Finite Group Databasebeta

← #14453484

Subgroups — #14453484

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
1C5×#5831C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#67×D20C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11749345C211yesmaximal, characteristic, complemented
7#11749278C211yesmaximal, characteristic, complemented
8#11749234C211yesmaximal, characteristic, complemented
9#11749152C211yesmaximal, characteristic, complemented
10#11749098C211yesmaximal, characteristic, complemented
11#11749028C211yesmaximal, characteristic, complemented
12#11748982C211yesmaximal, characteristic, complemented
13#11748527C211yesmaximal, characteristic, complemented
14#11748484C211yesmaximal, characteristic, complemented
15#11748456C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C2×C5×D3×Q8C2211yescharacteristic, complemented
19C22×C3×D20C2211yescharacteristic
20C2×D5×#67—21no—
21C2×D3×D20C2211yescharacteristic
22C2×#6717C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic
25C5×Q8×Dic3C2211yescharacteristic, complemented
26C5×#938—21no—
27C5×#938C2211yescharacteristic, complemented
28C5×#936—21no—
29C5×#936C2211yescharacteristic, complemented
30C4×C5×#67—21no—
31C4×C5×#67C2211yescharacteristic
32C5×#924—21no—
33C5×#924C2211yescharacteristic, complemented
34C3×#4095—24no—
35C2×C3×#688C2211yescharacteristic
36C2×C3×#688C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C2×C3×#686C2211yescharacteristic, complemented
39C2×C3×#681C2211yescharacteristic, complemented
40#91564—21no—
41D3×#688—24no—
42#91474—21no—
43#91458C2211yescharacteristic
44#91456C2211yescharacteristic
45Dic3×D20C2211yescharacteristic
46#91409—21no—
47C2×#6660C2211yescharacteristic, complemented
48C2×#6655C2211yescharacteristic
49C2×#6655C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90973C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90964C2211yescharacteristic
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#83953—51nomaximal, Hall
63C5×#548—31no—
64C2×#4095D311yescharacteristic, complemented
65C22×#688—31no—
66D4×D20—31no—
67#65527—31no—
68#65516—31no—
69#65347—31no—
70#65346—31no—
71#65338—31no—
72#65335—31no—
73#65327—31no—
74#65325—31no—
75#65316—31no—
76#65315—31no—
77#65300—31no—
78C23×C3×D5—21no—
79C22×D3×D5—21no—
80C3×C5×#41—22no—
81C3×C5×#41—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5—21no—
86C22×C3×C4×C5C2311yescharacteristic
87C2×#1220—21no—
88C2×D60C2311yescharacteristic
89C2×C5×#67—21no—
90C2×C5×#67D411yescharacteristic
91C5×D3×Q8—22no—
92C5×D3×Q8—41no—
93C2×C4×C5×D3—21no—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C5×Dic6—21no—
96C2×C5×Dic6C2311yescharacteristic
97C2×C3×D20—22no—
98C2×C3×D20—21no—
99C2×C3×D20—41no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102D5×#67—44no—
103C2×#1202—21no—
104C2×#1202—21no—
105C2×#1202—21no—
106C2×#1201—21no—
107C2×D5×Dic3—21no—
108D3×D20—22no—
109D3×D20—41no—
110#6717—22no—
111#6715—41no—
112#6714—21no—
113C4⋊Dic15C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C5×#217—21no—
117C5×#217—21no—
118C5×#217—21no—
119C5×#217—21no—
120C5×#217D411yescharacteristic
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×C4⋊Dic3—21no—
123C5×C4⋊Dic3C2311yescharacteristic
124C5×Dic3⋊C4—21no—
125C5×Dic3⋊C4D411yescharacteristic
126C4×C5×Dic3—21no—
127C4×C5×Dic3C2311yescharacteristic
128C3×#688—22no—
129C3×#688D414yescomplemented
130C3×#686—22no—
131C3×#686—22no—
132C3×#681—22no—
133C2×C3×#168C2311yescharacteristic
134C2×C3×#168C2311yescharacteristic
135#6665—21no—
136#6665—21no—
137#6660—22no—
138#6655—22no—
139#6655—41no—
140D3×#168—22no—
141C2×C3×AGL(1,ℤ/8)—51no—
142#5831D511yescharacteristic, complemented
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×Q8—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20C2×D311yescharacteristic
161C5×#124—31no—
162C5×#124—61no—
163C5×C22⋊Q8—31no—
164C5×C22⋊Q8—61no—
165C5×#121—31no—
166C5×#121—61no—
167C4×C5×Q8—31no—
168C4×C5×D4—31no—
169C4×C5×D4—61no—
170#4095—24no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—64no—
176C2×#688C2×D311yescharacteristic
177C2×#688C2×D311yescharacteristic, complemented
178C2×#686—31no—
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#3967—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×C5×D3C2×D411yescharacteristic
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—42no—
209C22×C3×D5—42no—
210C22×C3×D5—81no—
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8C2×D412yescomplemented
216C3×C5×D4—21no—
217C3×C5×D4—21no—
218C3×C5×D4—42no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—42no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225#1220—42no—
226C2×Dic15—21no—
227D60—21no—
228D60—21no—
229C5×#67—22no—
230C5×#67—42no—
231C2×C5×Dic3—21no—
232C2×C5×Dic3—21no—
233C2×C5×Dic3C2×D411yescharacteristic
234C2×C5×Dic3C2×D411yescharacteristic
235C2×C5×Dic3C2×D411yescharacteristic
236C4×C5×D3—21no—
237C4×C5×D3—21no—
238C4×C5×D3—42no—
239C5×Dic6—21no—
240C5×Dic6—21no—
241C5×Dic6—42no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—42no—
246C3×D20C2×D412yes—
247#1202—42no—
248#1202—42no—
249#1202—81no—
250#1201—42no—
251D5×Dic3—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×C3×#41C2×D511yescharacteristic, complemented
257C22×C3×D4—51no—
258C22×#67—101no—
259C2×D3×Q8C2×D511yescharacteristic, complemented
260C2×D3×D4—51no—
261C3×AGL(1,ℤ/8)—104no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C2×C3×M16—51no—
267#953—101no—
268Q8×Dic3C2×D511yescharacteristic, complemented
269C2×#215—51no—
270#940—51no—
271#939—101no—
272#938—21no—
273#938—51no—
274#938C2×D511yescharacteristic, complemented
275#937—101no—
276#936—21no—
277#936C2×D511yescharacteristic, complemented
278D4×Dic3—51no—
279C2×#214—51no—
280C2×#214—51no—
281C2×#213—51no—
282#930—51no—
283C4×#67—21no—
284C4×#67C2×D511yescharacteristic
285#924—21no—
286#924C2×D511yescharacteristic, complemented
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—
301C23×D5—21no—
302C23×D5—61no—
303C5×#41—22no—
304C5×#41—41no—
305C2×C5×Q8—31no—
306C2×C5×Q8—61no—
307C2×C5×Q8—62no—
308C2×C5×Q8—121no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—21no—
311C2×C5×D4—31no—
312C2×C5×D4—61no—
313C2×C5×D4C22×D311yescharacteristic
314C22×C4×C5—21no—
315C22×C4×C5—31no—
316C22×C4×C5—61no—
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320D4×D5—124no—
321C2×D20—22no—
322C2×D20—21no—
323C2×D20—31no—
324C2×D20—41no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—61no—
329C2×D20—121no—
330C2×D20C22×D311yescharacteristic
331C2×D20C22×D311yescharacteristic
332C2×C4×D5—61no—
333C5×C4⋊C4—31no—
334C5×C4⋊C4—31no—
335C5×C4⋊C4—61no—
336C5×C4⋊C4—61no—
337C5×C22⋊C4—31no—
338C5×C22⋊C4—31no—
339C5×C22⋊C4—61no—
340C5×C22⋊C4—61no—
341C5×C22⋊C4—61no—
342C5×C22⋊C4—61no—
343C42×C5—31no—
344C42×C5—61no—
345#688—22no—
346#688—62no—
347#688—62no—
348#688—62no—
349#688—121no—
350#688#6714yescomplemented
351#686—22no—
352#686—22no—
353#686—121no—
354#685—61no—
355#685—61no—
356#685—61no—
357C4⋊Dic5—31no—
358#681—22no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—62no—
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—51no—
365C22×SD16—151no—
366#548—31no—
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—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—21no—
390C2×C5×D3—21no—
391C2×C5×D3AGL(1,ℤ/8)12yescomplemented
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—84no—
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5—22no—
402C3×C4×C5C22×D411yescharacteristic
403C3×C4×C5H(5,𝔽2)11yescharacteristic
404Dic15—41no—
405C5×Dic3—21no—
406C5×Dic3—21no—
407C5×Dic3—21no—
408C5×Dic3—41no—
409C5×Dic3—41no—
410C24×C3—101no—
411C23×D3—101no—
412C3×#41—22no—
413C3×#41—41no—
414C2×C3×Q8C22×D511yescharacteristic
415C2×C3×D4—21no—
416C2×C3×D4—51no—
417C2×C3×D4—51no—
418C2×C3×D4—102no—
419C2×C3×D4—101no—
420C2×C3×D4—201no—
421C2×C3×D4C22×D511yescharacteristic
422C22×C3×C4—21no—
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—21no—
425C2×#67—101no—
426C2×#67—101no—
427C2×#67—101no—
428C2×#67—101no—
429C2×#67—101no—
430C2×#67—204no—
431C2×#67C22⋊D511yescharacteristic
432C22×Dic3—101no—
433D3×Q8—22no—
434D3×Q8—41no—
435D3×D4—102no—
436D3×D4—201no—
437C2×D12—51no—
438C2×C4×D3—21no—
439C2×C4×D3C22×D511yescharacteristic
440C2×Dic6—21no—
441C2×Dic6C22×D511yescharacteristic
442C3×SD16—54no—
443C3×SD16—102no—
444C3×D8—102no—
445C3×D8—102no—
446C3×M16—102no—
447C2×C3×C8—51no—
448C2×C3×C8—51no—
449#217—21no—
450#217—21no—
451#217—21no—
452#217—21no—
453#217—101no—
454#217—101no—
455#217C22⋊D511yescharacteristic
456#215—102no—
457#214—102no—
458#214—201no—
459#213—201no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4C22⋊D511yescharacteristic
462C4⋊Dic3—21no—
463C4⋊Dic3—51no—
464C4⋊Dic3C22×D511yescharacteristic
465Dic3⋊C4—21no—
466Dic3⋊C4C22⋊D511yescharacteristic
467C4×Dic3—21no—
468C4×Dic3C22×D511yescharacteristic
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471#204—102no—
472D3×C8—102no—
473C23×C5—21no—
474C23×C5—31no—
475C23×C5D3×D411yescharacteristic
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—42no—
479C22×D5—42no—
480C22×D5—61no—
481C22×D5—81no—
482C22×D5—122no—
483C22×D5—122no—
484C22×D5—241no—
485C5×Q8—21no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—122no—
489C5×Q8C2×#6712yescomplemented
490C5×D4—21no—
491C5×D4—21no—
492C5×D4—42no—
493C5×D4—62no—
494C5×D4—122no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—31no—
499C2×C4×C5—31no—
500C2×C4×C5—31no—
501C2×C4×C5—42no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—122no—
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—61no—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—42no—
516D20—61no—
517D20—61no—
518D20—122no—
519D20—122no—
520D20—241no—
521D20C2×#6712yes—
522C4×D5—122no—
523#168—21no—
524#168—61no—
525#168—61no—
526#168C2×#6712yescomplemented
527C2×#41D3×D511yescharacteristic, complemented
528C22×Q8—31no—
529C22×D4—51no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—104no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—51no—
541C2×D8—51no—
542C2×D8—151no—
543C2×M16—51no—
544C22×C8—151no—
545#127—151no—
546#124—31no—
547#124—61no—
548C22⋊Q8—31no—
549C22⋊Q8—61no—
550#121—31no—
551#121—61no—
552#121—151no—
553#121—151no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—31no—
558C4×D4—31no—
559C4×D4—61no—
560C4×D4—151no—
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—41no—
573C2×C3×C5—81no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577D15—81no—
578C3×D5—42no—
579C3×D5—81no—
580C5×D3—22no—
581C23×C3—21no—
582C23×C3—101no—
583C23×C3—101no—
584C23×C3—202no—
585C23×C3—202no—
586C23×C3—401no—
587C23×C3C2×C22⋊D511yescharacteristic
588C22×D3—101no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—21no—
594C3×Q8D4×D512yescomplemented
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—42no—
598C3×D4—52no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—101no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—42no—
607C2×C3×C4C2×C22⋊D511yescharacteristic
608C2×C3×C4C23×D511yescharacteristic
609#67—22no—
610#67—42no—
611#67—202no—
612#67—202no—
613#67—202no—
614#67—202no—
615#67—401no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—101no—
619C2×Dic3—202no—
620C2×Dic3C2×C22⋊D511yescharacteristic
621C2×Dic3C2×C22⋊D511yescharacteristic
622C2×Dic3C2×C22⋊D511yescharacteristic
623D12—101no—
624D12—101no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—42no—
628Dic6—21no—
629Dic6—21no—
630Dic6—42no—
631C3×C8—52no—
632C3×C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—32no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5C2×D3×D411yescharacteristic
645C2×D5—22no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—84no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—22no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—61no—
661C4×C5—121no—
662C4×C5—121no—
663C4×C5#100411yescharacteristic
664C4×C5C22×#6711yescharacteristic
665Dic5—121no—
666C24—101no—
667C24—301no—
668#41—22no—
669#41—41no—
670C2×Q8—31no—
671C2×Q8—61no—
672C2×Q8—62no—
673C2×Q8—121no—
674C2×Q8C2×D3×D511yescharacteristic
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—61no—
680C2×D4—102no—
681C2×D4—101no—
682C2×D4—151no—
683C2×D4—201no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—302no—
688C2×D4—301no—
689C2×D4—301no—
690C2×D4—601no—
691C2×D4—604no—
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—21no—
694C22×C4—31no—
695C22×C4—61no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—54no—
699SD16—102no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—102no—
705D8—102no—
706D8—601no—
707M16—102no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4—151no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—31no—
728C42—61no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—102no—
737C22×C3—201no—
738C22×C3—201no—
739C22×C3—201no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—404no—
743C22×C3C22×C22⋊D511yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—404no—
750C2×D3#409512yescomplemented
751C3×C4—22no—
752C3×C4—21no—
753C3×C4C2×D4×D511yescharacteristic
754C3×C4#414411yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—41no—
759Dic3—41no—
760Dic3—201no—
761C2×C5—41no—
762C2×C5—62no—
763C2×C5—81no—
764C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
765C2×C5#577511yescharacteristic
766C2×C5D4×#6711yescharacteristic
767D5—42no—
768D5—81no—
769D5—241no—
770C23—21no—
771C23—31no—
772C23—101no—
773C23—101no—
774C23—202no—
775C23—202no—
776C23—301no—
777C23—401no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23D3×C22⋊D511yescharacteristic
782Q8—21no—
783Q8—61no—
784Q8—61no—
785Q8—122no—
786Q8D5×#6712yescomplemented
787D4—21no—
788D4—21no—
789D4—42no—
790D4—52no—
791D4—62no—
792D4—101no—
793D4—101no—
794D4—101no—
795D4—122no—
796D4—202no—
797D4—301no—
798D4—301no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—42no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—122no—
816C2×C4—301no—
817C2×C4—602no—
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—301no—
823C8—301no—
824C2×C3—41no—
825C2×C3—81no—
826C2×C3—202no—
827C2×C3—401no—
828C2×C3D4×C22⋊D511yescharacteristic
829C2×C3C2×#409511yescharacteristic
830C2×C3#6617111yescharacteristic
831D3—22no—
832D3—401no—
833C5#8395311yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—61no—
842C22—61no—
843C22—102no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—404no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22—1204no—
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—22no—
857C4—61no—
858C4—61no—
859C4—61no—
860C4—121no—
861C4—121no—
862C4—601no—
863C4C2×D5×#6711yescharacteristic
864C4#9204911yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—41no—
867C2—62no—
868C2—81no—
869C2—202no—
870C2—401no—
871C2—1201no—
872C2D3×#409511yescharacteristic
873C2#1175532411yescharacteristic
874C2#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#3265
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×#5831C2semidirect
2. C2×C3×#4095C2semidirect
3. C2×D3×#688C2semidirect
4. #67×D20C2semidirect
5. #11751339C2semidirect
6. #11749345C2semidirect
7. #11749278C2semidirect
8. #11749234C2semidirect
9. #11749152C2semidirect
10. #11749098C2semidirect
11. #11749028C2semidirect
12. #11748982C2semidirect
13. #11748527C2semidirect
14. #11748484C2semidirect
15. #11748456C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C2×C5×D3×Q8C22semidirect
22. C2×#6717C22semidirect
23. C2×#6715C22semidirect
25. C5×Q8×Dic3C22semidirect
27. C5×#938C22semidirect
29. C5×#936C22semidirect
33. C5×#924C22semidirect
36. C2×C3×#688C22semidirect
38. C2×C3×#686C22semidirect
39. C2×C3×#681C22semidirect
47. C2×#6660C22semidirect
49. C2×#6655C22semidirect
50. C2×D3×#168C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90988C22semidirect
55. Dic3⋊#168C22semidirect
56. #90973C22semidirect
57. #90969C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
64. C2×#4095D3semidirect
129. C3×#688D4semidirect
142. #5831D5semidirect
156. C2×C5×#41C2×D3semidirect
177. C2×#688C2×D3semidirect
180. C2×#686C2×D3semidirect
183. C2×#681C2×D3semidirect
215. C3×C5×Q8C2×D4semidirect
255. C3×#168C2×D4semidirect
256. C2×C3×#41C2×D5semidirect
259. C2×D3×Q8C2×D5semidirect
268. Q8×Dic3C2×D5semidirect
274. #938C2×D5semidirect
277. #936C2×D5semidirect
286. #924C2×D5semidirect
350. #688#67semidirect
391. C2×C5×D3AGL(1,ℤ/8)semidirect
489. C5×Q8C2×#67semidirect
526. #168C2×#67semidirect
527. C2×#41D3×D5semidirect
594. C3×Q8D4×D5semidirect
729. C3×C5#3265semidirect
750. C2×D3#4095semidirect
786. Q8D5×#67semidirect
833. C5#83953semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
C5×#58312
C2×C3×#40952
C2×D3×#6882
#67×D202
#117513392
#117493452
#117492782
#117492342
#117491522
#117490982
#117490282
#117489822
#117485272
#117484842
#117484562
#106152733
#839535