Finite Group Databasebeta

← #14453842

Subgroups — #14453842

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
1C5×#5632C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic, complemented
3#11754667C211yesmaximal, characteristic
4C2×#91321C211yesmaximal, characteristic, complemented
5#11751148C211yesmaximal, characteristic, complemented
6C3×#65338C211yesmaximal, characteristic, complemented
7#11749319C211yesmaximal, characteristic, complemented
8#11749302C211yesmaximal, characteristic, complemented
9#11749233C211yesmaximal, characteristic, complemented
10#11748536C211yesmaximal, characteristic, complemented
11#11748484C211yesmaximal, characteristic, complemented
12#11747483C211yesmaximal, characteristic, complemented
13#11747447C211yesmaximal, characteristic, complemented
14#11747373C211yesmaximal, characteristic, complemented
15#11747231C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic, complemented
20C2×D3×D20C2211yescharacteristic
21C3×C5×C22⋊Q8C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic
24C5×#944C2211yescharacteristic, complemented
25C4×C5×#67C2211yescharacteristic
26C5×#897C2211yescharacteristic
27C5×#896—21no—
28C5×#888—21no—
29C5×#887C2211yescharacteristic, complemented
30C5×#67⋊C4—21no—
31C5×#878—21no—
32C2×C3×#688C2211yescharacteristic
33C3×#4076C2211yescharacteristic
34C2×C3×#681C2211yescharacteristic, complemented
35#91577—21no—
36#91533—21no—
37D3×#688—24no—
38#91473—21no—
39#91428C2211yescharacteristic
40#91365C2211yescharacteristic
41#91364C2211yescharacteristic
42#91354—21no—
43#91321—24no—
44C2×#6663C2211yescharacteristic, complemented
45C2×#6663C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic
47C2×#6660C2211yescharacteristic
48C2×#6655C2211yescharacteristic
49C2×#6655C2211yescharacteristic
50C2×D3×#168C2211yescharacteristic
51#91114C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53#91093C2211yescharacteristic
54C3×#3967C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic
56C3×#3939C2211yescharacteristic, complemented
57Dic3⋊#168C2211yescharacteristic, complemented
58#90972C2211yescharacteristic, complemented
59#90972C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic
61#90953C2211yescharacteristic, complemented
62#80835—51nomaximal, Hall
63C5×D4×Q8—31no—
64C2×#4088—31no—
65C22×#688—31no—
66#65884—31no—
67#65517—31no—
68#65516—31no—
69#65375—31no—
70#65372—31no—
71#65340—31no—
72#65338D311yescharacteristic, complemented
73#65336—31no—
74#65335—31no—
75#65317—31no—
76#65315—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82#6817—22no—
83#6817—41no—
84C2×D60C2311yescharacteristic
85C2×C4×D15—21no—
86C2×Dic30C2311yescharacteristic
87C2×C5×#67D411yescharacteristic
88C22×C5×Dic3—21no—
89C5×D3×Q8—22no—
90C5×D3×Q8—41no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C5×Dic6—22no—
94C2×C5×Dic6—21no—
95C2×C5×Dic6—21no—
96C2×C5×Dic6—41no—
97C2×C5×Dic6C2311yescharacteristic
98C2×C5×Dic6C2311yescharacteristic
99C2×C3×C22⋊D5—21no—
100C2×C3×D20C2311yescharacteristic
101C2×#1202—21no—
102C2×#1200—21no—
103D3×D20—22no—
104D3×D20—41no—
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C5×C22⋊C4—21no—
108#6718—41no—
109#6717—22no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217D411yescharacteristic
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4D411yescharacteristic
115C5×C4⋊Dic3—21no—
116C5×Dic3⋊C4—21no—
117C5×Dic3⋊C4—21no—
118C5×Dic3⋊C4—21no—
119C5×Dic3⋊C4D411yescharacteristic
120C4×C5×Dic3—21no—
121C4×C5×Dic3C2311yescharacteristic
122C3×#688—22no—
123C3×#685—21no—
124C3×C4⋊Dic5C2311yescharacteristic
125C3×#681—22no—
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128#6668—21no—
129#6667—21no—
130(C2×D3)⋊Dic5—21no—
131#6665—21no—
132#6665—21no—
133#6663—22no—
134#6663—22no—
135#6660—22no—
136#6660D414yescomplemented
137#6655—22no—
138#6655—41no—
139D3×#168—22no—
140C2×D3×SD16—51no—
141C2×#909—51no—
142#5632D511yescharacteristic, complemented
143#5612—51no—
144C3×#468—51no—
145#5167—51no—
146#5127—51no—
147#5047—51no—
148#5040—51no—
149#4889—51no—
150#4887—51no—
151#4818—51no—
152#4809—51no—
153#4776—51no—
154#4767—51no—
155C22×C5×Q8—31no—
156C22×C5×Q8—31no—
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8—31no—
160C5×C4⋊Q8—61no—
161C5×C22⋊Q8—31no—
162C5×C22⋊Q8—61no—
163C5×C22⋊Q8—61no—
164C5×C22⋊Q8C2×D311yescharacteristic, complemented
165C4×C5×Q8—31no—
166C4×C5×D4—31no—
167C4×C5×D4—61no—
168C2×#689—31no—
169C2×#689—31no—
170C2×#689—31no—
171#4088—64no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—64no—
178C2×#688C2×D311yescharacteristic
179#4083—61no—
180#4076C2×D311yescharacteristic
181#4070—31no—
182C2×#681C2×D311yescharacteristic, complemented
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3967C2×D311yescharacteristic, complemented
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941C2×D311yescharacteristic
197#3939C2×D311yescharacteristic, complemented
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C22×D15—21no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C3×D5—21no—
205C2×D3×D5—42no—
206C2×D3×D5—42no—
207C2×D3×D5—81no—
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2411yescharacteristic
216#1220—42no—
217C2×Dic15—21no—
218D60—21no—
219D60C2×D412yes—
220C4×D15—42no—
221Dic30—21no—
222Dic30—21no—
223C5×#67—22no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—42no—
227C2×C5×Dic3C2×D411yescharacteristic
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C4×C5×D3—21no—
231C4×C5×D3—21no—
232C4×C5×D3—42no—
233C5×Dic6—21no—
234C5×Dic6—21no—
235C5×Dic6—21no—
236C5×Dic6—42no—
237C5×Dic6—42no—
238C5×Dic6C2×D412yes—
239C3×C22⋊D5—81no—
240C2×C3×Dic5—21no—
241C3×D20—21no—
242C3×D20—21no—
243#1202—42no—
244#1200—81no—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×D3×Q8C2×D511yescharacteristic
250C2×D3×D4—51no—
251C2×#235—51no—
252C22×Dic6C2×D511yescharacteristic, complemented
253C2×C3×SD16—51no—
254C2×C3×M16—51no—
255C3×C22⋊Q8C2×D511yescharacteristic, complemented
256C3×#121—51no—
257#944C2×D511yescharacteristic, complemented
258C2×#216—51no—
259C2×#215—51no—
260#938—101no—
261#937—101no—
262#936—51no—
263C2×#214—51no—
264C2×#214—51no—
265C4×#67C2×D511yescharacteristic
266D3×SD16—104no—
267#909—104no—
268C2×Dic12—51no—
269C2×Dic12—51no—
270C2×#204—51no—
271C2×#204—51no—
272C2×D3×C8—51no—
273#897—51no—
274#897C2×D511yescharacteristic
275#896—21no—
276#893—51no—
277#888—21no—
278#887C2×D511yescharacteristic, complemented
279#883—101no—
280#67⋊C4—21no—
281D3×C22⋊C4—101no—
282#878—21no—
283C3×#107—51no—
284C3×#103—51no—
285C3×#102—51no—
286#830—51no—
287(C2×D3)⋊C8—51no—
288#815—51no—
289Dic3⋊C8—51no—
290#810—51no—
291#810—51no—
292#810—51no—
293#809—51no—
294C23×D5—61no—
295C2×C5×Q8—31no—
296C2×C5×Q8—31no—
297C2×C5×Q8—61no—
298C2×C5×Q8—62no—
299C2×C5×Q8—61no—
300C2×C5×Q8—62no—
301C2×C5×Q8—121no—
302C2×C5×Q8—121no—
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4—31no—
305C22×C4×C5—31no—
306C22×C4×C5—61no—
307C22×C4×C5—61no—
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—21no—
310C2×C22⋊D5—61no—
311#709—62no—
312#709—121no—
313C2×D20—31no—
314C2×D20—62no—
315C2×D20—61no—
316C2×D20—121no—
317C2×D20C22×D311yescharacteristic
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×Dic10—31no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4—31no—
323C5×C4⋊C4—61no—
324C5×C4⋊C4—61no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4C22×D311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—31no—
331C5×C22⋊C4—61no—
332C42×C5—31no—
333C42×C5—61no—
334C22⋊Dic5—61no—
335#689—62no—
336#689—62no—
337#689—121no—
338#688—22no—
339#688—34no—
340#688—62no—
341#688—62no—
342#688—62no—
343#688—121no—
344#685—21no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5C22×D311yescharacteristic
349#683—61no—
350#681—22no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—62no—
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—31no—
359#546—151no—
360#497—151no—
361#468—51no—
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—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5C22×D411yescharacteristic
375C2×D15—22no—
376C2×D15—41no—
377C2×D15—41no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C2×C5×D3#13712yescomplemented
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384D3×D5—84no—
385C3×C4×C5—21no—
386C3×C4×C5—41no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—41no—
391C3×Dic5—41no—
392C5×Dic3—21no—
393C5×Dic3—22no—
394C5×Dic3—21no—
395C5×Dic3—21no—
396C5×Dic3—41no—
397C23×D3—101no—
398C2×C3×Q8C22×D511yescharacteristic
399C2×C3×D4—51no—
400C2×C3×D4—101no—
401C22×C3×C4C22×D511yescharacteristic
402C2×#67—101no—
403C2×#67—101no—
404C2×#67C22⋊D511yescharacteristic
405C22×Dic3—21no—
406D3×Q8—22no—
407D3×Q8—41no—
408D3×D4—102no—
409D3×D4—201no—
410#235—102no—
411#235—201no—
412C2×D12—51no—
413C2×C4×D3—21no—
414C2×C4×D3—101no—
415C2×C4×D3—101no—
416C2×C4×D3C22×D511yescharacteristic
417C2×Dic6—22no—
418C2×Dic6—21no—
419C2×Dic6—21no—
420C2×Dic6—41no—
421C2×Dic6—51no—
422C2×Dic6C22×D511yescharacteristic
423C2×Dic6C22×D511yescharacteristic
424C3×SD16—102no—
425C3×M16—102no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4—51no—
430C3×C4⋊C4C22×D511yescharacteristic
431C3×C22⋊C4—21no—
432C3×C22⋊C4—101no—
433#217—101no—
434#217—101no—
435#217C22⋊D511yescharacteristic
436#216—201no—
437#215—102no—
438#214—102no—
439#214—201no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4C22⋊D511yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3—101no—
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4C22⋊D511yescharacteristic
450C4×Dic3—21no—
451C4×Dic3C22×D511yescharacteristic
452C2×C3⋊C8—51no—
453C2×C3⋊C8—51no—
454Dic12—102no—
455Dic12—102no—
456#204—54no—
457#204—102no—
458D3×C8—102no—
459C23×C5—31no—
460C23×C5D3×D411yescharacteristic
461C22×D5—21no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—32no—
469C5×Q8—61no—
470C5×Q8—61no—
471C5×Q8—61no—
472C5×Q8—122no—
473C5×Q8—122no—
474C5×D4—62no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—31no—
480C2×C4×C5—31no—
481C2×C4×C5—31no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—122no—
487C2×C4×C5—122no—
488C2×C4×C5D3×D411yescharacteristic
489C2×C4×C5C23×D311yescharacteristic
490C22⋊D5—81no—
491C22⋊D5—122no—
492C2×Dic5—21no—
493C2×Dic5—61no—
494D20—21no—
495D20—21no—
496D20—32no—
497D20—61no—
498D20—122no—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—61no—
502Dic10—61no—
503#168—21no—
504#168—61no—
505#168—61no—
506#168D3×D412yes—
507C2×#41—151no—
508C22×Q8—31no—
509C22×Q8—31no—
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—51no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—51no—
523C22×C8—151no—
524C4⋊Q8—31no—
525C4⋊Q8—61no—
526#124—151no—
527#123—301no—
528C22⋊Q8—31no—
529C22⋊Q8—61no—
530C22⋊Q8—61no—
531C22⋊Q8—151no—
532C22⋊Q8D3×D511yescharacteristic, complemented
533#121—51no—
534#121—301no—
535#120—301no—
536C4×Q8—31no—
537C4×D4—31no—
538C4×D4—61no—
539C4×D4—151no—
540C2×C22⋊C4—301no—
541#107—51no—
542C4⋊C8—151no—
543#103—51no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—51no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—41no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556D15—42no—
557C3×D5—81no—
558C5×D3—22no—
559C23×C3—101no—
560C23×C3C2×C22⋊D511yescharacteristic
561C22×D3—101no—
562C22×D3—202no—
563C22×D3—202no—
564C22×D3—401no—
565C22×D3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×D4—101no—
569C3×D4—101no—
570C3×D4—401no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—101no—
576C2×C3×C4C2×C22⋊D511yescharacteristic
577C2×C3×C4C23×D511yescharacteristic
578#67—22no—
579#67—202no—
580#67—202no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—42no—
584C2×Dic3—101no—
585C2×Dic3C2×C22⋊D511yescharacteristic
586C2×Dic3C2×C22⋊D511yescharacteristic
587C2×Dic3C2×C22⋊D511yescharacteristic
588D12—52no—
589D12—101no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—42no—
593C4×D3—202no—
594C4×D3—401no—
595Dic6—21no—
596Dic6—21no—
597Dic6—21no—
598Dic6—42no—
599Dic6—42no—
600Dic6—101no—
601Dic6—101no—
602Dic6D4×D512yes—
603C3×C8—52no—
604C3×C8—101no—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—32no—
611C22×C5—61no—
612C22×C5—61no—
613C22×C5C2×D3×D411yescharacteristic
614C2×D5—41no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—62no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—41no—
623C4×C5—41no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5—62no—
628C4×C5—121no—
629C4×C5C2×D3×D411yescharacteristic
630C4×C5#100911yescharacteristic
631Dic5—41no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—31no—
637C2×Q8—31no—
638C2×Q8—61no—
639C2×Q8—62no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—121no—
643C2×Q8—121no—
644C2×Q8—151no—
645C2×Q8C2×D3×D511yescharacteristic
646C2×D4—31no—
647C2×D4—51no—
648C2×D4—101no—
649C2×D4—151no—
650C2×D4—301no—
651C2×D4—302no—
652C2×D4—301no—
653C2×D4—601no—
654C22×C4—31no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—102no—
664SD16—154no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—102no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—31no—
677C4⋊C4—51no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—301no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—31no—
686C22⋊C4—31no—
687C22⋊C4—61no—
688C22⋊C4—101no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—31no—
694C42—61no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—201no—
700C22×C3—201no—
701C22×C3—201no—
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—102no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—404no—
709C2×D3#408812yescomplemented
710C3×C4—21no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—201no—
714C3×C4C2×D4×D511yescharacteristic
715C3×C4#414411yescharacteristic
716Dic3—22no—
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—201no—
722C2×C5—41no—
723C2×C5—62no—
724C2×C5#560911yescharacteristic
725C2×C5#577511yescharacteristic
726C2×C5D3×#13711yescharacteristic
727D5—81no—
728D5—122no—
729C23—31no—
730C23—101no—
731C23—301no—
732C23—602no—
733C23—602no—
734C23—1201no—
735C23D3×C22⋊D511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—32no—
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—122no—
743Q8—122no—
744Q8—301no—
745Q8—301no—
746D4—62no—
747D4—101no—
748D4—101no—
749D4—152no—
750D4—301no—
751D4—401no—
752D4—602no—
753D4—602no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—101no—
766C2×C4—122no—
767C2×C4—122no—
768C2×C4—301no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—301no—
776C8—301no—
777C2×C3—41no—
778C2×C3—401no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#408811yescharacteristic
781C2×C3#6617111yescharacteristic
782D3—22no—
783D3—202no—
784C5#8083511yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—32no—
789C22—61no—
790C22—61no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—302no—
795C22—601no—
796C22—601no—
797C22—1204no—
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—61no—
803C4—62no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—201no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202711yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—41no—
813C2—62no—
814C2—401no—
815C2—602no—
816C2#1175505311yescharacteristic
817C2D3×#408811yescharacteristic
818C2#1175532411yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11754667C2
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3266
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×#5632C2semidirect
2. C2×D3×#688C2semidirect
4. C2×#91321C2semidirect
5. #11751148C2semidirect
6. C3×#65338C2semidirect
7. #11749319C2semidirect
8. #11749302C2semidirect
9. #11749233C2semidirect
10. #11748536C2semidirect
11. #11748484C2semidirect
12. #11747483C2semidirect
13. #11747447C2semidirect
14. #11747373C2semidirect
15. #11747231C2semidirect
19. C22×C5×Dic6C22semidirect
21. C3×C5×C22⋊Q8C22semidirect
22. C2×#6718C22semidirect
24. C5×#944C22semidirect
29. C5×#887C22semidirect
34. C2×C3×#681C22semidirect
44. C2×#6663C22semidirect
45. C2×#6663C22semidirect
51. #91114C22semidirect
52. #91094C22semidirect
54. C3×#3967C22semidirect
56. C3×#3939C22semidirect
57. Dic3⋊#168C22semidirect
58. #90972C22semidirect
59. #90972C22semidirect
61. #90953C22semidirect
72. #65338D3semidirect
136. #6660D4semidirect
142. #5632D5semidirect
164. C5×C22⋊Q8C2×D3semidirect
182. C2×#681C2×D3semidirect
191. #3967C2×D3semidirect
197. #3939C2×D3semidirect
252. C22×Dic6C2×D5semidirect
255. C3×C22⋊Q8C2×D5semidirect
257. #944C2×D5semidirect
278. #887C2×D5semidirect
380. C2×C5×D3#137semidirect
532. C22⋊Q8D3×D5semidirect
695. C3×C5#3266semidirect
709. C2×D3#4088semidirect
784. C5#80835semidirect
811. C3#10615290semidirect

Maximal subgroups

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

subgroupindex
C5×#56322
C2×D3×#6882
#117546672
C2×#913212
#117511482
C3×#653382
#117493192
#117493022
#117492332
#117485362
#117484842
#117474832
#117474472
#117473732
#117472312
#106152903
#808355