Finite Group Databasebeta

← #14453772

Subgroups — #14453772

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic30C211yesmaximal, characteristic, complemented
2C5×#5550C211yesmaximal, characteristic
3C2×#91322C211yesmaximal, characteristic, complemented
4C22×#6659C211yesmaximal, characteristic, complemented
5C3×#65300C211yesmaximal, characteristic, complemented
6#11748565C211yesmaximal, characteristic, complemented
7#11748557C211yesmaximal, characteristic, complemented
8#11748553C211yesmaximal, characteristic, complemented
9#11748543C211yesmaximal, characteristic, complemented
10#11748534C211yesmaximal, characteristic, complemented
11#11748361C211yesmaximal, characteristic, complemented
12#11747098C211yesmaximal, characteristic, complemented
13#11747077C211yesmaximal, characteristic, complemented
14#11747056C211yesmaximal, characteristic, complemented
15#11746884C211yesmaximal, characteristic, complemented
16#10615237—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×Dic30C2211yescharacteristic, complemented
19C2×C5×#235C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22D4×Dic15—21no—
23#91813C2211yescharacteristic
24#91813C2211yescharacteristic, complemented
25#91777—21no—
26#91767—21no—
27#91767—21no—
28#91758C2211yescharacteristic, complemented
29C4×Dic30C2211yescharacteristic, complemented
30C5×#937—21no—
31C5×#930C2211yescharacteristic
32C5×#924C2211yescharacteristic
33C5×#894—21no—
34C5×#884—21no—
35C5×D3×C22⋊C4—21no—
36C5×#875C2211yescharacteristic
37C4×C5×D12C2211yescharacteristic
38C2×C3×#681C2211yescharacteristic, complemented
39C22×C3×#168C2211yescharacteristic
40#91322—24no—
41C2×#6663C2211yescharacteristic, complemented
42C2×#6663C2211yescharacteristic, complemented
43C2×#6663C2211yescharacteristic, complemented
44C2×#6659—24no—
45C2×#6659C2211yescharacteristic
46C2×#6659C2211yescharacteristic
47C2×#6659C2211yescharacteristic
48C2×#6659C2211yescharacteristic
49C2×#6659C2211yescharacteristic
50C2×#6659C2211yescharacteristic
51C3×C22⋊#168C2211yescharacteristic
52C3×C22⋊#168C2211yescharacteristic, complemented
53C3×C4⋊#168C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90975C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90967C2211yescharacteristic
61#90967C2211yescharacteristic
62#79495—51nomaximal, Hall
63C5×#546—31no—
64C2×#4097—31no—
65C22×#687—31no—
66D4×Dic10—31no—
67#65528—31no—
68#65507—31no—
69#65349—31no—
70#65343—31no—
71#65340—31no—
72#65339—31no—
73#65331—31no—
74#65329—31no—
75#65308—31no—
76#65307—31no—
77#65300D311yescharacteristic, complemented
78C23×C5×D3—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×Dic15—21no—
83C22×Dic15—21no—
84C2×Dic30—22no—
85C2×Dic30—22no—
86C2×Dic30—21no—
87C2×Dic30—21no—
88C2×Dic30—41no—
89C2×Dic30—41no—
90C2×Dic30C2311yescharacteristic
91C2×Dic30C2311yescharacteristic
92C2×Dic30C2311yescharacteristic
93C2×C5×#67—21no—
94C2×C5×#67—21no—
95C5×#235—22no—
96C5×#235—41no—
97C2×C5×D12—22no—
98C2×C5×D12—21no—
99C2×C5×D12—41no—
100C2×C5×D12C2311yescharacteristic
101C2×C5×D12C2311yescharacteristic
102C2×C4×C5×D3—21no—
103C2×C4×C5×D3—21no—
104C2×C5×Dic6C2311yescharacteristic
105C3×C5×C4⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C42×C5C2311yescharacteristic
109#6719—21no—
110#6719—21no—
111C4⋊Dic15—21no—
112C4⋊Dic15—21no—
113C4⋊Dic15C2311yescharacteristic
114#6712—21no—
115#6712—21no—
116#6712—21no—
117C4×Dic15—21no—
118C5×#217—21no—
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×C4⋊Dic3C2311yescharacteristic
124C5×Dic3⋊C4—21no—
125C3×#681—22no—
126C2×C3×#168—22no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6663—22no—
132#6663—22no—
133#6663—41no—
134#6659—22no—
135#6659—22no—
136#6659—22no—
137#6659—22no—
138#6659—41no—
139#6659D414yescomplemented
140C2×#909—51no—
141C22×#204—51no—
142#5550D511yescharacteristic
143D4×Dic6—51no—
144C3×#435—51no—
145#5134—51no—
146#5116—51no—
147#4845—51no—
148#4841—51no—
149#4739—51no—
150#4738—51no—
151#4733—51no—
152#4731—51no—
153#4715—51no—
154#4710—51no—
155C2×C5×#41—31no—
156C22×C5×D4—31no—
157C22×Dic10—31no—
158C22×Dic10—31no—
159C5×#124—31no—
160C5×#123—61no—
161C5×C22⋊Q8—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#120—61no—
165C4×C5×D4—31no—
166C4×C5×D4C2×D311yescharacteristic
167C2×C5×C22⋊C4—61no—
168#4097—64no—
169C2×#689—31no—
170C2×#689—31no—
171C2×#689—31no—
172D4×Dic5—61no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—31no—
177C2×#687—31no—
178C2×#687—31no—
179C2×#687—64no—
180#4070—31no—
181#4070—31no—
182C2×#681C2×D311yescharacteristic, complemented
183C22×#168C2×D311yescharacteristic
184#4034—61no—
185#4024—61no—
186#4024—61no—
187#4015—31no—
188C4×Dic10—31no—
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168C2×D311yescharacteristic
193C22⋊#168C2×D311yescharacteristic, complemented
194#3942—31no—
195#3942—31no—
196#3942—31no—
197#3939—31no—
198C4⋊#168C2×D311yescharacteristic, complemented
199#3935C2×D311yescharacteristic, complemented
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—42no—
206C22×C5×D3—42no—
207C22×C5×D3—81no—
208C3×C5×D4—22no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218C2×Dic15—21no—
219C2×Dic15—21no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—42no—
223C2×Dic15—42no—
224Dic30—21no—
225Dic30—21no—
226Dic30—21no—
227Dic30—21no—
228Dic30—21no—
229Dic30—42no—
230Dic30—42no—
231Dic30C2×D412yes—
232C5×#67—42no—
233C5×#67—81no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C5×D12—21no—
237C5×D12—21no—
238C5×D12—21no—
239C5×D12—42no—
240C5×D12C2×D412yes—
241C4×C5×D3—42no—
242C4×C5×D3—81no—
243C5×Dic6—21no—
244C5×Dic6—21no—
245C3×#168—21no—
246C3×#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×#235C2×D511yescharacteristic
250C22×D12C2×D511yescharacteristic
251C22×Dic6—51no—
252C22×Dic6—51no—
253C2×C3×M16—51no—
254C22×C3×C8—51no—
255C3×C4×D4C2×D511yescharacteristic
256#937—21no—
257D4×Dic3—101no—
258#930C2×D511yescharacteristic
259#924—51no—
260#924—51no—
261#924C2×D511yescharacteristic
262#909—104no—
263C2×Dic12—51no—
264C2×Dic12—51no—
265C2×Dic12—51no—
266C2×#204—51no—
267C2×#204—51no—
268C2×#204—51no—
269C2×#204—51no—
270C2×#204—51no—
271C2×#204—51no—
272C2×#204—104no—
273#894—21no—
274#888—101no—
275#884—21no—
276D3×C22⋊C4—21no—
277#878—101no—
278#878—101no—
279#875C2×D511yescharacteristic
280C4×D12C2×D511yescharacteristic
281#869—51no—
282C4×Dic6—51no—
283C3×C4⋊C8—51no—
284C3×C22⋊C8—51no—
285C3×C22⋊C8—51no—
286C3×#97—51no—
287#821—51no—
288#821—51no—
289#818—51no—
290#816—51no—
291#816—51no—
292#816—51no—
293#816—51no—
294C24×C5—61no—
295C5×#41—62no—
296C5×#41—121no—
297C2×C5×Q8—31no—
298C2×C5×D4—31no—
299C2×C5×D4—31no—
300C2×C5×D4—62no—
301C2×C5×D4—61no—
302C2×C5×D4—61no—
303C2×C5×D4—61no—
304C2×C5×D4—121no—
305C2×C5×D4D1211yescharacteristic
306C22×C4×C5—61no—
307C22×C4×C5—61no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—61no—
311C22×Dic5—61no—
312C2×Dic10—31no—
313C2×Dic10—31no—
314C2×Dic10—31no—
315C2×Dic10—62no—
316C2×Dic10—62no—
317C2×Dic10—61no—
318C2×Dic10—61no—
319C2×Dic10—121no—
320C2×Dic10—121no—
321C5×C4⋊C4—31no—
322C5×C4⋊C4—61no—
323C5×C4⋊C4D1211yescharacteristic
324C5×C22⋊C4—61no—
325C5×C22⋊C4—61no—
326C5×C22⋊C4—61no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C5×C22⋊C4D1211yescharacteristic
330C5×C22⋊C4D1211yescharacteristic
331C42×C5C22×D311yescharacteristic
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#689—62no—
335#689—62no—
336#689—121no—
337#687—34no—
338#687—62no—
339#687—62no—
340#687—62no—
341#687—62no—
342#687—121no—
343C4⋊Dic5—31no—
344C4⋊Dic5—61no—
345C4⋊Dic5—61no—
346#683—61no—
347#683—61no—
348#683—61no—
349C4×Dic5—61no—
350#681—22no—
351C2×#168—22no—
352C2×#168C22×D311yescharacteristic
353C2×#168C22×D311yescharacteristic
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546—31no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—51no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×C5×D3—22no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394Dic15—41no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C23×D3—21no—
398C2×C3×D4C22⋊D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C2×#67—21no—
402C2×#67—21no—
403C22×Dic3—101no—
404C22×Dic3—101no—
405#235—22no—
406#235—41no—
407C2×D12—22no—
408C2×D12—21no—
409C2×D12—41no—
410C2×D12C22×D511yescharacteristic
411C2×D12C22×D511yescharacteristic
412C2×C4×D3—21no—
413C2×C4×D3—21no—
414C2×Dic6—51no—
415C2×Dic6—51no—
416C2×Dic6—51no—
417C2×Dic6—102no—
418C2×Dic6—102no—
419C2×Dic6—101no—
420C2×Dic6—101no—
421C2×Dic6—201no—
422C2×Dic6—201no—
423C2×Dic6C22×D511yescharacteristic
424C3×M16—102no—
425C2×C3×C8—51no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C2×C3×C8—51no—
429C2×C3×C8—102no—
430C3×C4⋊C4C22⋊D511yescharacteristic
431C3×C22⋊C4C22⋊D511yescharacteristic
432C3×C22⋊C4C22⋊D511yescharacteristic
433C3×C42C22×D511yescharacteristic
434#217—21no—
435#217—101no—
436#217—101no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441C4⋊Dic3—51no—
442C4⋊Dic3—101no—
443C4⋊Dic3—101no—
444C4⋊Dic3C22×D511yescharacteristic
445Dic3⋊C4—21no—
446Dic3⋊C4—101no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449C4×Dic3—101no—
450Dic12—102no—
451Dic12—102no—
452Dic12—201no—
453#204—54no—
454#204—102no—
455#204—102no—
456#204—102no—
457#204—102no—
458#204—201no—
459C23×C5—61no—
460C23×C5—61no—
461C23×C5—122no—
462C23×C5—122no—
463C23×C5—241no—
464C23×C5C2×D1211yescharacteristic
465C23×C5C2×D1211yescharacteristic
466C5×Q8—61no—
467C5×Q8—61no—
468C5×D4—22no—
469C5×D4—32no—
470C5×D4—61no—
471C5×D4—61no—
472C5×D4—61no—
473C5×D4—122no—
474C5×D4—122no—
475C5×D4—241no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—122no—
483C2×C4×C5—241no—
484C2×C4×C5C2×D1211yescharacteristic
485C2×C4×C5C2×D1211yescharacteristic
486C2×C4×C5C2×D1211yescharacteristic
487C2×C4×C5C2×D1211yescharacteristic
488C2×C4×C5C23×D311yescharacteristic
489C2×Dic5—61no—
490C2×Dic5—61no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—122no—
494C2×Dic5—122no—
495Dic10—32no—
496Dic10—61no—
497Dic10—61no—
498Dic10—61no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10—122no—
503#168—21no—
504#168—21no—
505#168—21no—
506#168D3×D412yes—
507C2×#41—31no—
508C22×Q8—151no—
509C22×Q8—151no—
510C22×D4—31no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—51no—
523C22×C8—51no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—31no—
527#123—61no—
528C22⋊Q8—31no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—31no—
534#121—61no—
535#120—61no—
536C4×Q8—151no—
537C4×D4—31no—
538C4×D4—301no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—61no—
541#107—151no—
542C4⋊C8—51no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—51no—
550C22⋊C8—51no—
551#97—51no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C5×D3—42no—
558C5×D3—81no—
559C23×C3C2×C22⋊D511yescharacteristic
560C23×C3C2×C22⋊D511yescharacteristic
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—42no—
564C22×D3—42no—
565C22×D3—81no—
566C3×D4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4C2×C22⋊D511yescharacteristic
572C2×C3×C4C2×C22⋊D511yescharacteristic
573C2×C3×C4C2×C22⋊D511yescharacteristic
574C2×C3×C4C2×C22⋊D511yescharacteristic
575C2×C3×C4C23×D511yescharacteristic
576#67—42no—
577#67—81no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—101no—
584C2×Dic3—202no—
585C2×Dic3—202no—
586D12—21no—
587D12—21no—
588D12—21no—
589D12—42no—
590D12D4×D512yes—
591C4×D3—42no—
592C4×D3—81no—
593Dic6—21no—
594Dic6—21no—
595Dic6—52no—
596Dic6—101no—
597Dic6—101no—
598Dic6—101no—
599Dic6—101no—
600Dic6—101no—
601Dic6—202no—
602Dic6—202no—
603C3×C8—52no—
604C3×C8—101no—
605C3×C8—101no—
606C3×C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5—62no—
613C22×C5—121no—
614C22×C5—121no—
615C22×C5—121no—
616C22×C5—121no—
617C22×C5—121no—
618C22×C5—244no—
619C22×C5#90912yescomplemented
620C22×C5C22×D1211yescharacteristic
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—121no—
626C4×C5—121no—
627C4×C5C2×D3×D411yescharacteristic
628C4×C5#100911yescharacteristic
629Dic5—62no—
630Dic5—121no—
631Dic5—121no—
632Dic5—121no—
633C24—61no—
634#41—62no—
635#41—121no—
636C2×Q8—31no—
637C2×Q8—151no—
638C2×Q8—151no—
639C2×Q8—151no—
640C2×Q8—302no—
641C2×Q8—302no—
642C2×Q8—301no—
643C2×Q8—301no—
644C2×Q8—601no—
645C2×Q8—601no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—121no—
653C2×D4#120311yescharacteristic
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4C2×D3×D511yescharacteristic
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—51no—
673C2×C8—51no—
674C2×C8—102no—
675C4⋊C4—31no—
676C4⋊C4—61no—
677C4⋊C4—151no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4#120311yescharacteristic
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#120311yescharacteristic
692C22⋊C4#120311yescharacteristic
693C42—301no—
694C42C2×D3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3#409712yescomplemented
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—22no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—84no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4C2×D4×D511yescharacteristic
715C3×C4#414411yescharacteristic
716Dic3—41no—
717Dic3—41no—
718Dic3—102no—
719Dic3—201no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5—122no—
725C2×C5—241no—
726C2×C5D4×D1211yescharacteristic
727C2×C5C2×#90911yescharacteristic
728C2×C5#575111yescharacteristic
729C23—61no—
730C23—61no—
731C23—122no—
732C23—122no—
733C23—241no—
734C23C2×#120311yescharacteristic
735C23C2×#120311yescharacteristic
736Q8—61no—
737Q8—61no—
738Q8—152no—
739Q8—301no—
740Q8—301no—
741Q8—301no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8—602no—
746D4—22no—
747D4—32no—
748D4—61no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—122no—
761C2×C4—241no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—602no—
767C2×C4—602no—
768C2×C4C2×#120311yescharacteristic
769C2×C4C2×#120311yescharacteristic
770C2×C4C2×#120311yescharacteristic
771C2×C4C2×#120311yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—101no—
776C8—101no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#409711yescharacteristic
781C2×C3#6617011yescharacteristic
782D3—42no—
783D3—81no—
784C5#7949511yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—62no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—244no—
797C22#9132212yescomplemented
798C22C22×#120311yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—121no—
804C4—121no—
805C4—302no—
806C4—601no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202711yescharacteristic
811C3#1061523711yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—122no—
815C2—241no—
816C2C2×#9132211yescharacteristic
817C2D4×#120311yescharacteristic
818C2#1175530711yescharacteristic
subgroupG/H
centerC22C22×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5550C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×Dic30C2semidirect
3. C2×#91322C2semidirect
4. C22×#6659C2semidirect
5. C3×#65300C2semidirect
6. #11748565C2semidirect
7. #11748557C2semidirect
8. #11748553C2semidirect
9. #11748543C2semidirect
10. #11748534C2semidirect
11. #11748361C2semidirect
12. #11747098C2semidirect
13. #11747077C2semidirect
14. #11747056C2semidirect
15. #11746884C2semidirect
18. C22×Dic30C22semidirect
24. #91813C22semidirect
28. #91758C22semidirect
29. C4×Dic30C22semidirect
38. C2×C3×#681C22semidirect
41. C2×#6663C22semidirect
42. C2×#6663C22semidirect
43. C2×#6663C22semidirect
52. C3×C22⋊#168C22semidirect
53. C3×C4⋊#168C22semidirect
54. C3×#3935C22semidirect
55. #90988C22semidirect
56. #90975C22semidirect
57. #90975C22semidirect
58. #90975C22semidirect
59. #90973C22semidirect
77. #65300D3semidirect
139. #6659D4semidirect
182. C2×#681C2×D3semidirect
193. C22⋊#168C2×D3semidirect
198. C4⋊#168C2×D3semidirect
199. #3935C2×D3semidirect
376. C22×C3×C5#137semidirect
619. C22×C5#909semidirect
695. C3×C5#3266semidirect
701. C22×C3#4097semidirect
784. C5#79495semidirect
797. C22#91322semidirect
811. C3#10615237semidirect

Maximal subgroups

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

subgroupindex
D4×Dic302
C5×#55502
C2×#913222
C22×#66592
C3×#653002
#117485652
#117485572
#117485532
#117485432
#117485342
#117483612
#117470982
#117470772
#117470562
#117468842
#106152373
#794955