
410C3×C4×C5C22×D411yescharacteristic
411C3×C4×C5H(5,𝔽2)11yescharacteristic
412Dic15—21no—
413Dic15—21no—
414Dic15—21no—
415Dic15—41no—
416C24×C3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C2×C3×Q8C22×D511yescharacteristic
420C2×C3×D4—22no—
421C2×C3×D4—21no—
422C2×C3×D4—41no—
423C2×C3×D4C22×D511yescharacteristic
424C2×C3×D4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C2×#67—51no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—101no—
431C2×#67—101no—
432C2×#67—204no—
433C22×Dic3—101no—
434#239—102no—
435#239—201no—
436D3×D4—102no—
437D3×D4—201no—
438C2×D12—51no—
439C2×D12—51no—
440C2×D12—51no—
441C2×D12—102no—
442C2×D12—101no—
443C2×D12—101no—
444C2×D12—101no—
445C2×D12—201no—
446C2×C4×D3—51no—
447C2×C4×D3—101no—
448C2×C4×D3—101no—
449C3×SD16—22no—
450C3×SD16—41no—
451C2×C3×C8C22×D511yescharacteristic
452C2×C3×C8C22×D511yescharacteristic
453C3×C4⋊C4—21no—
454C3×C4⋊C4C22×D511yescharacteristic
455C3×C22⋊C4—21no—
456#217—51no—
457#217—101no—
458#217—101no—
459#215—102no—
460#213—54no—
461#213—102no—
462#213—102no—
463#213—102no—
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—
471Dic3⋊C4—51no—
472C4×Dic3—51no—
473C2×C3⋊C8—51no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—102no—
476D24—102no—
477D24—201no—
478ΓL(1,𝔽25)—102no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—42no—
482C23×C5—42no—
483C23×C5—81no—
484C23×C5D3×D411yescharacteristic
485C22×D5—31no—
486C22×D5—61no—
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—42no—
501C5×D4D3×D412yes—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5D3×D411yescharacteristic
507C2×C4×C5C23×D311yescharacteristic
508C22⋊D5—62no—
509C22⋊D5—122no—
510C22⋊D5—122no—
511C22⋊D5—122no—
512C22⋊D5—122no—
513C22⋊D5—241no—
514C2×Dic5—31no—
515C2×Dic5—31no—
516C2×Dic5—31no—
517C2×Dic5—61no—
518C2×Dic5—122no—
519D20—32no—
520D20—61no—
521D20—61no—
522D20—61no—
523D20—61no—
524D20—61no—
525D20—122no—
526D20—122no—
527D20—241no—
528C4×D5—61no—
529C4×D5—61no—
530C4×D5—122no—
531C4×D5—241no—
532C5×C8—21no—
533C5×C8—21no—
534#168—32no—
535#168—61no—
536C2×#41—151no—
537C22×D4—151no—
538C22×D4—151no—
539C22×D4—301no—
540C22×D4C2×D1511yescharacteristic
541AGL(1,ℤ/8)—304no—
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—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127—151no—
555#124—151no—
556#123—301no—
557C22⋊Q8C2×D1511yescharacteristic, complemented
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#102C2×D1511yescharacteristic, complemented
577#102C2×D1511yescharacteristic, complemented
578C22⋊C8—151no—
579C22⋊C8C2×D1511yescharacteristic, complemented
580#97—151no—
581C2×C3×C5—22no—
582C2×C3×C5—42no—
583C2×C3×C5—81no—
584C2×C3×C5D4211yescharacteristic
585C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
586C2×C3×C5#57611yescharacteristic
587D15—41no—
588D15—42no—
589D15—81no—
590D15—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—81no—
596C23×C3D4×D511yescharacteristic
597C22×D3—51no—
598C22×D3—101no—
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—42no—
613C3×D4D4×D512yes—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4D4×D511yescharacteristic
619C2×C3×C4C23×D511yescharacteristic
620#67—102no—
621#67—202no—
622#67—202no—
623#67—202no—
624#67—202no—
625#67—401no—
626C2×Dic3—51no—
627C2×Dic3—51no—
628C2×Dic3—51no—
629C2×Dic3—101no—
630C2×Dic3—202no—
631D12—52no—
632D12—101no—
633D12—101no—
634D12—101no—
635D12—101no—
636D12—101no—
637D12—202no—
638D12—202no—
639D12—401no—
640C4×D3—101no—
641C4×D3—101no—
642C4×D3—202no—
643C4×D3—401no—
644C3×C8—21no—
645C3×C8—21no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—22no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—84no—
657C22×C5#91412yescomplemented
658C22×C5C2×D3×D411yescharacteristic
659C2×D5—61no—
660C2×D5—61no—
661C2×D5—61no—
662C2×D5—62no—
663C2×D5—121no—
664C2×D5—121no—
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—41no—
676C4×C5C2×D3×D411yescharacteristic
677C4×C5#100411yescharacteristic
678Dic5—61no—
679Dic5—61no—
680Dic5—61no—
681Dic5—121no—
682C24—21no—
683C24—301no—
684C24—301no—
685#41—302no—
686#41—601no—
687C2×Q8C22×D1511yescharacteristic
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—151no—
692C2×D4—151no—
693C2×D4—151no—
694C2×D4—151no—
695C2×D4—302no—
696C2×D4—301no—
697C2×D4—301no—
698C2×D4—301no—
699C2×D4—301no—
700C2×D4—301no—
701C2×D4—302no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—301no—
705C2×D4—601no—
706C2×D4—601no—
707C2×D4—604no—
708C2×D4C22×D1511yescharacteristic
709C2×D4C22×D1511yescharacteristic
710C22×C4—151no—
711C22×C4—301no—
712C22×C4—301no—
713C22×C4—301no—
714C22×C4C22×D1511yescharacteristic
715SD16—22no—
716SD16—41no—
717SD16—302no—
718D8—154no—
719D8—302no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—151no—
726C2×C8—151no—
727C2×C8—302no—
728C2×C8C22×D1511yescharacteristic
729C2×C8C22×D1511yescharacteristic
730C4⋊C4—21no—
731C4⋊C4—151no—
732C4⋊C4—151no—
733C4⋊C4C22×D1511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—151no—
736C22⋊C4—151no—
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—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—84no—
755C22×C3#406012yescomplemented
756C22×C3C2×D4×D511yescharacteristic
757C2×D3—101no—
758C2×D3—101no—
759C2×D3—101no—
760C2×D3—102no—
761C2×D3—201no—
762C2×D3—201no—
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—41no—
774C3×C4C2×D4×D511yescharacteristic
775C3×C4#414411yescharacteristic
776Dic3—101no—
777Dic3—101no—
778Dic3—101no—
779Dic3—201no—
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—81no—
783C2×C5#559011yescharacteristic
784C2×C5C2×#91411yescharacteristic
785C2×C5#577411yescharacteristic
786D5—121no—
787D5—122no—
788D5—241no—
789D5—241no—
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—81no—
795C23—151no—
796C23—301no—
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—42no—
812D4—152no—
813D4—302no—
814D4—301no—
815D4—301no—
816D4—301no—
817D4—301no—
818D4—301no—
819D4—602no—
820D4—602no—
821D4—602no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—1201no—
826D4—1201no—
827D4D4×D1512yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—151no—
833C2×C4—151no—
834C2×C4—151no—
835C2×C4—301no—
836C2×C4—301no—
837C2×C4—301no—
838C2×C4—602no—
839C2×C4—602no—
840C2×C4—1201no—
841C2×C4D4×D1511yescharacteristic
842C2×C4C23×D1511yescharacteristic
843C8—21no—
844C8—21no—
845C8—152no—
846C8—301no—
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3#6592411yescharacteristic
851C2×C3C2×#406011yescharacteristic
852C2×C3#6610811yescharacteristic
853D3—201no—
854D3—202no—
855D3—401no—
856D3—401no—
857C5#8016611yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—84no—
867C22—301no—
868C22—302no—
869C22—301no—
870C22—301no—
871C22—601no—
872C22—601no—
873C22—601no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—1204no—
880C22—1204no—
881C22#9180312yescomplemented
882C22C2×D4×D1511yescharacteristic
883C4—21no—
884C4—41no—
885C4—41no—
886C4—301no—
887C4—301no—
888C4—301no—
889C4—601no—
890C4C2×D4×D1511yescharacteristic
891C4#9209511yescharacteristic
892C3#1061189711yescharacteristic, complemented, Sylow
893C2—22no—
894C2—42no—
895C2—81no—
896C2—601no—
897C2—602no—
898C2—1201no—
899C2—1201no—
900C2#1175634911yescharacteristic
901C2C2×#9180311yescharacteristic
902C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#450C2
socleC22×C3×C5C22×D4
hypercenter#450D15
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. D4×#1220C2semidirect
2. C22×#6715C2semidirect
3. C2×#91803C2semidirect
4. #11756389C2semidirect
5. C3×C5×#450C2semidirect
6. #11751277C2semidirect
7. #11751273C2semidirect
8. #11751266C2semidirect
9. #11751149C2semidirect
10. #11750887C2semidirect
11. #11750886C2semidirect
12. #11750883C2semidirect
13. #11750874C2semidirect
14. #11750833C2semidirect
15. #11750831C2semidirect
19. C2×#6821C22semidirect
20. C2×D4×D15C22semidirect
21. C22×D60C22semidirect
22. C2×C3×C5×SD16C22semidirect
23. C2×C3×C5×SD16C22semidirect
24. C3×C5×C22⋊Q8C22semidirect
26. #91836C22semidirect
27. C2×#6717C22semidirect
28. #91829C22semidirect
30. #91827C22semidirect
32. D4×Dic15C22semidirect
36. C2×#6715C22semidirect
37. C2×#6715C22semidirect
40. C22×C3⋊#168C22semidirect
42. C2×D120C22semidirect
43. C2×D120C22semidirect
44. C2×#6705C22semidirect
46. #91784C22semidirect
48. #91782C22semidirect
51. C3×C5×#102C22semidirect
52. C3×C5×#102C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. #91119C22semidirect
55. #91105C22semidirect
56. #91105C22semidirect
57. #91104C22semidirect
58. #91099C22semidirect
59. #91098C22semidirect
60. #91093C22semidirect
61. #91092C22semidirect
67. C5×#450D3semidirect
125. #6715D4semidirect
145. C3×#450D5semidirect
161. C2×C5×SD16C2×D3semidirect
162. C2×C5×SD16C2×D3semidirect
163. C5×C22⋊Q8C2×D3semidirect
190. C5×#102C2×D3semidirect
191. C5×#102C2×D3semidirect
192. C5×C22⋊C8C2×D3semidirect
250. D60C2×D4semidirect
258. C3⋊#168C2×D4semidirect
264. C2×C3×SD16C2×D5semidirect
265. C2×C3×SD16C2×D5semidirect
266. C3×C22⋊Q8C2×D5semidirect
293. C3×#102C2×D5semidirect
294. C3×#102C2×D5semidirect
295. C3×C22⋊C8C2×D5semidirect
376. #450D15semidirect
391. C22×C3×C5AGL(1,ℤ/8)semidirect
543. C2×SD16C2×D15semidirect
544. C2×SD16C2×D15semidirect
557. C22⋊Q8C2×D15semidirect
576. #102C2×D15semidirect
577. #102C2×D15semidirect
579. C22⋊C8C2×D15semidirect
657. C22×C5#914semidirect
745. C3×C5#3264semidirect
755. C22×C3#4060semidirect
857. C5#80166semidirect
881. C22#91803semidirect
892. C3#10611897semidirect

Maximal subgroups

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

subgroupindex
D4×#12202
C22×#67152
C2×#918032
#117563892
C3×C5×#4502
#117512772
#117512732
#117512662
#117511492
#117508872
#117508862
#117508832
#117508742
#117508332
#117508312
#106118973
#801665