Finite Group Databasebeta

← #14453491

Subgroups — #14453491

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×#5576C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#11752745C211yesmaximal, characteristic, complemented
5#11751127C211yesmaximal, characteristic, complemented
6C3×#65316C211yesmaximal, characteristic, complemented
7#11749281C211yesmaximal, characteristic, complemented
8#11749278C211yesmaximal, characteristic, complemented
9#11747483C211yesmaximal, characteristic, complemented
10#11747482C211yesmaximal, characteristic, complemented
11#11747323C211yesmaximal, characteristic, complemented
12#11747319C211yesmaximal, characteristic, complemented
13#11747046C211yesmaximal, characteristic, complemented
14#11747041C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic, complemented
18C2×C5×D3×Q8C2211yescharacteristic, complemented
19C2×#6777—21no—
20C2×D3×D20C2211yescharacteristic
21C2×D3×D20C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic
24C4×D60C2211yescharacteristic
25C5×#897—21no—
26C5×#897C2211yescharacteristic, complemented
27C5×#895—21no—
28C5×#895C2211yescharacteristic, complemented
29C5×#875—21no—
30C5×#875C2211yescharacteristic, complemented
31C4×C5×D12—21no—
32C4×C5×D12C2211yescharacteristic
33C2×C3×#688C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic, complemented
35C3×#4020C2211yescharacteristic
36#91504—24no—
37D3×#688—24no—
38#91474—21no—
39#91474—21no—
40#91465—21no—
41#91456C2211yescharacteristic
42#91456C2211yescharacteristic
43C2×#6660C2211yescharacteristic
44C2×#6655C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic
47C2×#6652C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91093C2211yescharacteristic
53#91091C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80404—51nomaximal, Hall
63C5×#548—31no—
64C2×#4095—31no—
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#65316D311yescharacteristic, complemented
76#65315—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C22×D3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C5×#239—22no—
84C5×#239—41no—
85C5×D3×Q8—22no—
86C5×D3×Q8—41no—
87C2×C5×D12—21no—
88C2×C5×D12—21no—
89C2×C5×D12D411yescharacteristic
90C2×C5×D12C2311yescharacteristic
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3—21no—
93C2×C4×C5×D3C2311yescharacteristic
94C2×C4×C5×D3C2311yescharacteristic
95C2×C5×Dic6—21no—
96C2×C5×Dic6C2311yescharacteristic
97C2×C3×D20—21no—
98C2×C3×D20—21no—
99C2×C3×D20C2311yescharacteristic
100C2×C3×D20C2311yescharacteristic
101C2×#1202—21no—
102C2×#1202—21no—
103C2×#1201—21no—
104C2×#1201—21no—
105#6777—44no—
106D3×D20—22no—
107D3×D20—22no—
108D3×D20—41no—
109D3×D20—41no—
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C42×C5—21no—
113C3×C42×C5C2311yescharacteristic
114#6717D414yescomplemented
115#6714—21no—
116C4⋊Dic15C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
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×(C2×D3)⋊C4D411yescharacteristic
125C5×C4⋊Dic3—21no—
126C5×C4⋊Dic3D411yescharacteristic
127C3×#688—22no—
128C3×#688—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6665—21no—
132#6665—21no—
133#6660—22no—
134#6655—22no—
135#6655—41no—
136#6654—22no—
137#6652—22no—
138#6652—41no—
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×SD16—51no—
143#5717—51no—
144#5576D511yescharacteristic, complemented
145C3×#460—51no—
146#5172—51no—
147#5170—51no—
148#5074—51no—
149#5026—51no—
150#4844—51no—
151#4836—51no—
152#4780—51no—
153#4776—51no—
154#4775—51no—
155#4773—51no—
156C2×C5×#41—31no—
157C22×C5×Q8—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124—31no—
162C5×#124—61no—
163C5×C22⋊Q8—31no—
164C5×C22⋊Q8—61no—
165C5×#121—31no—
166C5×#121—61no—
167C4×C5×Q8C2×D311yescharacteristic, complemented
168C4×C5×D4—31no—
169C4×C5×D4—61no—
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—64no—
176C2×#688C2×D311yescharacteristic, complemented
177C2×#688C2×D311yescharacteristic, complemented
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4076—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020C2×D311yescharacteristic
189C4×D20—31no—
190#3967—31no—
191#3967—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941C2×D311yescharacteristic, complemented
197#3941C2×D311yescharacteristic, complemented
198#3939—31no—
199C4⋊#168C2×D311yescharacteristic, complemented
200#3935—31no—
201#3265—151noSylow
202C22×D15—21no—
203C22×C5×D3—21no—
204C22×C5×D3C2×D411yescharacteristic
205C22×C5×D3C2×D411yescharacteristic
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C2×D3×D5—42no—
209C2×D3×D5—42no—
210C2×D3×D5—42no—
211C2×D3×D5—42no—
212C2×D3×D5—81no—
213C2×D3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8C2×D412yescomplemented
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2411yescharacteristic
221C2×Dic15—21no—
222D60—21no—
223D60C2×D412yes—
224C4×D15—42no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3C2×D411yescharacteristic
227C2×C5×Dic3C2×D411yescharacteristic
228C5×D12—22no—
229C5×D12—21no—
230C5×D12—21no—
231C5×D12—42no—
232C5×D12—42no—
233C4×C5×D3—21no—
234C4×C5×D3—21no—
235C4×C5×D3—21no—
236C4×C5×D3—21no—
237C4×C5×D3—42no—
238C4×C5×D3—42no—
239C5×Dic6—21no—
240C5×Dic6—21no—
241C5×Dic6—42no—
242C3×D20—21no—
243C3×D20—21no—
244C3×D20—21no—
245C3×D20—21no—
246C3×D20—42no—
247C3×D20—81no—
248#1202—42no—
249#1202—42no—
250#1201—42no—
251#1201—42no—
252C3⋊#168—21no—
253C3⋊#168C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C2×#239C2×D511yescharacteristic, complemented
257C2×D3×Q8C2×D511yescharacteristic, complemented
258C2×D3×D4—51no—
259C2×D3×D4—51no—
260C2×D3×D4—101no—
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C3×#127—51no—
264C3×C4×Q8C2×D511yescharacteristic, complemented
265C2×#215—51no—
266#938—51no—
267#938—51no—
268#938—101no—
269#937—101no—
270#937—101no—
271C2×#214—51no—
272C2×#214—51no—
273C2×#213—51no—
274C2×#213—51no—
275#914—104no—
276D3×SD16—104no—
277C2×D24—51no—
278C2×#204—51no—
279C2×ΓL(1,𝔽25)—51no—
280C2×D3×C8—51no—
281#897—21no—
282#897C2×D511yescharacteristic, complemented
283#895—21no—
284#895C2×D511yescharacteristic, complemented
285#875—21no—
286#875C2×D511yescharacteristic, complemented
287C4×D12—21no—
288C4×D12—51no—
289C4×D12C2×D511yescharacteristic
290C3×C4⋊C8—51no—
291C3×#102—51no—
292C3×#102—51no—
293#835—51no—
294#821—51no—
295(C2×D3)⋊C8—51no—
296(C2×D3)⋊C8—51no—
297#816—51no—
298#809—51no—
299#807—51no—
300#803—51no—
301C23×D5—61no—
302C23×D5—61no—
303C5×#41—62no—
304C5×#41—121no—
305C2×C5×Q8—31no—
306C2×C5×Q8—61no—
307C2×C5×Q8—62no—
308C2×C5×Q8—121no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—31no—
311C2×C5×D4—31no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5—61no—
317C22×C4×C5—61no—
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320D4×D5—124no—
321C2×D20—21no—
322C2×D20—21no—
323C2×D20—31no—
324C2×D20—62no—
325C2×D20—62no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—121no—
329C2×D20—121no—
330C2×D20C22×D311yescharacteristic
331C2×D20C22×D311yescharacteristic
332C2×C4×D5—61no—
333C5×C4⋊C4—21no—
334C5×C4⋊C4—31no—
335C5×C4⋊C4—61no—
336C5×C4⋊C4C22×D311yescharacteristic
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—21no—
344C42×C5C22×D311yescharacteristic
345#688—22no—
346#688—22no—
347#688—34no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—62no—
352#686—62no—
353#686—121no—
354#685—61no—
355#685—61no—
356#685—61no—
357C4⋊Dic5—31no—
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361C2×#168—62no—
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—31no—
367D42—151no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—51no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5C22×D411yescharacteristic
380C2×D15—22no—
381C2×D15—41no—
382C2×D15—41no—
383C2×C5×D3—21no—
384C2×C5×D3—21no—
385C2×C5×D3—21no—
386C2×C5×D3—21no—
387C2×C5×D3—21no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3AGL(1,ℤ/8)12yescomplemented
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398D3×D5—84no—
399D3×D5—84no—
400C3×C4×C5—22no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—41no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406Dic15—41no—
407C5×Dic3—21no—
408C5×Dic3—21no—
409C5×Dic3—41no—
410C23×D3—101no—
411C23×D3—101no—
412C2×C3×Q8C22×D511yescharacteristic
413C2×C3×D4—51no—
414C2×C3×D4—51no—
415C2×C3×D4—101no—
416C2×C3×D4—101no—
417C2×#67—101no—
418C2×#67—101no—
419C2×#67—101no—
420C2×#67—101no—
421#239—22no—
422#239—41no—
423D3×Q8—22no—
424D3×Q8—41no—
425D3×D4—102no—
426D3×D4—102no—
427D3×D4—201no—
428D3×D4—201no—
429D3×D4—204no—
430C2×D12—21no—
431C2×D12—21no—
432C2×D12—51no—
433C2×D12C22⋊D511yescharacteristic
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—21no—
437C2×C4×D3—101no—
438C2×C4×D3C22×D511yescharacteristic
439C2×C4×D3C22×D511yescharacteristic
440C2×Dic6—21no—
441C2×Dic6C22×D511yescharacteristic
442C3×SD16—102no—
443C3×SD16—102no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C3×C4⋊C4—21no—
447C3×C4⋊C4C22×D511yescharacteristic
448C3×C42—21no—
449C3×C42C22×D511yescharacteristic
450#217—101no—
451#217—101no—
452#215—54no—
453#214—102no—
454#214—201no—
455#213—102no—
456#213—201no—
457(C2×D3)⋊C4—21no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4—21no—
460(C2×D3)⋊C4—21no—
461(C2×D3)⋊C4—101no—
462(C2×D3)⋊C4C22⋊D511yescharacteristic
463(C2×D3)⋊C4C22⋊D511yescharacteristic
464C4⋊Dic3—21no—
465C4⋊Dic3—51no—
466C4⋊Dic3C22⋊D511yescharacteristic
467C2×C3⋊C8—51no—
468C2×C3⋊C8—51no—
469D24—102no—
470#204—102no—
471ΓL(1,𝔽25)—102no—
472D3×C8—102no—
473C23×C5—31no—
474C23×C5—31no—
475C23×C5—61no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—61no—
479C22×D5—122no—
480C22×D5—122no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5—241no—
485C5×Q8—21no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—122no—
489C5×Q8D3×D412yescomplemented
490C5×D4—62no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—122no—
494C5×D4—122no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—31no—
498C2×C4×C5—31no—
499C2×C4×C5—61no—
500C2×C4×C5—61no—
501C2×C4×C5—61no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—122no—
505C2×C4×C5—122no—
506C2×C4×C5D3×D411yescharacteristic
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—61no—
512D20—21no—
513D20—21no—
514D20—21no—
515D20—21no—
516D20—32no—
517D20—42no—
518D20—61no—
519D20—81no—
520D20—122no—
521D20—122no—
522C4×D5—122no—
523#168—21no—
524#168—21no—
525#168—32no—
526#168—61no—
527C2×#41—31no—
528C22×Q8—31no—
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—151no—
545#127—51no—
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×Q8D3×D511yescharacteristic, complemented
558C4×D4—31no—
559C4×D4—61no—
560C4×D4—151no—
561#107—151no—
562C4⋊C8—51no—
563#103—151no—
564#103—151no—
565#102—51no—
566#102—51no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5D4211yescharacteristic
573C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
574C2×C3×C5#57711yescharacteristic
575D15—42no—
576C3×D5—81no—
577C3×D5—81no—
578C5×D3—22no—
579C5×D3—41no—
580C5×D3—81no—
581C23×C3—101no—
582C23×C3—101no—
583C22×D3—21no—
584C22×D3—101no—
585C22×D3—202no—
586C22×D3—202no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—401no—
590C22×D3—401no—
591C22×D3C2×C22⋊D511yescharacteristic
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—21no—
594C3×Q8D4×D512yescomplemented
595C3×D4—101no—
596C3×D4—101no—
597C3×D4—101no—
598C3×D4—101no—
599C3×D4—202no—
600C3×D4—401no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4C2×C22⋊D511yescharacteristic
604C2×C3×C4C2×C22⋊D511yescharacteristic
605C2×C3×C4C23×D511yescharacteristic
606#67—202no—
607#67—202no—
608#67—202no—
609#67—202no—
610C2×Dic3—21no—
611C2×Dic3—101no—
612C2×Dic3C2×C22⋊D511yescharacteristic
613C2×Dic3C2×C22⋊D511yescharacteristic
614D12—22no—
615D12—21no—
616D12—21no—
617D12—42no—
618D12—42no—
619D12—52no—
620D12—101no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—202no—
628Dic6—21no—
629Dic6—21no—
630Dic6—42no—
631C3×C8—101no—
632C3×C8—101no—
633C3⋊C8—52no—
634C3⋊C8—101no—
635C22×C5—32no—
636C22×C5—61no—
637C22×C5—61no—
638C22×C5—61no—
639C22×C5—61no—
640C22×C5—61no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5—121no—
644C22×C5C2×D3×D411yescharacteristic
645C2×D5—41no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—62no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—22no—
659C4×C5—41no—
660C4×C5—61no—
661C4×C5—61no—
662C4×C5—121no—
663C4×C5C2×D3×D411yescharacteristic
664C4×C5#100911yescharacteristic
665Dic5—121no—
666C24—301no—
667C24—301no—
668#41—62no—
669#41—121no—
670C2×Q8—31no—
671C2×Q8—61no—
672C2×Q8—62no—
673C2×Q8—121no—
674C2×Q8C2×D3×D511yescharacteristic
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—151no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—302no—
687C2×D4—302no—
688C2×D4—301no—
689C2×D4—301no—
690C2×D4—601no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—301no—
698SD16—102no—
699SD16—102no—
700SD16—154no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—21no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—151no—
717C4⋊C4C2×D3×D511yescharacteristic
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—21no—
728C42C2×D3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—201no—
731C22×C3—201no—
732C22×C3—201no—
733C22×C3—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3C22×C22⋊D511yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—102no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—404no—
749C2×D3—404no—
750C2×D3#409512yescomplemented
751C3×C4—22no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—41no—
755C3×C4C2×D4×D511yescharacteristic
756C3×C4#414411yescharacteristic
757Dic3—21no—
758Dic3—21no—
759Dic3—41no—
760Dic3—201no—
761C2×C5—62no—
762C2×C5—121no—
763C2×C5—241no—
764C2×C5#560911yescharacteristic
765C2×C5#576211yescharacteristic
766C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
767D5—81no—
768D5—81no—
769D5—122no—
770C23—31no—
771C23—31no—
772C23—61no—
773C23—101no—
774C23—101no—
775C23—301no—
776C23—602no—
777C23—602no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23—1201no—
782Q8—21no—
783Q8—61no—
784Q8—61no—
785Q8—122no—
786Q8#677712yescomplemented
787D4—62no—
788D4—61no—
789D4—61no—
790D4—101no—
791D4—101no—
792D4—101no—
793D4—101no—
794D4—122no—
795D4—122no—
796D4—152no—
797D4—202no—
798D4—301no—
799D4—401no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—602no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—122no—
814C2×C4—122no—
815C2×C4—301no—
816C2×C4—602no—
817C2×C4D3×C22⋊D511yescharacteristic
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—101no—
821C8—101no—
822C8—152no—
823C8—301no—
824C2×C3—401no—
825C2×C3—401no—
826C2×C3D4×C22⋊D511yescharacteristic
827C2×C3C2×#409511yescharacteristic
828C2×C3#6617111yescharacteristic
829D3—22no—
830D3—41no—
831D3—81no—
832D3—202no—
833C5#8040411yescharacteristic, complemented, Sylow
834C22—32no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—201no—
844C22—201no—
845C22—201no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—302no—
850C22—601no—
851C22—601no—
852C22—1204no—
853C22—1204no—
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—21no—
857C4—22no—
858C4—41no—
859C4—61no—
860C4—61no—
861C4—121no—
862C4—601no—
863C4C2×#677711yescharacteristic
864C4#9201811yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—62no—
867C2—121no—
868C2—241no—
869C2—401no—
870C2—401no—
871C2—602no—
872C2#1175465711yescharacteristic
873C2#1175509111yescharacteristic
874C2D3×#409511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5576C2semidirect
2. C2×#91504C2semidirect
3. C2×D3×#688C2semidirect
4. #11752745C2semidirect
5. #11751127C2semidirect
6. C3×#65316C2semidirect
7. #11749281C2semidirect
8. #11749278C2semidirect
9. #11747483C2semidirect
10. #11747482C2semidirect
11. #11747323C2semidirect
12. #11747319C2semidirect
13. #11747046C2semidirect
14. #11747041C2semidirect
15. #11746999C2semidirect
17. C2×C5×#239C22semidirect
18. C2×C5×D3×Q8C22semidirect
22. C3×C4×C5×Q8C22semidirect
26. C5×#897C22semidirect
28. C5×#895C22semidirect
30. C5×#875C22semidirect
33. C2×C3×#688C22semidirect
34. C2×C3×#688C22semidirect
44. C2×#6655C22semidirect
45. C2×#6655C22semidirect
47. C2×#6652C22semidirect
48. C2×#6652C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91119C22semidirect
53. #91091C22semidirect
54. #91087C22semidirect
55. C3×#3941C22semidirect
56. C3×#3941C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90973C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65316D3semidirect
114. #6717D4semidirect
144. #5576D5semidirect
167. C4×C5×Q8C2×D3semidirect
176. C2×#688C2×D3semidirect
177. C2×#688C2×D3semidirect
196. #3941C2×D3semidirect
197. #3941C2×D3semidirect
199. C4⋊#168C2×D3semidirect
215. C3×C5×Q8C2×D4semidirect
253. C3⋊#168C2×D4semidirect
256. C2×#239C2×D5semidirect
257. C2×D3×Q8C2×D5semidirect
264. C3×C4×Q8C2×D5semidirect
282. #897C2×D5semidirect
284. #895C2×D5semidirect
286. #875C2×D5semidirect
391. C2×C5×D3AGL(1,ℤ/8)semidirect
489. C5×Q8D3×D4semidirect
557. C4×Q8D3×D5semidirect
594. C3×Q8D4×D5semidirect
729. C3×C5#3265semidirect
750. C2×D3#4095semidirect
786. Q8#6777semidirect
833. C5#80404semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
C5×#55762
C2×#915042
C2×D3×#6882
#117527452
#117511272
C3×#653162
#117492812
#117492782
#117474832
#117474822
#117473232
#117473192
#117470462
#117470412
#117469992
#106152733
#804045