Finite Group Databasebeta

← #14453587

Subgroups — #14453587

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×#5633C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic, complemented
3#11754661C211yesmaximal, characteristic, complemented
4C2×#91305C211yesmaximal, characteristic, complemented
5#11751147C211yesmaximal, characteristic, complemented
6C3×#65338C211yesmaximal, characteristic, complemented
7#11749342C211yesmaximal, characteristic, complemented
8#11749279C211yesmaximal, characteristic, complemented
9#11749236C211yesmaximal, characteristic, complemented
10#11748517C211yesmaximal, characteristic, complemented
11#11748484C211yesmaximal, characteristic, complemented
12#11747482C211yesmaximal, characteristic, complemented
13#11747446C211yesmaximal, characteristic, complemented
14#11747404C211yesmaximal, characteristic, complemented
15#11747231C211yesmaximal, characteristic, complemented
16#10615273—31nomaximal, Hall
17C22×D60C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic, complemented
19C2×C5×#235C2211yescharacteristic, complemented
20C2×#6790—21no—
21C2×D3×D20C2211yescharacteristic
22C3×C5×C22⋊Q8C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic
24C2×#6717C2211yescharacteristic, complemented
25C5×#947C2211yescharacteristic, complemented
26C4×C5×#67C2211yescharacteristic
27C5×#896—21no—
28C5×#895C2211yescharacteristic, complemented
29C5×#893—21no—
30C5×#887C2211yescharacteristic, complemented
31C5×#885—21no—
32C5×#884—21no—
33C2×C3×#688C2211yescharacteristic, complemented
34C3×#4076C2211yescharacteristic
35C2×C3×#681C2211yescharacteristic, complemented
36#91572—21no—
37D3×#688—24no—
38#91476—21no—
39#91460C2211yescharacteristic
40#91459—21no—
41#91458C2211yescharacteristic
42#91428C2211yescharacteristic
43C2×#6660C2211yescharacteristic
44C2×#6660C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46#91305—24no—
47C2×#6654C2211yescharacteristic
48C2×#6654C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91114C2211yescharacteristic, complemented
52#91093C2211yescharacteristic
53#91093C2211yescharacteristic, complemented
54C3×#3967C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic, complemented
56C3×#3939C2211yescharacteristic, complemented
57Dic3⋊#168C2211yescharacteristic, complemented
58#90972C2211yescharacteristic, complemented
59#90966C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80834—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#65338D311yescharacteristic, complemented
72#65335—31no—
73#65327—31no—
74#65325—31no—
75#65316—31no—
76#65315—31no—
77#65300—31no—
78C23×D15—21no—
79C22×D3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×D60—22no—
83C2×D60—21no—
84C2×D60—41no—
85C2×D60C2311yescharacteristic
86C2×D60C2311yescharacteristic
87C2×C5×#67—21no—
88C2×C5×#67D411yescharacteristic
89C5×D3×Q8—22no—
90C5×D3×Q8—41no—
91C5×#235—22no—
92C5×#235—41no—
93C2×C5×D12—21no—
94C2×C5×D12C2311yescharacteristic
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3—21no—
97C2×C4×C5×D3C2311yescharacteristic
98C2×C5×Dic6—21no—
99C2×C5×Dic6C2311yescharacteristic
100C2×C3×C22⋊D5—21no—
101C2×C3×D20C2311yescharacteristic
102#6790—44no—
103C2×#1203—21no—
104C2×#1202—21no—
105C2×#1202—21no—
106C2×#1202—21no—
107C2×#1200—21no—
108D3×D20—22no—
109D3×D20—41no—
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113#6717—22no—
114#6717—41no—
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×#217D411yescharacteristic
118C5×(C2×D3)⋊C4—21no—
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×Dic3⋊C4—21no—
123C5×Dic3⋊C4D411yescharacteristic
124C4×C5×Dic3—21no—
125C4×C5×Dic3C2311yescharacteristic
126C3×#688—22no—
127C3×#685—21no—
128C3×C4⋊Dic5C2311yescharacteristic
129C3×#681—22no—
130C2×C3×#168C2311yescharacteristic
131C2×C3×#168C2311yescharacteristic
132#6667—21no—
133#6667—21no—
134#6660—22no—
135#6660D414yescomplemented
136#6655—22no—
137#6654—22no—
138#6654—22no—
139#6652—41no—
140D3×#168—22no—
141C2×D3×SD16—51no—
142C2×#908—51no—
143#5633D511yescharacteristic, complemented
144#5609—51no—
145C3×#468—51no—
146#5176—51no—
147#5127—51no—
148#5046—51no—
149#5037—51no—
150#4889—51no—
151#4883—51no—
152#4819—51no—
153#4806—51no—
154#4773—51no—
155#4762—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—61no—
164C5×C22⋊Q8C2×D311yescharacteristic, complemented
165C5×#121—31no—
166C5×#121—61no—
167C4×C5×Q8—31no—
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—31no—
176C2×#688—64no—
177C2×#688C2×D311yescharacteristic, complemented
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4076C2×D311yescharacteristic
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#3967C2×D311yescharacteristic, complemented
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941C2×D311yescharacteristic, complemented
198#3939C2×D311yescharacteristic, complemented
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—81no—
208C22×C5×D3—21no—
209C22×C5×D3C2×D411yescharacteristic
210C22×C3×D5—21no—
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222D60—21no—
223D60—21no—
224D60—21no—
225D60—42no—
226D60C2×D412yes—
227C5×#67—22no—
228C5×#67—42no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3C2×D411yescharacteristic
231C2×C5×Dic3C2×D411yescharacteristic
232C2×C5×Dic3C2×D411yescharacteristic
233C5×D12—21no—
234C5×D12—21no—
235C5×D12—42no—
236C4×C5×D3—21no—
237C4×C5×D3—21no—
238C4×C5×D3—42no—
239C4×C5×D3—42no—
240C5×Dic6—21no—
241C5×Dic6—42no—
242C5×Dic6C2×D412yescomplemented
243C3×C22⋊D5—42no—
244C2×C3×Dic5—21no—
245C3×D20—21no—
246C3×D20—21no—
247#1203—42no—
248#1202—42no—
249#1202—42no—
250#1202—81no—
251#1200—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C2×D3×Q8C2×D511yescharacteristic, complemented
257C2×D3×D4—51no—
258C2×D3×D4—101no—
259C2×#235C2×D511yescharacteristic, complemented
260C22×D12—51no—
261C2×C3×SD16—51no—
262C2×C3×M16—51no—
263C3×C22⋊Q8C2×D511yescharacteristic, complemented
264C3×#121—51no—
265#947C2×D511yescharacteristic, complemented
266C2×#215—51no—
267C2×#215—51no—
268#940—51no—
269#937—101no—
270C2×#214—51no—
271C2×#213—51no—
272C4×#67C2×D511yescharacteristic
273D3×SD16—104no—
274#908—104no—
275C2×D24—51no—
276C2×D24—51no—
277C2×#204—51no—
278C2×#204—51no—
279C2×D3×C8—51no—
280#896—21no—
281#895—51no—
282#895C2×D511yescharacteristic, complemented
283#893—21no—
284#893—51no—
285#887C2×D511yescharacteristic, complemented
286#885—21no—
287#884—21no—
288#884—101no—
289#882—101no—
290C3×#107—51no—
291C3×#103—51no—
292C3×#102—51no—
293#830—51no—
294(C2×D3)⋊C8—51no—
295#815—51no—
296Dic3⋊C8—51no—
297#810—51no—
298#809—51no—
299#809—51no—
300#809—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—61no—
316C22×C4×C5—61no—
317C22×C4×C5C22×D311yescharacteristic
318C2×C22⋊D5—21no—
319C2×C22⋊D5—61no—
320D4×D5—124no—
321C2×D20—31no—
322C2×D20—31no—
323C2×D20—62no—
324C2×D20—62no—
325C2×D20—61no—
326C2×D20—61no—
327C2×D20—61no—
328C2×D20—61no—
329C2×D20—121no—
330C2×D20—121no—
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—21no—
338C5×C22⋊C4—31no—
339C5×C22⋊C4—31no—
340C5×C22⋊C4—61no—
341C5×C22⋊C4—61no—
342C5×C22⋊C4—61no—
343C42×C5—31no—
344C42×C5—61no—
345#688—22no—
346#688—34no—
347#688—62no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—62no—
352#686—62no—
353#686—121no—
354#685—21no—
355#685—61no—
356#685—61no—
357C4⋊Dic5C22×D311yescharacteristic
358#681—22no—
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—51no—
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×C5C22×D411yescharacteristic
383C2×D15—22no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—84no—
390C2×C5×D3—21no—
391C2×C5×D3—21no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3AGL(1,ℤ/8)12yescomplemented
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403C3×C4×C5C22×D411yescharacteristic
404C3×C4×C5H(5,𝔽2)11yescharacteristic
405C3×Dic5—41no—
406C5×Dic3—21no—
407C5×Dic3—22no—
408C5×Dic3—21no—
409C5×Dic3—21no—
410C23×D3—101no—
411C23×D3—101no—
412C2×C3×Q8C22×D511yescharacteristic
413C2×C3×D4—51no—
414C2×C3×D4—101no—
415C22×C3×C4C22×D511yescharacteristic
416C2×#67—21no—
417C2×#67—101no—
418C2×#67—101no—
419C2×#67—101no—
420C2×#67C22⋊D511yescharacteristic
421D3×Q8—22no—
422D3×Q8—41no—
423D3×D4—102no—
424D3×D4—201no—
425D3×D4—204no—
426#235—22no—
427#235—41no—
428C2×D12—21no—
429C2×D12—51no—
430C2×D12—51no—
431C2×D12—102no—
432C2×D12—101no—
433C2×D12—101no—
434C2×D12—201no—
435C2×D12C22×D511yescharacteristic
436C2×C4×D3—21no—
437C2×C4×D3—21no—
438C2×C4×D3—101no—
439C2×C4×D3C22×D511yescharacteristic
440C2×Dic6—21no—
441C2×Dic6C22×D511yescharacteristic
442C3×SD16—102no—
443C3×M16—102no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C3×C4⋊C4—21no—
447C3×C4⋊C4—51no—
448C3×C4⋊C4C22×D511yescharacteristic
449C3×C22⋊C4—21no—
450C3×C22⋊C4—101no—
451#217C22⋊D511yescharacteristic
452#215—102no—
453#215—201no—
454#214—102no—
455#213—201no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—21no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4C22⋊D511yescharacteristic
462Dic3⋊C4—21no—
463Dic3⋊C4C22⋊D511yescharacteristic
464C4×Dic3—21no—
465C4×Dic3C22×D511yescharacteristic
466C2×C3⋊C8—51no—
467C2×C3⋊C8—51no—
468D24—102no—
469D24—102no—
470#204—54no—
471#204—102no—
472D3×C8—102no—
473C23×C5—31no—
474C23×C5—61no—
475C23×C5D3×D411yescharacteristic
476C22×D5—21no—
477C22×D5—61no—
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—21no—
487C5×Q8—32no—
488C5×Q8—61no—
489C5×Q8—122no—
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—21no—
498C2×C4×C5—21no—
499C2×C4×C5—31no—
500C2×C4×C5—31no—
501C2×C4×C5—31no—
502C2×C4×C5—61no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—122no—
506C2×C4×C5—122no—
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—42no—
510C22⋊D5—122no—
511C2×Dic5—21no—
512D20—21no—
513D20—21no—
514D20—32no—
515D20—61no—
516D20—61no—
517D20—61no—
518D20—122no—
519D20—122no—
520D20—122no—
521D20—241no—
522C4×D5—122no—
523#168—21no—
524#168—61no—
525#168—61no—
526#168D3×D412yescomplemented
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—151no—
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—51no—
544C22×C8—151no—
545#127—151no—
546#124—31no—
547#124—61no—
548C22⋊Q8—61no—
549C22⋊Q8D3×D511yescharacteristic, complemented
550#121—31no—
551#121—51no—
552#121—61no—
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—51no—
562C4⋊C8—151no—
563#103—51no—
564#103—151no—
565#102—51no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—41no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—42no—
577D15—81no—
578C3×D5—81no—
579C5×D3—22no—
580C5×D3—81no—
581C23×C3—101no—
582C23×C3C2×C22⋊D511yescharacteristic
583C22×D3—21no—
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—202no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—202no—
590C22×D3—401no—
591C22×D3—401no—
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—21no—
594C3×Q8—21no—
595C3×D4—101no—
596C3×D4—101no—
597C3×D4—202no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—101no—
603C2×C3×C4C2×C22⋊D511yescharacteristic
604C2×C3×C4C23×D511yescharacteristic
605#67—22no—
606#67—42no—
607#67—202no—
608#67—202no—
609#67—401no—
610C2×Dic3—21no—
611C2×Dic3C2×C22⋊D511yescharacteristic
612C2×Dic3C2×C22⋊D511yescharacteristic
613C2×Dic3C2×C22⋊D511yescharacteristic
614D12—21no—
615D12—21no—
616D12—42no—
617D12—52no—
618D12—101no—
619D12—101no—
620D12—101no—
621D12—202no—
622D12—202no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—202no—
628Dic6—21no—
629Dic6—42no—
630Dic6D4×D512yescomplemented
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—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—62no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—41no—
658C4×C5—41no—
659C4×C5—61no—
660C4×C5—61no—
661C4×C5—61no—
662C4×C5—62no—
663C4×C5C2×D3×D411yescharacteristic
664C4×C5#100911yescharacteristic
665Dic5—41no—
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—61no—
679C2×D4—61no—
680C2×D4—101no—
681C2×D4—151no—
682C2×D4—151no—
683C2×D4—302no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—302no—
688C2×D4—301no—
689C2×D4—301no—
690C2×D4—601no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—102no—
699SD16—154no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—102no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—21no—
714C4⋊C4—31no—
715C4⋊C4—51no—
716C4⋊C4—61no—
717C4⋊C4C2×D3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—101no—
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—201no—
734C22×C3—201no—
735C22×C3—201no—
736C22×C3C22×C22⋊D511yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—102no—
743C2×D3—201no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—404no—
749C2×D3—404no—
750C2×D3#409512yescomplemented
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—201no—
755C3×C4C2×D4×D511yescharacteristic
756C3×C4#414411yescharacteristic
757Dic3—22no—
758Dic3—21no—
759Dic3—21no—
760Dic3—21no—
761C2×C5—41no—
762C2×C5—62no—
763C2×C5—241no—
764C2×C5#560911yescharacteristic
765C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
766C2×C5#577811yescharacteristic
767D5—81no—
768D5—122no—
769D5—241no—
770C23—31no—
771C23—61no—
772C23—101no—
773C23—301no—
774C23—301no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—602no—
779C23—1201no—
780C23—1201no—
781C23D3×C22⋊D511yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—32no—
785Q8—61no—
786Q8—122no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—101no—
791D4—101no—
792D4—122no—
793D4—122no—
794D4—152no—
795D4—202no—
796D4—301no—
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—21no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—101no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—602no—
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—301no—
823C8—301no—
824C2×C3—41no—
825C2×C3—401no—
826C2×C3D4×C22⋊D511yescharacteristic
827C2×C3C2×#409511yescharacteristic
828C2×C3#6617111yescharacteristic
829D3—22no—
830D3—81no—
831D3—202no—
832D3—401no—
833C5#8083411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—32no—
838C22—61no—
839C22—61no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—201no—
844C22—201no—
845C22—201no—
846C22—302no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—601no—
852C22—1204no—
853C22—1204no—
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—41no—
857C4—41no—
858C4—61no—
859C4—62no—
860C4—61no—
861C4—61no—
862C4—201no—
863C4D3×D4×D511yescharacteristic
864C4#9202711yescharacteristic
865C3#1061527311yescharacteristic, complemented, Sylow
866C2—41no—
867C2—62no—
868C2—241no—
869C2—401no—
870C2—602no—
871C2—1201no—
872C2#1175505311yescharacteristic
873C2#1175509211yescharacteristic
874C2D3×#409511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C5×#5633C2semidirect
2. C2×D3×#688C2semidirect
3. #11754661C2semidirect
4. C2×#91305C2semidirect
5. #11751147C2semidirect
6. C3×#65338C2semidirect
7. #11749342C2semidirect
8. #11749279C2semidirect
9. #11749236C2semidirect
10. #11748517C2semidirect
11. #11748484C2semidirect
12. #11747482C2semidirect
13. #11747446C2semidirect
14. #11747404C2semidirect
15. #11747231C2semidirect
18. C2×C5×D3×Q8C22semidirect
19. C2×C5×#235C22semidirect
22. C3×C5×C22⋊Q8C22semidirect
24. C2×#6717C22semidirect
25. C5×#947C22semidirect
28. C5×#895C22semidirect
30. C5×#887C22semidirect
33. C2×C3×#688C22semidirect
35. C2×C3×#681C22semidirect
44. C2×#6660C22semidirect
45. C2×#6655C22semidirect
48. C2×#6654C22semidirect
49. C2×#6652C22semidirect
50. C2×D3×#168C22semidirect
51. #91114C22semidirect
53. #91093C22semidirect
54. C3×#3967C22semidirect
55. C3×#3941C22semidirect
56. C3×#3939C22semidirect
57. Dic3⋊#168C22semidirect
58. #90972C22semidirect
59. #90966C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
71. #65338D3semidirect
135. #6660D4semidirect
143. #5633D5semidirect
164. C5×C22⋊Q8C2×D3semidirect
177. C2×#688C2×D3semidirect
183. C2×#681C2×D3semidirect
191. #3967C2×D3semidirect
197. #3941C2×D3semidirect
198. #3939C2×D3semidirect
242. C5×Dic6C2×D4semidirect
255. C3×#168C2×D4semidirect
256. C2×D3×Q8C2×D5semidirect
259. C2×#235C2×D5semidirect
263. C3×C22⋊Q8C2×D5semidirect
265. #947C2×D5semidirect
282. #895C2×D5semidirect
285. #887C2×D5semidirect
395. C2×C5×D3AGL(1,ℤ/8)semidirect
526. #168D3×D4semidirect
549. C22⋊Q8D3×D5semidirect
630. Dic6D4×D5semidirect
729. C3×C5#3265semidirect
750. C2×D3#4095semidirect
833. C5#80834semidirect
865. C3#10615273semidirect

Maximal subgroups

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

subgroupindex
C5×#56332
C2×D3×#6882
#117546612
C2×#913052
#117511472
C3×#653382
#117493422
#117492792
#117492362
#117485172
#117484842
#117474822
#117474462
#117474042
#117472312
#106152733
#808345