Finite Group Databasebeta

← #14453290

Subgroups — #14453290

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
1C22×#6715C211yesmaximal, characteristic, complemented
2C5×D4×#67C211yesmaximal, characteristic, complemented
3C2×#91496C211yesmaximal, characteristic, complemented
4#11754382C211yesmaximal, characteristic, complemented
5C3×#65507C211yesmaximal, characteristic, complemented
6#11749162C211yesmaximal, characteristic, complemented
7#11749080C211yesmaximal, characteristic, complemented
8#11749076C211yesmaximal, characteristic, complemented
9#11749037C211yesmaximal, characteristic, complemented
10#11749033C211yesmaximal, characteristic, complemented
11#11748989C211yesmaximal, characteristic, complemented
12#11748987C211yesmaximal, characteristic, complemented
13#11748547C211yesmaximal, characteristic, complemented
14#11748525C211yesmaximal, characteristic, complemented
15#11748508C211yesmaximal, characteristic, complemented
16#10615219—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×D60C2211yescharacteristic, complemented
19C22×C5×#67—21no—
20C2×C5×D3×D4C2211yescharacteristic, complemented
21C2×#6769C2211yescharacteristic, complemented
22C2×#6715—24no—
23C2×#6715C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25C2×#6715C2211yescharacteristic, complemented
26C2×#6715C2211yescharacteristic, complemented
27C22×C3⋊#168C2211yescharacteristic, complemented
28C5×#953—21no—
29C5×#940C2211yescharacteristic, complemented
30C5×#939—21no—
31C5×#938C2211yescharacteristic, complemented
32C5×#937—21no—
33C5×D4×Dic3C2211yescharacteristic, complemented
34C5×#930C2211yescharacteristic
35C4×C5×#67C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#687C2211yescharacteristic, complemented
38C3×#4070C2211yescharacteristic, complemented
39#91573—21no—
40#91561—21no—
41#91496—24no—
42#91460C2211yescharacteristic, complemented
43#91433—21no—
44#91428C2211yescharacteristic, complemented
45#91420—21no—
46#91374C2211yescharacteristic, complemented
47C2×#6656C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49C2×#6654C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C3×#3964C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×C22⋊#168C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90969C2211yescharacteristic, complemented
59#90966C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80166—51nomaximal, Hall
63C5×D42—31no—
64C2×#4078—31no—
65C22×#686—31no—
66#65884—31no—
67#65507D311yescharacteristic, complemented
68#65506—31no—
69#65363—31no—
70#65361—31no—
71#65330—31no—
72#65328—31no—
73#65326—31no—
74#65325—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C23×D15—21no—
80C23×C5×D3—21no—
81C2×C3×C5×D4—22no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2311yescharacteristic
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—41no—
90C2×D60C2311yescharacteristic
91C2×D60C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C2×C5×#67—21no—
95C2×C5×#67—21no—
96C2×C5×#67—21no—
97C2×C5×#67—44no—
98C2×C5×#67D411yescharacteristic
99C22×C5×Dic3—21no—
100C5×D3×D4—22no—
101C5×D3×D4—41no—
102C2×C5×D12C2311yescharacteristic
103C2×C4×C5×D3C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C2×#1203—21no—
106C2×#1203—21no—
107C2×#1200—21no—
108C2×#1200—21no—
109#6769—22no—
110#6769—41no—
111#6715—22no—
112#6715—22no—
113#6715—22no—
114#6715D414yescomplemented
115C2×C3⋊#168—22no—
116C2×C3⋊#168C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C5×#217—21no—
119C5×#217—21no—
120C5×#217D411yescharacteristic
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×C4⋊Dic3C2311yescharacteristic
124C5×Dic3⋊C4D411yescharacteristic
125C4×C5×Dic3C2311yescharacteristic
126C3×C22⋊Dic5—21no—
127C3×#687—22no—
128C3×#687—41no—
129C3×C4⋊Dic5C2311yescharacteristic
130C3×#683—21no—
131C2×C3×#168C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133#6667—21no—
134#6667—21no—
135#6667—21no—
136#6667—21no—
137#6656—22no—
138#6654—22no—
139#6654—41no—
140#6650—22no—
141D4×#67D511yescharacteristic, complemented
142C22×#213—51no—
143C2×#914—51no—
144#5630—51no—
145C3×#450—51no—
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×D4—31no—
157C22×C5×D4—61no—
158C22×C5×D4C2×D311yescharacteristic
159C2×#709—31no—
160C22×D20—31no—
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169#4083—61no—
170C2×#687—31no—
171C2×#687C2×D311yescharacteristic, complemented
172C2×#687C2×D311yescharacteristic, complemented
173#4078—64no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—64no—
181#4076—31no—
182#4070C2×D311yescharacteristic, complemented
183C2×#681—31no—
184C22×#168—31no—
185#4040—61no—
186#4030—61no—
187D5×C22⋊C4—61no—
188#4021—31no—
189C4×D20—31no—
190#3964—31no—
191#3964C2×D311yescharacteristic, complemented
192#3964C2×D311yescharacteristic, complemented
193C22⋊#168—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3942—31no—
196#3941—31no—
197#3941—31no—
198#3940—31no—
199C4⋊#168—31no—
200#3935—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—42no—
211C22×D15—42no—
212C22×D15—81no—
213C22×C5×D3—21no—
214C22×C5×D3—42no—
215C22×C5×D3—42no—
216C22×C5×D3—81no—
217C22×C5×D3C2×D411yescharacteristic
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4C2×D412yes—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227D60—21no—
228D60—21no—
229D60—21no—
230D60—42no—
231D60C2×D412yescomplemented
232C5×#67—22no—
233C5×#67—42no—
234C5×#67—42no—
235C5×#67—42no—
236C5×#67—42no—
237C5×#67—81no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—42no—
240C2×C5×Dic3C2×D411yescharacteristic
241C2×C5×Dic3C2×D411yescharacteristic
242C2×C5×Dic3C2×D411yescharacteristic
243C5×D12—21no—
244C5×D12—21no—
245C4×C5×D3—21no—
246C4×C5×D3—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C3×Dic10—21no—
250C3×Dic10—21no—
251#1203—42no—
252#1203—81no—
253#1200—42no—
254#1200—81no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C22×C3×D4C2×D511yescharacteristic
260C22×#67—21no—
261C2×#239—51no—
262C2×D3×D4C2×D511yescharacteristic, complemented
263C22×D12—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—51no—
266C3×C22⋊Q8—51no—
267#953—21no—
268#947—51no—
269C2×#215—51no—
270#940C2×D511yescharacteristic, complemented
271#939—21no—
272#938C2×D511yescharacteristic, complemented
273#937—21no—
274D4×Dic3C2×D511yescharacteristic, complemented
275C2×#213—51no—
276C2×#213—51no—
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—104no—
280#930C2×D511yescharacteristic
281C4×#67C2×D511yescharacteristic
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×#102—51no—
294C3×#102—51no—
295C3×C22⋊C8—51no—
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—
305C24×C5—61no—
306C23×D5—61no—
307C2×C5×D4—22no—
308C2×C5×D4—21no—
309C2×C5×D4—31no—
310C2×C5×D4—31no—
311C2×C5×D4—41no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—61no—
315C2×C5×D4—62no—
316C2×C5×D4—61no—
317C2×C5×D4—61no—
318C2×C5×D4—121no—
319C2×C5×D4—124no—
320C2×C5×D4C22×D311yescharacteristic
321C2×C5×D4C22×D311yescharacteristic
322C22×C4×C5—31no—
323C22×C4×C5—61no—
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—61no—
326C2×C22⋊D5—61no—
327#709—62no—
328#709—121no—
329C2×D20—31no—
330C2×D20—31no—
331C2×D20—62no—
332C2×D20—61no—
333C2×D20—121no—
334C2×C4×D5—61no—
335C2×C4×D5—61no—
336C2×Dic10C22×D311yescharacteristic
337C5×C4⋊C4—31no—
338C5×C4⋊C4—31no—
339C5×C22⋊C4—31no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—61no—
342C5×C22⋊C4—61no—
343C5×C22⋊C4—61no—
344C42×C5—31no—
345C22⋊Dic5—21no—
346#687—22no—
347#687—41no—
348#687—62no—
349#686—34no—
350#686—62no—
351#686—62no—
352#686—62no—
353#686—62no—
354#686—121no—
355#685—61no—
356#685—61no—
357#685—61no—
358#685—61no—
359C4⋊Dic5C22×D311yescharacteristic
360#683—21no—
361#681—62no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—62no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—151no—
370D42—31no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—51no—
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—22no—
394C2×D15—41no—
395C2×D15—41no—
396C2×D15—41no—
397C2×D15—41no—
398C2×D15—41no—
399C2×D15—84no—
400C2×C5×D3—21no—
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—41no—
404C2×C5×D3—41no—
405C2×C5×D3—41no—
406C2×C5×D3—84no—
407C3×C4×C5—21no—
408C3×C4×C5C22×D411yescharacteristic
409C3×C4×C5H(5,𝔽2)11yescharacteristic
410C3×Dic5—41no—
411C3×Dic5—41no—
412C5×Dic3—21no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C24×C3—21no—
417C23×D3—21no—
418C23×D3—101no—
419C2×C3×Q8—51no—
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—21no—
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—21no—
430C2×#67—21no—
431C2×#67—44no—
432C2×#67C22⋊D511yescharacteristic
433C22×Dic3—21no—
434#239—102no—
435#239—201no—
436D3×D4—22no—
437D3×D4—41no—
438C2×D12—51no—
439C2×D12—51no—
440C2×D12—102no—
441C2×D12—101no—
442C2×D12—101no—
443C2×D12—101no—
444C2×D12—201no—
445C2×D12C22×D511yescharacteristic
446C2×C4×D3—101no—
447C2×C4×D3—101no—
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—201no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4—51no—
454C3×C4⋊C4—101no—
455C3×C22⋊C4—101no—
456#217—21no—
457#217—21no—
458#217C22⋊D511yescharacteristic
459#215—102no—
460#213—54no—
461#213—102no—
462#213—102no—
463#213—102no—
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—101no—
466(C2×D3)⋊C4—101no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4—101no—
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3C22×D511yescharacteristic
471Dic3⋊C4C22⋊D511yescharacteristic
472C4×Dic3C22×D511yescharacteristic
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—31no—
482C23×C5—42no—
483C23×C5—42no—
484C23×C5—61no—
485C23×C5—81no—
486C23×C5—122no—
487C23×C5—122no—
488C23×C5—241no—
489C23×C5D3×D411yescharacteristic
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—21no—
498C5×D4—42no—
499C5×D4—62no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—122no—
505C5×D4—122no—
506C5×D4—241no—
507C5×D4D3×D412yes—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—31no—
511C2×C4×C5—31no—
512C2×C4×C5—31no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—122no—
517C2×C4×C5D3×D411yescharacteristic
518C2×C4×C5C23×D311yescharacteristic
519C22⋊D5—122no—
520C22⋊D5—241no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523D20—32no—
524D20—61no—
525D20—61no—
526D20—61no—
527D20—122no—
528C4×D5—122no—
529C4×D5—241no—
530Dic10—21no—
531Dic10—21no—
532#168—21no—
533#168—21no—
534#168—32no—
535#168—61no—
536C2×#41—151no—
537C22×D4—31no—
538C22×D4—61no—
539C22×D4—151no—
540C22×D4D3×D511yescharacteristic
541AGL(1,ℤ/8)—304no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—151no—
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—31no—
555#124—151no—
556#123—301no—
557C22⋊Q8—51no—
558#121—31no—
559#121—31no—
560#121—61no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—61no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—301no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—51no—
574#102—51no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—51no—
579C22⋊C8—151no—
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—42no—
588D15—81no—
589C5×D3—41no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—81no—
596C23×C3C2×C22⋊D511yescharacteristic
597C22×D3—21no—
598C22×D3—42no—
599C22×D3—42no—
600C22×D3—81no—
601C22×D3—101no—
602C22×D3—101no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
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—101no—
617C2×C3×C4—101no—
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C23×D511yescharacteristic
620#67—22no—
621#67—42no—
622#67—42no—
623#67—42no—
624#67—42no—
625#67—81no—
626C2×Dic3—21no—
627C2×Dic3—42no—
628C2×Dic3C2×C22⋊D511yescharacteristic
629C2×Dic3C2×C22⋊D511yescharacteristic
630C2×Dic3C2×C22⋊D511yescharacteristic
631D12—21no—
632D12—21no—
633D12—52no—
634D12—101no—
635D12—101no—
636D12—101no—
637D12—202no—
638D12—202no—
639D12—401no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—202no—
643C4×D3—401no—
644C3×C8—101no—
645C3×C8—101no—
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—61no—
657C22×C5—61no—
658C22×C5—61no—
659C22×C5—84no—
660C22×C5—121no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—244no—
664C22×C5#91412yescomplemented
665C22×C5C2×D3×D411yescharacteristic
666C2×D5—62no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—121no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—61no—
675C4×C5—61no—
676C4×C5—61no—
677C4×C5—121no—
678C4×C5C2×D3×D411yescharacteristic
679C4×C5#100411yescharacteristic
680Dic5—41no—
681Dic5—41no—
682C24—21no—
683C24—61no—
684C24—301no—
685#41—302no—
686#41—601no—
687C2×Q8—51no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—41no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—62no—
697C2×D4—61no—
698C2×D4—61no—
699C2×D4—121no—
700C2×D4—124no—
701C2×D4—151no—
702C2×D4—151no—
703C2×D4—302no—
704C2×D4—301no—
705C2×D4—301no—
706C2×D4—301no—
707C2×D4—601no—
708C2×D4C2×D3×D511yescharacteristic
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—61no—
712C22×C4—301no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—102no—
716SD16—201no—
717SD16—302no—
718D8—154no—
719D8—302no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—51no—
733C4⋊C4—101no—
734C22⋊C4—31no—
735C22⋊C4—31no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—101no—
740C22⋊C4—301no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—31no—
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#407812yescomplemented
756C22×C3C22×C22⋊D511yescharacteristic
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—84no—
764C2×D3—102no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—201no—
770C2×D3—404no—
771C3×C4—21no—
772C3×C4—201no—
773C3×C4—201no—
774C3×C4C2×D4×D511yescharacteristic
775C3×C4#414411yescharacteristic
776Dic3—21no—
777Dic3—21no—
778Dic3—21no—
779Dic3—41no—
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—81no—
783C2×C5—121no—
784C2×C5—241no—
785C2×C5#559011yescharacteristic
786C2×C5C2×#91411yescharacteristic
787C2×C5#577411yescharacteristic
788D5—122no—
789D5—241no—
790C23—21no—
791C23—21no—
792C23—31no—
793C23—42no—
794C23—42no—
795C23—61no—
796C23—81no—
797C23—122no—
798C23—122no—
799C23—241no—
800C23—301no—
801C23—301no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23D3×C22⋊D511yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—42no—
812D4—62no—
813D4—61no—
814D4—61no—
815D4—122no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—152no—
820D4—241no—
821D4—301no—
822D4—301no—
823D4—301no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4#679012yes—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—122no—
839C2×C4—602no—
840C2×C4—1201no—
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—101no—
844C8—101no—
845C8—152no—
846C8—301no—
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3C2×#407811yescharacteristic
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3#6616911yescharacteristic
853D3—41no—
854D3—81no—
855D3—202no—
856D3—401no—
857C5#8016611yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—84no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—244no—
874C22—302no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—601no—
880C22—1204no—
881C22#9149612yescomplemented
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—61no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—201no—
889C4—201no—
890C4C2×#679011yescharacteristic
891C4#9204911yescharacteristic
892C3#1061521911yescharacteristic, complemented, Sylow
893C2—22no—
894C2—42no—
895C2—81no—
896C2—121no—
897C2—241no—
898C2—602no—
899C2—1201no—
900C2#1175469811yescharacteristic
901C2C2×#9149611yescharacteristic
902C2#1175544011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6715C2semidirect
2. C5×D4×#67C2semidirect
3. C2×#91496C2semidirect
4. #11754382C2semidirect
5. C3×#65507C2semidirect
6. #11749162C2semidirect
7. #11749080C2semidirect
8. #11749076C2semidirect
9. #11749037C2semidirect
10. #11749033C2semidirect
11. #11748989C2semidirect
12. #11748987C2semidirect
13. #11748547C2semidirect
14. #11748525C2semidirect
15. #11748508C2semidirect
18. C22×D60C22semidirect
20. C2×C5×D3×D4C22semidirect
21. C2×#6769C22semidirect
25. C2×#6715C22semidirect
26. C2×#6715C22semidirect
27. C22×C3⋊#168C22semidirect
29. C5×#940C22semidirect
31. C5×#938C22semidirect
33. C5×D4×Dic3C22semidirect
36. C2×C3×#687C22semidirect
37. C2×C3×#687C22semidirect
38. C3×#4070C22semidirect
42. #91460C22semidirect
44. #91428C22semidirect
46. #91374C22semidirect
47. C2×#6656C22semidirect
48. C2×#6654C22semidirect
49. C2×#6654C22semidirect
50. C2×#6650C22semidirect
51. C3×#3964C22semidirect
52. C3×#3964C22semidirect
53. C3×C22⋊#168C22semidirect
54. #90986C22semidirect
55. Dic3⋊#168C22semidirect
56. #90970C22semidirect
57. #90969C22semidirect
58. #90969C22semidirect
59. #90966C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
67. #65507D3semidirect
114. #6715D4semidirect
141. D4×#67D5semidirect
171. C2×#687C2×D3semidirect
172. C2×#687C2×D3semidirect
182. #4070C2×D3semidirect
191. #3964C2×D3semidirect
192. #3964C2×D3semidirect
194. C22⋊#168C2×D3semidirect
231. D60C2×D4semidirect
256. C3⋊#168C2×D4semidirect
262. C2×D3×D4C2×D5semidirect
270. #940C2×D5semidirect
272. #938C2×D5semidirect
274. D4×Dic3C2×D5semidirect
391. C22×C3×C5AGL(1,ℤ/8)semidirect
664. C22×C5#914semidirect
745. C3×C5#3264semidirect
755. C22×C3#4078semidirect
857. C5#80166semidirect
881. C22#91496semidirect
892. C3#10615219semidirect

Maximal subgroups

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

subgroupindex
C22×#67152
C5×D4×#672
C2×#914962
#117543822
C3×#655072
#117491622
#117490802
#117490762
#117490372
#117490332
#117489892
#117489872
#117485472
#117485252
#117485082
#106152193
#801665