Finite Group Databasebeta

← #14453545

Subgroups — #14453545

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
1C22×#6716C211yesmaximal, characteristic, complemented
2C5×D4×#67C211yesmaximal, characteristic, complemented
3C2×#91494C211yesmaximal, characteristic, complemented
4#11754369C211yesmaximal, characteristic, complemented
5C3×#65506C211yesmaximal, characteristic, complemented
6#11749157C211yesmaximal, characteristic, complemented
7#11749079C211yesmaximal, characteristic, complemented
8#11749071C211yesmaximal, characteristic, complemented
9#11749057C211yesmaximal, characteristic, complemented
10#11749056C211yesmaximal, characteristic, complemented
11#11749014C211yesmaximal, characteristic, complemented
12#11749013C211yesmaximal, characteristic, complemented
13#11748553C211yesmaximal, characteristic, complemented
14#11748522C211yesmaximal, characteristic, complemented
15#11748508C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×Dic30C2211yescharacteristic, complemented
19C22×C5×#67—21no—
20C2×C5×D3×D4C2211yescharacteristic
21C2×#6765C2211yescharacteristic, complemented
22C2×#6716—24no—
23C2×#6716C2211yescharacteristic
24C2×#6716C2211yescharacteristic
25C2×#6716C2211yescharacteristic, complemented
26C2×#6716C2211yescharacteristic, complemented
27C22×C3⋊#168C2211yescharacteristic, complemented
28C5×#953—21no—
29C5×#940C2211yescharacteristic
30C5×#939—21no—
31C5×#938C2211yescharacteristic
32C5×#937—21no—
33C5×D4×Dic3C2211yescharacteristic
34C5×#930C2211yescharacteristic
35C4×C5×#67C2211yescharacteristic
36C2×C3×#686C2211yescharacteristic
37C2×C3×#686C2211yescharacteristic, complemented
38C3×#4076C2211yescharacteristic, complemented
39#91571—21no—
40#91559—21no—
41#91494—24no—
42#91462—21no—
43#91431—21no—
44#91365C2211yescharacteristic, complemented
45#91364C2211yescharacteristic, complemented
46#91340C2211yescharacteristic, complemented
47C2×#6659C2211yescharacteristic, complemented
48C2×#6659C2211yescharacteristic, complemented
49C2×#6652C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51C3×#3964C2211yescharacteristic
52C3×#3964C2211yescharacteristic, complemented
53C3×C22⋊#168C2211yescharacteristic, complemented
54#90989C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90975C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80025—51nomaximal, Hall
63C5×D42—31no—
64C22×#687—31no—
65C2×#4078—31no—
66#65886—31no—
67#65507—31no—
68#65506D311yescharacteristic, complemented
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326—31no—
75#65307—31no—
76#65305—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×Dic15—21no—
87C2×Dic30—22no—
88C2×Dic30—21no—
89C2×Dic30—41no—
90C2×Dic30C2311yescharacteristic
91C2×Dic30C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C2×C5×#67—21no—
95C2×C5×#67—21no—
96C2×C5×#67—21no—
97C2×C5×#67—44no—
98C2×C5×#67D411yescharacteristic
99C22×C5×Dic3—21no—
100C5×D3×D4—22no—
101C5×D3×D4—41no—
102C2×C5×D12C2311yescharacteristic
103C2×C4×C5×D3C2311yescharacteristic
104C2×C3×C22⋊D5—21no—
105C2×C3×D20C2311yescharacteristic
106C2×#1201—21no—
107C2×D5×Dic3—21no—
108#6765—22no—
109#6765—41no—
110#6716—22no—
111#6716—22no—
112#6716—22no—
113#6716D414yescomplemented
114C2×C3⋊#168—22no—
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×#217—21no—
118C5×#217—21no—
119C5×#217D411yescharacteristic
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×C4⋊Dic3C2311yescharacteristic
123C5×Dic3⋊C4D411yescharacteristic
124C4×C5×Dic3C2311yescharacteristic
125C3×#686—22no—
126C3×#686—41no—
127C3×#685—21no—
128C3×C4⋊Dic5C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6669—21no—
132#6668—21no—
133(C2×D3)⋊Dic5—21no—
134#6665—21no—
135#6665—21no—
136Dic3×Dic5—21no—
137#6659—22no—
138#6659—41no—
139#6652—22no—
140#6650—22no—
141D4×#67D511yescharacteristic, complemented
142C22×#214—51no—
143C2×#911—51no—
144#5598—51no—
145C3×#447—51no—
146#5158—51no—
147#5154—51no—
148#5153—51no—
149#5038—51no—
150#4780—51no—
151#4776—51no—
152#4762—51no—
153#4757—51no—
154#4738—51no—
155#4730—51no—
156C22×C5×D4—31no—
157C22×C5×D4—61no—
158C22×C5×D4C2×D311yescharacteristic
159C2×#709—31no—
160C22×Dic10—31no—
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#4085—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—64no—
177#4078—64no—
178C2×#686—31no—
179C2×#686C2×D311yescharacteristic
180C2×#686C2×D311yescharacteristic, complemented
181#4076C2×D311yescharacteristic, complemented
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10—31no—
190#3964—31no—
191#3964C2×D311yescharacteristic
192#3964C2×D311yescharacteristic, complemented
193C22⋊#168—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3942—31no—
196#3942—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—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—
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—42no—
218C3×C5×D4C2×D412yes—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—42no—
226Dic30—21no—
227Dic30—21no—
228Dic30—21no—
229Dic30—42no—
230Dic30C2×D412yescomplemented
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×C22⋊D5—42no—
247C2×C3×Dic5—21no—
248C3×D20—21no—
249C3×D20—21no—
250#1201—42no—
251D5×Dic3—42no—
252C3⋊#168—21no—
253C3⋊#168C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C22×C3×D4C2×D511yescharacteristic
257C22×#67—21no—
258C2×#237—51no—
259C2×D3×D4C2×D511yescharacteristic
260C22×Dic6—51no—
261C2×C3×D8—51no—
262C2×C3×D8—51no—
263C3×#121—51no—
264#953—21no—
265#940C2×D511yescharacteristic
266#939—21no—
267#939—101no—
268#938C2×D511yescharacteristic
269#937—21no—
270#936—51no—
271D4×Dic3—101no—
272D4×Dic3C2×D511yescharacteristic
273C2×#214—51no—
274C2×#214—51no—
275C2×#214—51no—
276C2×#214—51no—
277C2×#214—104no—
278C2×#213—51no—
279#930C2×D511yescharacteristic
280C4×#67C2×D511yescharacteristic
281C22×C3⋊C8—51no—
282#911—104no—
283C2×#204—51no—
284C2×#204—51no—
285C2×ΓL(1,𝔽25)—51no—
286#897—51no—
287#887—51no—
288#885—101no—
289#878—101no—
290C3×#102—51no—
291C3×#102—51no—
292C3×C22⋊C8—51no—
293#832—51no—
294(C2×D3)⋊C8—51no—
295#816—51no—
296#816—51no—
297#815—51no—
298Dic3⋊C8—51no—
299#809—51no—
300#807—51no—
301C24×C5—21no—
302C24×C5—61no—
303C2×C5×D4—22no—
304C2×C5×D4—21no—
305C2×C5×D4—31no—
306C2×C5×D4—31no—
307C2×C5×D4—41no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—62no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4—124no—
316C2×C5×D4C22×D311yescharacteristic
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—31no—
319C22×C4×C5—61no—
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—21no—
322C2×C22⋊D5—61no—
323C22×Dic5—61no—
324#709—62no—
325#709—121no—
326C2×D20C22×D311yescharacteristic
327C2×C4×D5—61no—
328C2×Dic10—31no—
329C2×Dic10—31no—
330C2×Dic10—62no—
331C2×Dic10—61no—
332C2×Dic10—121no—
333C5×C4⋊C4—31no—
334C5×C4⋊C4—31no—
335C5×C22⋊C4—31no—
336C5×C22⋊C4—31no—
337C5×C22⋊C4—61no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C42×C5—31no—
341C22⋊Dic5—61no—
342#687—34no—
343#687—62no—
344#687—62no—
345#687—62no—
346#687—62no—
347#687—121no—
348#686—22no—
349#686—41no—
350#686—62no—
351#685—21no—
352#685—61no—
353#685—61no—
354C4⋊Dic5C22×D311yescharacteristic
355#683—61no—
356#683—61no—
357C4×Dic5—61no—
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—151no—
367D42—31no—
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—51no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—22no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—84no—
388C22×C3×C5AGL(1,ℤ/8)12yescomplemented
389C22×C3×C5C22×D411yescharacteristic
390C2×C5×D3—21no—
391C2×C5×D3—21no—
392C2×C5×D3—21no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—84no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C3×C4×C5—21no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403Dic15—22no—
404Dic15—41no—
405C3×Dic5—41no—
406C5×Dic3—21no—
407C5×Dic3—21no—
408C5×Dic3—21no—
409C5×Dic3—41no—
410C24×C3—21no—
411C23×D3—21no—
412C2×C3×D4—22no—
413C2×C3×D4—21no—
414C2×C3×D4—41no—
415C2×C3×D4—51no—
416C2×C3×D4—101no—
417C2×C3×D4C22×D511yescharacteristic
418C2×C3×D4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C2×#67—21no—
421C2×#67—21no—
422C2×#67—21no—
423C2×#67—21no—
424C2×#67—21no—
425C2×#67—44no—
426C2×#67—101no—
427C2×#67C22⋊D511yescharacteristic
428C22×Dic3—21no—
429C22×Dic3—101no—
430C22×Dic3—101no—
431#237—102no—
432#237—201no—
433D3×D4—22no—
434D3×D4—41no—
435C2×D12C22×D511yescharacteristic
436C2×C4×D3C22×D511yescharacteristic
437C2×Dic6—51no—
438C2×Dic6—51no—
439C2×Dic6—102no—
440C2×Dic6—101no—
441C2×Dic6—201no—
442C3×D8—102no—
443C3×D8—201no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C3×C4⋊C4—51no—
447C3×C22⋊C4—101no—
448#217—21no—
449#217—21no—
450#217—101no—
451#217—101no—
452#217C22⋊D511yescharacteristic
453#214—54no—
454#214—102no—
455#214—102no—
456#214—102no—
457#213—102no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4C22⋊D511yescharacteristic
461C4⋊Dic3—101no—
462C4⋊Dic3C22×D511yescharacteristic
463Dic3⋊C4—101no—
464Dic3⋊C4C22⋊D511yescharacteristic
465C4×Dic3—101no—
466C4×Dic3C22×D511yescharacteristic
467C2×C3⋊C8—51no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—102no—
470#204—102no—
471#204—201no—
472ΓL(1,𝔽25)—102no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—31no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—61no—
479C23×C5—81no—
480C23×C5—122no—
481C23×C5—122no—
482C23×C5—241no—
483C23×C5D3×D411yescharacteristic
484C22×D5—21no—
485C5×D4—21no—
486C5×D4—21no—
487C5×D4—21no—
488C5×D4—42no—
489C5×D4—62no—
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—122no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—241no—
497C5×D4D3×D412yes—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—31no—
501C2×C4×C5—31no—
502C2×C4×C5—31no—
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—42no—
510C22⋊D5—122no—
511C2×Dic5—21no—
512C2×Dic5—61no—
513C2×Dic5—61no—
514C2×Dic5—122no—
515D20—21no—
516D20—21no—
517C4×D5—122no—
518Dic10—32no—
519Dic10—61no—
520Dic10—61no—
521Dic10—61no—
522Dic10—122no—
523#168—21no—
524#168—21no—
525#168—32no—
526#168—61no—
527C2×#41—151no—
528C22×Q8—151no—
529C22×D4—31no—
530C22×D4—61no—
531C22×D4D3×D511yescharacteristic
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
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—151no—
544C22×C8—151no—
545#127—31no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—31no—
551#121—31no—
552#121—51no—
553#121—61no—
554#121—301no—
555#120—61no—
556#120—61no—
557C4×Q8—151no—
558C4×D4—31no—
559C4×D4—31no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—51no—
566#102—51no—
567#102—151no—
568#102—151no—
569C22⋊C8—51no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—42no—
574C2×C3×C5—81no—
575C2×C3×C5D4211yescharacteristic
576C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
577C2×C3×C5#57711yescharacteristic
578C3×D5—81no—
579C5×D3—41no—
580C5×D3—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—81no—
586C23×C3—101no—
587C23×C3C2×C22⋊D511yescharacteristic
588C22×D3—21no—
589C22×D3—42no—
590C22×D3—42no—
591C22×D3—81no—
592C22×D3C2×C22⋊D511yescharacteristic
593C3×D4—21no—
594C3×D4—21no—
595C3×D4—21no—
596C3×D4—42no—
597C3×D4—101no—
598C3×D4—101no—
599C3×D4—202no—
600C3×D4D4×D512yes—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—101no—
604C2×C3×C4C2×C22⋊D511yescharacteristic
605C2×C3×C4C23×D511yescharacteristic
606#67—22no—
607#67—42no—
608#67—42no—
609#67—42no—
610#67—42no—
611#67—81no—
612#67—202no—
613C2×Dic3—21no—
614C2×Dic3—42no—
615C2×Dic3—101no—
616C2×Dic3—101no—
617C2×Dic3—202no—
618C2×Dic3—202no—
619C2×Dic3C2×C22⋊D511yescharacteristic
620C2×Dic3C2×C22⋊D511yescharacteristic
621C2×Dic3C2×C22⋊D511yescharacteristic
622D12—21no—
623D12—21no—
624C4×D3—21no—
625C4×D3—21no—
626Dic6—52no—
627Dic6—101no—
628Dic6—101no—
629Dic6—101no—
630Dic6—202no—
631C3×C8—101no—
632C3×C8—101no—
633C3⋊C8—52no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—22no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—61no—
644C22×C5—61no—
645C22×C5—61no—
646C22×C5—84no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—121no—
650C22×C5—244no—
651C22×C5#91112yescomplemented
652C22×C5C2×D3×D411yescharacteristic
653C2×D5—41no—
654C2×D5—41no—
655C2×D5—41no—
656C4×C5—21no—
657C4×C5—61no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—121no—
661C4×C5C2×D3×D411yescharacteristic
662C4×C5#100411yescharacteristic
663Dic5—41no—
664Dic5—62no—
665Dic5—121no—
666C24—21no—
667C24—61no—
668#41—302no—
669#41—601no—
670C2×Q8—151no—
671C2×Q8—151no—
672C2×Q8—302no—
673C2×Q8—301no—
674C2×Q8—601no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—41no—
680C2×D4—51no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—62no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—101no—
688C2×D4—121no—
689C2×D4—124no—
690C2×D4—301no—
691C2×D4C2×D3×D511yescharacteristic
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—301no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—102no—
705D8—201no—
706D8—302no—
707M16—302no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—51no—
716C4⋊C4—301no—
717C4⋊C4—301no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—101no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—31no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—84no—
739C22×C3—201no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3#407812yescomplemented
743C22×C3C22×C22⋊D511yescharacteristic
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—84no—
751C3×C4—21no—
752C3×C4—201no—
753C3×C4C2×D4×D511yescharacteristic
754C3×C4#414411yescharacteristic
755Dic3—21no—
756Dic3—21no—
757Dic3—21no—
758Dic3—41no—
759Dic3—102no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—42no—
763C2×C5—81no—
764C2×C5—121no—
765C2×C5—241no—
766C2×C5#559011yescharacteristic
767C2×C5C2×#91111yescharacteristic
768C2×C5#577511yescharacteristic
769D5—81no—
770C23—21no—
771C23—21no—
772C23—31no—
773C23—42no—
774C23—42no—
775C23—61no—
776C23—81no—
777C23—101no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23D3×C22⋊D511yescharacteristic
782Q8—152no—
783Q8—301no—
784Q8—301no—
785Q8—301no—
786Q8—602no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—42no—
791D4—62no—
792D4—61no—
793D4—61no—
794D4—101no—
795D4—101no—
796D4—122no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—202no—
801D4—241no—
802D4—602no—
803D4#679012yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—101no—
813C2×C4—122no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—602no—
817C2×C4—602no—
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—101no—
821C8—101no—
822C8—152no—
823C8—301no—
824C2×C3—22no—
825C2×C3—42no—
826C2×C3—81no—
827C2×C3—401no—
828C2×C3C2×#407811yescharacteristic
829C2×C3D4×C22⋊D511yescharacteristic
830C2×C3#6617011yescharacteristic
831D3—41no—
832D3—81no—
833C5#8002511yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—84no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—201no—
850C22—201no—
851C22—201no—
852C22—244no—
853C22#9149412yescomplemented
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—121no—
860C4—201no—
861C4—302no—
862C4—601no—
863C4C2×#679011yescharacteristic
864C4#9204911yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—22no—
867C2—42no—
868C2—81no—
869C2—121no—
870C2—241no—
871C2—401no—
872C2C2×#9149411yescharacteristic
873C2#1175472011yescharacteristic
874C2#1175544011yescharacteristic
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#3265
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. C22×#6716C2semidirect
2. C5×D4×#67C2semidirect
3. C2×#91494C2semidirect
4. #11754369C2semidirect
5. C3×#65506C2semidirect
6. #11749157C2semidirect
7. #11749079C2semidirect
8. #11749071C2semidirect
9. #11749057C2semidirect
10. #11749056C2semidirect
11. #11749014C2semidirect
12. #11749013C2semidirect
13. #11748553C2semidirect
14. #11748522C2semidirect
15. #11748508C2semidirect
18. C22×Dic30C22semidirect
21. C2×#6765C22semidirect
25. C2×#6716C22semidirect
26. C2×#6716C22semidirect
27. C22×C3⋊#168C22semidirect
37. C2×C3×#686C22semidirect
38. C3×#4076C22semidirect
44. #91365C22semidirect
45. #91364C22semidirect
46. #91340C22semidirect
47. C2×#6659C22semidirect
48. C2×#6659C22semidirect
49. C2×#6652C22semidirect
50. C2×#6650C22semidirect
52. C3×#3964C22semidirect
53. C3×C22⋊#168C22semidirect
54. #90989C22semidirect
55. Dic3⋊#168C22semidirect
56. #90975C22semidirect
57. #90975C22semidirect
58. #90966C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
68. #65506D3semidirect
113. #6716D4semidirect
141. D4×#67D5semidirect
180. C2×#686C2×D3semidirect
181. #4076C2×D3semidirect
192. #3964C2×D3semidirect
194. C22⋊#168C2×D3semidirect
230. Dic30C2×D4semidirect
253. C3⋊#168C2×D4semidirect
388. C22×C3×C5AGL(1,ℤ/8)semidirect
651. C22×C5#911semidirect
729. C3×C5#3265semidirect
742. C22×C3#4078semidirect
833. C5#80025semidirect
853. C22#91494semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
C22×#67162
C5×D4×#672
C2×#914942
#117543692
C3×#655062
#117491572
#117490792
#117490712
#117490572
#117490562
#117490142
#117490132
#117485532
#117485222
#117485082
#106152223
#800255