Finite Group Databasebeta

← #14453229

Subgroups — #14453229

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×#5829C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#67×D20C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11749398C211yesmaximal, characteristic, complemented
7#11749342C211yesmaximal, characteristic, complemented
8#11749274C211yesmaximal, characteristic, complemented
9#11749228C211yesmaximal, characteristic, complemented
10#11749099C211yesmaximal, characteristic, complemented
11#11749032C211yesmaximal, characteristic, complemented
12#11748988C211yesmaximal, characteristic, complemented
13#11748515C211yesmaximal, characteristic, complemented
14#11748510C211yesmaximal, characteristic, complemented
15#11748484C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×C5×D3×D4C2211yescharacteristic, complemented
19C22×C3×D20C2211yescharacteristic, complemented
20C2×D5×#67—21no—
21C2×D3×D20C2211yescharacteristic
22C2×#6717C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic, complemented
25C5×#947C2211yescharacteristic, complemented
26C5×#946C2211yescharacteristic, complemented
27C5×#939—21no—
28C5×#937—21no—
29C5×D4×Dic3C2211yescharacteristic, complemented
30C5×#930C2211yescharacteristic, complemented
31C5×#929—21no—
32C4×C5×#67C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4—21no—
34C3×#4095—24no—
35C2×C3×#688C2211yescharacteristic, complemented
36C2×C3×#688C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#681C2211yescharacteristic, complemented
40#91564—21no—
41D3×#686—24no—
42#91474—21no—
43#91458C2211yescharacteristic, complemented
44#91456C2211yescharacteristic
45Dic3×D20C2211yescharacteristic, complemented
46#91409—21no—
47C2×#6654C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90969C2211yescharacteristic, complemented
57#90967C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#83952—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095D311yescharacteristic, complemented
65C22×#686—31no—
66D4×D20—31no—
67#65527—31no—
68#65506—31no—
69#65347—31no—
70#65346—31no—
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325—31no—
75#65304—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C3×D5—21no—
80C22×D3×D5—21no—
81C3×C5×#41—22no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5—21no—
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—21no—
89C2×D60C2311yescharacteristic
90C2×C5×#67—21no—
91C2×C5×#67—21no—
92C2×C5×#67D411yescharacteristic
93C22×C5×Dic3—21no—
94C5×D3×D4—22no—
95C5×D3×D4—41no—
96C2×C5×D12C2311yescharacteristic
97C2×C4×C5×D3C2311yescharacteristic
98C2×C3×D20—22no—
99C2×C3×D20—21no—
100C2×C3×D20—41no—
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103D5×#67—44no—
104C2×#1202—21no—
105C2×#1202—21no—
106C2×#1202—21no—
107C2×#1201—21no—
108C2×D5×Dic3—21no—
109D3×D20—22no—
110D3×D20—41no—
111#6717—41no—
112#6715—22no—
113#6714—21no—
114C4⋊Dic15C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×#217—21no—
118C5×#217D411yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4D411yescharacteristic
124C5×C4⋊Dic3C2311yescharacteristic
125C5×Dic3⋊C4—21no—
126C5×Dic3⋊C4D411yescharacteristic
127C4×C5×Dic3C2311yescharacteristic
128C3×#688—22no—
129C3×#688—22no—
130C3×#686—22no—
131C3×#686D414yescomplemented
132C3×#681—22no—
133C2×C3×#168C2311yescharacteristic
134C2×C3×#168C2311yescharacteristic
135#6665—21no—
136#6665—21no—
137#6654—22no—
138#6652—22no—
139#6652—41no—
140D3×#168—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142#5829D511yescharacteristic, complemented
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×D4—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20C2×D311yescharacteristic, complemented
161C5×#124—31no—
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—31no—
165C5×#121—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169C2×C5×C22⋊C4—61no—
170#4095—24no—
171C2×#688—31no—
172C2×#688C2×D311yescharacteristic, complemented
173C2×#688C2×D311yescharacteristic, complemented
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—64no—
179C2×#686C2×D311yescharacteristic
180C2×#686C2×D311yescharacteristic, complemented
181#4076—31no—
182#4076—31no—
183C2×#681C2×D311yescharacteristic, complemented
184C22×#168—31no—
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020—31no—
189C4×D20—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—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×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—81no—
209C22×C5×D3C2×D411yescharacteristic
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—81no—
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4C2×D412yescomplemented
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2411yescharacteristic
229#1220—42no—
230C2×Dic15—21no—
231D60—21no—
232D60—21no—
233C5×#67—22no—
234C5×#67—42no—
235C5×#67—81no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—81no—
238C2×C5×Dic3C2×D411yescharacteristic
239C2×C5×Dic3C2×D411yescharacteristic
240C2×C5×Dic3C2×D411yescharacteristic
241C5×D12—21no—
242C5×D12—21no—
243C4×C5×D3—21no—
244C4×C5×D3—21no—
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—42no—
249C3×D20C2×D412yes—
250#1202—42no—
251#1202—42no—
252#1202—81no—
253#1201—42no—
254D5×Dic3—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C3×#168—21no—
258C3×#168C2×D412yescomplemented
259C2×C3×#41C2×D511yescharacteristic, complemented
260C22×C3×D4—51no—
261C22×#67—101no—
262C2×D3×D4—51no—
263C2×D3×D4C2×D511yescharacteristic, complemented
264C3×AGL(1,ℤ/8)—104no—
265C2×C3×SD16—51no—
266C2×C3×SD16—51no—
267C2×C3×D8—51no—
268C2×C3×D8—51no—
269C2×C3×M16—51no—
270#953—101no—
271#947C2×D511yescharacteristic, complemented
272#946C2×D511yescharacteristic, complemented
273C2×#215—51no—
274#940—51no—
275#939—21no—
276#939—101no—
277#938—51no—
278#937—21no—
279#937—101no—
280D4×Dic3—51no—
281D4×Dic3C2×D511yescharacteristic, complemented
282C2×#213—51no—
283C2×#213—51no—
284C2×#213—51no—
285#930—51no—
286#930C2×D511yescharacteristic, complemented
287#929—21no—
288C4×#67C2×D511yescharacteristic
289C2×(C2×D3)⋊C4—21no—
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—61no—
305C23×D5—21no—
306C23×D5—61no—
307C5×#41—22no—
308C5×#41—41no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—21no—
311C2×C5×D4—31no—
312C2×C5×D4—31no—
313C2×C5×D4—61no—
314C2×C5×D4—62no—
315C2×C5×D4—61no—
316C2×C5×D4—121no—
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—21no—
319C22×C4×C5—31no—
320C22×C4×C5—61no—
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324D4×D5—124no—
325C2×D20—22no—
326C2×D20—21no—
327C2×D20—31no—
328C2×D20—41no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—121no—
334C2×D20C22×D311yescharacteristic
335C2×D20C22×D311yescharacteristic
336C2×C4×D5—61no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4—31no—
339C5×C4⋊C4—61no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4—61no—
343C5×C22⋊C4—61no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4—61no—
346C5×C22⋊C4—61no—
347C42×C5—31no—
348#688—22no—
349#688—22no—
350#688—121no—
351#686—22no—
352#686—62no—
353#686—62no—
354#686—62no—
355#686—121no—
356#686#6714yescomplemented
357#685—61no—
358#685—61no—
359#685—61no—
360C4⋊Dic5—31no—
361#681—22no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—62no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—51no—
368C22×D8—151no—
369#546—31no—
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—21no—
384C22×C3×C5—21no—
385C22×C3×C5—21no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—84no—
398C2×C5×D3AGL(1,ℤ/8)12yescomplemented
399C2×C3×D5—22no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—84no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411Dic15—41no—
412C5×Dic3—21no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C24×C3—101no—
417C23×D3—21no—
418C23×D3—101no—
419C3×#41—22no—
420C3×#41—41no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—21no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—102no—
426C2×C3×D4—101no—
427C2×C3×D4—201no—
428C2×C3×D4C22×D511yescharacteristic
429C22×C3×C4—21no—
430C22×C3×C4C22×D511yescharacteristic
431C2×#67—21no—
432C2×#67—21no—
433C2×#67—101no—
434C2×#67—101no—
435C2×#67—101no—
436C2×#67—101no—
437C2×#67—101no—
438C2×#67—204no—
439C2×#67C22⋊D511yescharacteristic
440C22×Dic3—21no—
441C22×Dic3—101no—
442D3×D4—22no—
443D3×D4—41no—
444D3×D4—102no—
445D3×D4—201no—
446C2×D12—51no—
447C2×D12C22×D511yescharacteristic
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×SD16—102no—
451C3×D8—54no—
452C3×D8—102no—
453C3×M16—102no—
454C2×C3×C8—51no—
455C2×C3×C8—51no—
456#217—21no—
457#217—101no—
458#217—101no—
459#217C22⋊D511yescharacteristic
460#215—201no—
461#213—102no—
462#213—102no—
463#213—201no—
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—21no—
467(C2×D3)⋊C4—21no—
468(C2×D3)⋊C4—101no—
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3—51no—
471C4⋊Dic3C22×D511yescharacteristic
472Dic3⋊C4—21no—
473Dic3⋊C4C22⋊D511yescharacteristic
474C4×Dic3C22×D511yescharacteristic
475C2×C3⋊C8—51no—
476C2×C3⋊C8—51no—
477D24—102no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—31no—
481C23×C5—61no—
482C23×C5—122no—
483C23×C5—122no—
484C23×C5—241no—
485C23×C5D3×D411yescharacteristic
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—61no—
491C22×D5—81no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—42no—
499C5×D4—62no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—122no—
503C5×D4—241no—
504C5×D4C2×#6712yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—31no—
509C2×C4×C5—31no—
510C2×C4×C5—31no—
511C2×C4×C5—42no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—241no—
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—122no—
519C22⋊D5—122no—
520C2×Dic5—61no—
521D20—21no—
522D20—21no—
523D20—21no—
524D20—42no—
525D20—61no—
526D20—61no—
527D20—122no—
528D20—122no—
529D20—241no—
530D20C2×#6712yes—
531C4×D5—122no—
532#168—21no—
533#168—61no—
534#168—61no—
535#168C2×#6712yescomplemented
536C2×#41D3×D511yescharacteristic, complemented
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—104no—
542C2×SD16—51no—
543C2×SD16—51no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—51no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—51no—
553C22×C8—151no—
554#127—151no—
555#124—31no—
556#123—61no—
557C22⋊Q8—31no—
558#121—31no—
559#121—61no—
560#121—151no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—301no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—61no—
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—41no—
582C2×C3×C5—42no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586D15—81no—
587C3×D5—42no—
588C3×D5—81no—
589C5×D3—22no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—202no—
595C23×C3—202no—
596C23×C3—401no—
597C23×C3C2×C22⋊D511yescharacteristic
598C22×D3—21no—
599C22×D3—42no—
600C22×D3—42no—
601C22×D3—81no—
602C22×D3—101no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—42no—
611C3×D4—52no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—101no—
615C3×D4—202no—
616C3×D4D4×D512yescomplemented
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—42no—
621C2×C3×C4C2×C22⋊D511yescharacteristic
622C2×C3×C4C23×D511yescharacteristic
623#67—22no—
624#67—42no—
625#67—81no—
626#67—202no—
627#67—202no—
628#67—202no—
629#67—202no—
630#67—401no—
631C2×Dic3—21no—
632C2×Dic3—81no—
633C2×Dic3—101no—
634C2×Dic3—202no—
635C2×Dic3C2×C22⋊D511yescharacteristic
636C2×Dic3C2×C22⋊D511yescharacteristic
637C2×Dic3C2×C22⋊D511yescharacteristic
638D12—21no—
639D12—21no—
640D12—101no—
641D12—101no—
642C4×D3—21no—
643C4×D3—21no—
644C3×C8—52no—
645C3×C8—101no—
646C3⋊C8—101no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—22no—
652C22×C5—32no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—244no—
661C22×C5C2×D3×D411yescharacteristic
662C2×D5—22no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—84no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—121no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—41no—
675C4×C5—61no—
676C4×C5—61no—
677C4×C5—61no—
678C4×C5—121no—
679C4×C5#100411yescharacteristic
680C4×C5C22×#6711yescharacteristic
681Dic5—121no—
682C24—61no—
683C24—101no—
684C24—301no—
685#41—22no—
686#41—41no—
687C2×Q8C2×D3×D511yescharacteristic
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—61no—
694C2×D4—62no—
695C2×D4—61no—
696C2×D4—102no—
697C2×D4—101no—
698C2×D4—121no—
699C2×D4—151no—
700C2×D4—201no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—302no—
705C2×D4—301no—
706C2×D4—301no—
707C2×D4—601no—
708C2×D4—604no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—31no—
712C22×C4—61no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—102no—
716SD16—102no—
717SD16—601no—
718D8—54no—
719D8—102no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—102no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—61no—
733C4⋊C4—151no—
734C22⋊C4—31no—
735C22⋊C4—31no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—31no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—102no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3—201no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—404no—
759C22×C3C22×C22⋊D511yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—84no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3#409512yescomplemented
771C3×C4—21no—
772C3×C4—41no—
773C3×C4C2×D4×D511yescharacteristic
774C3×C4#414411yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—201no—
780C2×C5—41no—
781C2×C5—42no—
782C2×C5—62no—
783C2×C5—241no—
784C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
785C2×C5#577411yescharacteristic
786C2×C5D4×#6711yescharacteristic
787D5—42no—
788D5—81no—
789D5—241no—
790C23—21no—
791C23—31no—
792C23—61no—
793C23—101no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—202no—
798C23—202no—
799C23—241no—
800C23—301no—
801C23—401no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23D3×C22⋊D511yescharacteristic
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—42no—
810D4—52no—
811D4—62no—
812D4—61no—
813D4—61no—
814D4—101no—
815D4—101no—
816D4—101no—
817D4—122no—
818D4—202no—
819D4—241no—
820D4—301no—
821D4—301no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4D5×#6712yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—42no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—241no—
839C2×C4—301no—
840C2×C4—602no—
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—52no—
844C8—101no—
845C8—301no—
846C8—301no—
847C2×C3—42no—
848C2×C3—41no—
849C2×C3—202no—
850C2×C3—401no—
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3C2×#409511yescharacteristic
853C2×C3#6616911yescharacteristic
854D3—22no—
855D3—81no—
856D3—401no—
857C5#8395211yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—32no—
863C22—41no—
864C22—41no—
865C22—61no—
866C22—61no—
867C22—102no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—404no—
878C22—601no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—41no—
885C4—61no—
886C4—61no—
887C4—61no—
888C4—121no—
889C4—601no—
890C4C2×D5×#6711yescharacteristic
891C4#9204911yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—41no—
894C2—42no—
895C2—62no—
896C2—202no—
897C2—241no—
898C2—401no—
899C2—1201no—
900C2D3×#409511yescharacteristic
901C2#1175532311yescharacteristic
902C2#67×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C5×#5829C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×D3×#686C2semidirect
4. #67×D20C2semidirect
5. #11751339C2semidirect
6. #11749398C2semidirect
7. #11749342C2semidirect
8. #11749274C2semidirect
9. #11749228C2semidirect
10. #11749099C2semidirect
11. #11749032C2semidirect
12. #11748988C2semidirect
13. #11748515C2semidirect
14. #11748510C2semidirect
15. #11748484C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×C5×D3×D4C22semidirect
19. C22×C3×D20C22semidirect
22. C2×#6717C22semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
25. C5×#947C22semidirect
26. C5×#946C22semidirect
29. C5×D4×Dic3C22semidirect
30. C5×#930C22semidirect
35. C2×C3×#688C22semidirect
36. C2×C3×#688C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#681C22semidirect
43. #91458C22semidirect
45. Dic3×D20C22semidirect
47. C2×#6654C22semidirect
49. C2×#6652C22semidirect
50. C2×D3×#168C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90985C22semidirect
55. Dic3⋊#168C22semidirect
56. #90969C22semidirect
57. #90967C22semidirect
58. #90964C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
64. C2×#4095D3semidirect
131. C3×#686D4semidirect
142. #5829D5semidirect
156. C2×C5×#41C2×D3semidirect
160. C22×D20C2×D3semidirect
172. C2×#688C2×D3semidirect
173. C2×#688C2×D3semidirect
180. C2×#686C2×D3semidirect
183. C2×#681C2×D3semidirect
222. C3×C5×D4C2×D4semidirect
258. C3×#168C2×D4semidirect
259. C2×C3×#41C2×D5semidirect
263. C2×D3×D4C2×D5semidirect
271. #947C2×D5semidirect
272. #946C2×D5semidirect
281. D4×Dic3C2×D5semidirect
286. #930C2×D5semidirect
356. #686#67semidirect
398. C2×C5×D3AGL(1,ℤ/8)semidirect
504. C5×D4C2×#67semidirect
535. #168C2×#67semidirect
536. C2×#41D3×D5semidirect
616. C3×D4D4×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4095semidirect
827. D4D5×#67semidirect
857. C5#83952semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#58292
C2×C3×#40952
C2×D3×#6862
#67×D202
#117513392
#117493982
#117493422
#117492742
#117492282
#117490992
#117490322
#117489882
#117485152
#117485102
#117484842
#106152333
#839525