Finite Group Databasebeta

← #14453289

Subgroups — #14453289

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
1C5×D4×#67C211yesmaximal, characteristic, complemented
2C22×C3×#686C211yesmaximal, characteristic, complemented
3C2×#91494C211yesmaximal, characteristic, complemented
4#11754305C211yesmaximal, characteristic, complemented
5#11751319C211yesmaximal, characteristic, complemented
6#11749157C211yesmaximal, characteristic, complemented
7#11749079C211yesmaximal, characteristic, complemented
8#11749071C211yesmaximal, characteristic, complemented
9#11749032C211yesmaximal, characteristic, complemented
10#11749029C211yesmaximal, characteristic, complemented
11#11748988C211yesmaximal, characteristic, complemented
12#11748981C211yesmaximal, characteristic, complemented
13#11748533C211yesmaximal, characteristic, complemented
14#11748510C211yesmaximal, characteristic, complemented
15#11748500C211yesmaximal, characteristic, complemented
16#10615219—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C5×#67—21no—
19C2×C5×D3×D4C2211yescharacteristic, complemented
20C22×C3×D20C2211yescharacteristic, complemented
21C2×#6765C2211yescharacteristic, complemented
22C2×#6716C2211yescharacteristic, complemented
23C2×#6716C2211yescharacteristic, complemented
24#91813C2211yescharacteristic, complemented
25C5×#953—21no—
26C5×#940C2211yescharacteristic, complemented
27C5×#939—21no—
28C5×#938C2211yescharacteristic, complemented
29C5×#937—21no—
30C5×D4×Dic3C2211yescharacteristic, complemented
31C5×#930C2211yescharacteristic
32C4×C5×#67C2211yescharacteristic
33C2×C3×#686—24no—
34C2×C3×#686C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic
36C2×C3×#686C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic, complemented
38C22×C3×#168C2211yescharacteristic, complemented
39#91563—21no—
40D5×#217—21no—
41#91494—24no—
42#91456C2211yescharacteristic, complemented
43Dic3×D20C2211yescharacteristic, complemented
44#91408—21no—
45#91407—21no—
46#91364C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90967C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#83837—51nomaximal, Hall
63C5×D42—31no—
64C2×#4078—31no—
65C22×#686D311yescharacteristic, complemented
66#65884—31no—
67#65507—31no—
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×C5×D3—21no—
80C23×C3×D5—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×Dic30C2311yescharacteristic
88C2×C5×#67—21no—
89C2×C5×#67—21no—
90C2×C5×#67—21no—
91C2×C5×#67—21no—
92C2×C5×#67—21no—
93C2×C5×#67—44no—
94C2×C5×#67D411yescharacteristic
95C22×C5×Dic3—21no—
96C5×D3×D4—22no—
97C5×D3×D4—41no—
98C2×C5×D12C2311yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C2×C3×D20—22no—
101C2×C3×D20—21no—
102C2×C3×D20—41no—
103C2×C3×D20C2311yescharacteristic
104C2×C3×D20C2311yescharacteristic
105C2×#1201—21no—
106C2×#1201—21no—
107C2×D5×Dic3—21no—
108C2×D5×Dic3—21no—
109#6765—22no—
110#6765—41no—
111#6719—21no—
112#6716—22no—
113#6716—41no—
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
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×#686—22no—
127C3×#686—22no—
128C3×#686—22no—
129C3×#686D414yescomplemented
130C2×C3×#168—22no—
131C2×C3×#168C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133#6665—21no—
134#6665—21no—
135#6665—21no—
136#6665—21no—
137#6659—22no—
138#6652—22no—
139#6652—41no—
140#6650—22no—
141C22×C3×D8—51no—
142#5806—51no—
143D4×#67D511yescharacteristic, complemented
144C2×#911—51no—
145#5218—51no—
146#5217—51no—
147#5159—51no—
148#5158—51no—
149#5156—51no—
150#5154—51no—
151#5153—51no—
152#5152—51no—
153#5150—51no—
154#5114—51no—
155#5111—51no—
156C22×C5×D4—31no—
157C22×C5×D4—61no—
158C22×C5×D4C2×D311yescharacteristic
159C2×#709—31no—
160C22×D20C2×D311yescharacteristic, complemented
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×#687—31no—
172C2×#687—31no—
173#4078—64no—
174C2×#686—24no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686C2×D311yescharacteristic
178C2×#686C2×D311yescharacteristic
179C2×#686C2×D311yescharacteristic, complemented
180C2×#686C2×D311yescharacteristic, complemented
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168C2×D311yescharacteristic, complemented
185#4040—61no—
186#4030—61no—
187D5×C22⋊C4—61no—
188#4021—31no—
189C4×D20—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
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×C5×D3—21no—
209C22×C5×D3—42no—
210C22×C5×D3—42no—
211C22×C5×D3—81no—
212C22×C5×D3C2×D411yescharacteristic
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—42no—
216C22×C3×D5—42no—
217C22×C3×D5—81no—
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
227C2×Dic15—21no—
228C2×Dic15—21no—
229Dic30—21no—
230Dic30—21no—
231C5×#67—22no—
232C5×#67—42no—
233C5×#67—42no—
234C5×#67—42no—
235C5×#67—42no—
236C5×#67—81no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—42no—
239C2×C5×Dic3C2×D411yescharacteristic
240C2×C5×Dic3C2×D411yescharacteristic
241C2×C5×Dic3C2×D411yescharacteristic
242C5×D12—21no—
243C5×D12—21no—
244C4×C5×D3—21no—
245C4×C5×D3—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×D20—42no—
250C3×D20C2×D412yescomplemented
251#1201—42no—
252#1201—81no—
253D5×Dic3—42no—
254D5×Dic3—81no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C22×C3×D4—51no—
260C22×C3×D4C2×D511yescharacteristic
261C22×#67—21no—
262C2×#237—51no—
263C2×D3×D4C2×D511yescharacteristic, complemented
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×D8—51no—
267C2×C3×D8—51no—
268C2×C3×D8—104no—
269C22×C3×C8—51no—
270#953—21no—
271#953—101no—
272C2×#217—101no—
273#940C2×D511yescharacteristic, complemented
274#939—21no—
275#939—101no—
276#938—51no—
277#938C2×D511yescharacteristic, complemented
278#937—21no—
279#936—51no—
280#935—101no—
281D4×Dic3—51no—
282D4×Dic3C2×D511yescharacteristic, complemented
283C2×#214—51no—
284C2×#214—51no—
285C2×#213—51no—
286C2×#213—51no—
287#930C2×D511yescharacteristic
288C4×#67C2×D511yescharacteristic
289#924—51no—
290#911—104no—
291C2×#204—51no—
292C2×ΓL(1,𝔽25)—51no—
293#832—51no—
294#832—51no—
295#832—51no—
296#832—51no—
297#830—51no—
298#821—51no—
299(C2×D3)⋊C8—51no—
300#817—51no—
301#816—51no—
302#815—51no—
303Dic3⋊C8—51no—
304C24×C5—21no—
305C24×C5—61no—
306C23×D5—21no—
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—22no—
330C2×D20—21no—
331C2×D20—41no—
332C2×D20C22×D311yescharacteristic
333C2×D20C22×D311yescharacteristic
334C2×C4×D5—61no—
335C2×C4×D5—61no—
336C2×Dic10—31no—
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—61no—
346#687—62no—
347#687—62no—
348#687—121no—
349#686—22no—
350#686—22no—
351#686—22no—
352#686—62no—
353#686—121no—
354#686#6714yescomplemented
355#685—61no—
356#685—61no—
357#685—61no—
358#685—61no—
359C4⋊Dic5—31no—
360#683—61no—
361#681—62no—
362C2×#168—22no—
363C2×#168—31no—
364C2×#168—31no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—51no—
369#546—151no—
370D42—31no—
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—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×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—21no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C2×C5×D3—84no—
400C2×C3×D5—22no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5C22×D411yescharacteristic
409C3×C4×C5H(5,𝔽2)11yescharacteristic
410Dic15—41no—
411Dic15—41no—
412C5×Dic3—21no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C24×C3—21no—
417C24×C3—101no—
418C23×D3—21no—
419C2×C3×D4—22no—
420C2×C3×D4—21no—
421C2×C3×D4—41no—
422C2×C3×D4—51no—
423C2×C3×D4—51no—
424C2×C3×D4—102no—
425C2×C3×D4—101no—
426C2×C3×D4—201no—
427C2×C3×D4C22×D511yescharacteristic
428C2×C3×D4C22×D511yescharacteristic
429C22×C3×C4C22×D511yescharacteristic
430C2×#67—21no—
431C2×#67—21no—
432C2×#67—21no—
433C2×#67—21no—
434C2×#67—21no—
435C2×#67—44no—
436C2×#67—101no—
437C2×#67—101no—
438C2×#67C22⋊D511yescharacteristic
439C22×Dic3—21no—
440C22×Dic3—101no—
441C22×Dic3—101no—
442#237—102no—
443#237—201no—
444D3×D4—22no—
445D3×D4—41no—
446C2×D12C22×D511yescharacteristic
447C2×C4×D3C22×D511yescharacteristic
448C2×Dic6—51no—
449C3×D8—54no—
450C3×D8—102no—
451C3×D8—102no—
452C3×D8—102no—
453C2×C3×C8—51no—
454C2×C3×C8—51no—
455C2×C3×C8—102no—
456#217—21no—
457#217—21no—
458#217—101no—
459#217—101no—
460#217—101no—
461#217—101no—
462#217—101no—
463#217C22⋊D511yescharacteristic
464#214—102no—
465#214—201no—
466#213—102no—
467#213—201no—
468(C2×D3)⋊C4—21no—
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3—51no—
471C4⋊Dic3C22×D511yescharacteristic
472Dic3⋊C4—101no—
473Dic3⋊C4C22⋊D511yescharacteristic
474C4×Dic3C22×D511yescharacteristic
475C2×C3⋊C8—51no—
476C2×C3⋊C8—51no—
477#204—102no—
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—21no—
491C22×D5—21no—
492C22×D5—42no—
493C22×D5—42no—
494C22×D5—81no—
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×D4C2×#6712yes—
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—61no—
522C2×Dic5—61no—
523D20—21no—
524D20—21no—
525D20—21no—
526D20—42no—
527D20C2×#6712yescomplemented
528C4×D5—122no—
529C4×D5—241no—
530Dic10—61no—
531Dic10—61no—
532#168—21no—
533#168—61no—
534#168—61no—
535#168C2×#6712yescomplemented
536C2×#41—151no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—61no—
540C22×D4D3×D511yescharacteristic
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—51no—
548C2×D8—51no—
549C2×D8—104no—
550C2×D8—151no—
551C2×D8—151no—
552C2×M16—151no—
553C22×C8—51no—
554#127—31no—
555#124—151no—
556#123—301no—
557C22⋊Q8—151no—
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—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—22no—
582C2×C3×C5—42no—
583C2×C3×C5—81no—
584C2×C3×C5D4211yescharacteristic
585C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
586C2×C3×C5#57611yescharacteristic
587C3×D5—42no—
588C3×D5—81no—
589C5×D3—41no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—21no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—81no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—202no—
599C23×C3—202no—
600C23×C3—401no—
601C23×C3C2×C22⋊D511yescharacteristic
602C22×D3—21no—
603C22×D3—42no—
604C22×D3—42no—
605C22×D3—81no—
606C22×D3C2×C22⋊D511yescharacteristic
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—21no—
610C3×D4—42no—
611C3×D4—52no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—101no—
615C3×D4—202no—
616C3×D4D4×D512yes—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4C2×C22⋊D511yescharacteristic
620C2×C3×C4C23×D511yescharacteristic
621#67—22no—
622#67—42no—
623#67—42no—
624#67—42no—
625#67—42no—
626#67—81no—
627#67—202no—
628#67—401no—
629C2×Dic3—21no—
630C2×Dic3—42no—
631C2×Dic3—101no—
632C2×Dic3—101no—
633C2×Dic3—202no—
634C2×Dic3—401no—
635C2×Dic3C2×C22⋊D511yescharacteristic
636C2×Dic3C2×C22⋊D511yescharacteristic
637C2×Dic3C2×C22⋊D511yescharacteristic
638D12—21no—
639D12—21no—
640C4×D3—21no—
641C4×D3—21no—
642Dic6—101no—
643Dic6—101no—
644C3×C8—52no—
645C3×C8—101no—
646C3⋊C8—101no—
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#91112yescomplemented
665C22×C5C2×D3×D411yescharacteristic
666C2×D5—22no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—41no—
670C2×D5—41no—
671C2×D5—41no—
672C2×D5—84no—
673C4×C5—21no—
674C4×C5—61no—
675C4×C5—61no—
676C4×C5—61no—
677C4×C5—121no—
678C4×C5#100411yescharacteristic
679C4×C5C22×#6711yescharacteristic
680Dic5—121no—
681Dic5—121no—
682C24—21no—
683C24—61no—
684C24—101no—
685#41—302no—
686#41—601no—
687C2×Q8—151no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—41no—
693C2×D4—51no—
694C2×D4—51no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—62no—
699C2×D4—61no—
700C2×D4—61no—
701C2×D4—102no—
702C2×D4—101no—
703C2×D4—121no—
704C2×D4—124no—
705C2×D4—201no—
706C2×D4—301no—
707C2×D4—301no—
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—302no—
716SD16—302no—
717SD16—601no—
718D8—54no—
719D8—102no—
720D8—102no—
721D8—102no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—102no—
728C2×C8—151no—
729C2×C8—151no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—151no—
733C4⋊C4—301no—
734C22⋊C4—31no—
735C22⋊C4—31no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—301no—
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—102no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—201no—
759C22×C3—201no—
760C22×C3—201no—
761C22×C3—404no—
762C22×C3#407812yescomplemented
763C22×C3C22×C22⋊D511yescharacteristic
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—21no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C3×C4—21no—
772C3×C4C2×D4×D511yescharacteristic
773C3×C4#414411yescharacteristic
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—201no—
779Dic3—201no—
780C2×C5—22no—
781C2×C5—42no—
782C2×C5—81no—
783C2×C5—121no—
784C2×C5—241no—
785C2×C5C2×#91111yescharacteristic
786C2×C5#575711yescharacteristic
787C2×C5D4×#6711yescharacteristic
788D5—42no—
789D5—81no—
790C23—21no—
791C23—21no—
792C23—31no—
793C23—42no—
794C23—42no—
795C23—61no—
796C23—81no—
797C23—101no—
798C23—101no—
799C23—122no—
800C23—122no—
801C23—202no—
802C23—202no—
803C23—241no—
804C23—401no—
805C23D3×C22⋊D511yescharacteristic
806Q8—301no—
807Q8—301no—
808D4—21no—
809D4—21no—
810D4—21no—
811D4—42no—
812D4—52no—
813D4—62no—
814D4—61no—
815D4—61no—
816D4—101no—
817D4—101no—
818D4—101no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—122no—
823D4—202no—
824D4—241no—
825D4—602no—
826D4—1201no—
827D4D5×#6712yes—
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—122no—
837C2×C4—301no—
838C2×C4—301no—
839C2×C4—602no—
840C2×C4—1201no—
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—301no—
846C8—301no—
847C2×C3—22no—
848C2×C3—42no—
849C2×C3—81no—
850C2×C3—202no—
851C2×C3—401no—
852C2×C3C2×#407811yescharacteristic
853C2×C3D4×C22⋊D511yescharacteristic
854C2×C3#6616911yescharacteristic
855D3—41no—
856D3—81no—
857C5#8383711yescharacteristic, 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—102no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—201no—
875C22—201no—
876C22—201no—
877C22—201no—
878C22—201no—
879C22—244no—
880C22—404no—
881C22#9149412yescomplemented
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—61no—
885C4—61no—
886C4—61no—
887C4—121no—
888C4—601no—
889C4—601no—
890C4C2×D5×#6711yescharacteristic
891C4#9204911yescharacteristic
892C3#1061521911yescharacteristic, complemented, Sylow
893C2—22no—
894C2—42no—
895C2—81no—
896C2—121no—
897C2—202no—
898C2—241no—
899C2—401no—
900C2#1175469711yescharacteristic
901C2C2×#9149411yescharacteristic
902C2#67×C22⋊D511yescharacteristic
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. C5×D4×#67C2semidirect
2. C22×C3×#686C2semidirect
3. C2×#91494C2semidirect
4. #11754305C2semidirect
5. #11751319C2semidirect
6. #11749157C2semidirect
7. #11749079C2semidirect
8. #11749071C2semidirect
9. #11749032C2semidirect
10. #11749029C2semidirect
11. #11748988C2semidirect
12. #11748981C2semidirect
13. #11748533C2semidirect
14. #11748510C2semidirect
15. #11748500C2semidirect
19. C2×C5×D3×D4C22semidirect
20. C22×C3×D20C22semidirect
21. C2×#6765C22semidirect
22. C2×#6716C22semidirect
23. C2×#6716C22semidirect
24. #91813C22semidirect
26. C5×#940C22semidirect
28. C5×#938C22semidirect
30. C5×D4×Dic3C22semidirect
36. C2×C3×#686C22semidirect
37. C2×C3×#686C22semidirect
38. C22×C3×#168C22semidirect
42. #91456C22semidirect
43. Dic3×D20C22semidirect
46. #91364C22semidirect
47. C2×#6659C22semidirect
48. C2×#6652C22semidirect
49. C2×#6652C22semidirect
50. C2×#6650C22semidirect
51. #91116C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90985C22semidirect
55. Dic3⋊#168C22semidirect
56. #90975C22semidirect
57. #90967C22semidirect
58. #90964C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
65. C22×#686D3semidirect
129. C3×#686D4semidirect
143. D4×#67D5semidirect
160. C22×D20C2×D3semidirect
179. C2×#686C2×D3semidirect
180. C2×#686C2×D3semidirect
184. C22×#168C2×D3semidirect
250. C3×D20C2×D4semidirect
258. C3×#168C2×D4semidirect
263. C2×D3×D4C2×D5semidirect
273. #940C2×D5semidirect
277. #938C2×D5semidirect
282. D4×Dic3C2×D5semidirect
354. #686#67semidirect
391. C22×C3×C5AGL(1,ℤ/8)semidirect
527. D20C2×#67semidirect
535. #168C2×#67semidirect
664. C22×C5#911semidirect
745. C3×C5#3264semidirect
762. C22×C3#4078semidirect
857. C5#83837semidirect
881. C22#91494semidirect
892. C3#10615219semidirect

Maximal subgroups

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

subgroupindex
C5×D4×#672
C22×C3×#6862
C2×#914942
#117543052
#117513192
#117491572
#117490792
#117490712
#117490322
#117490292
#117489882
#117489812
#117485332
#117485102
#117485002
#106152193
#838375