Finite Group Databasebeta

← #14453740

Subgroups — #14453740

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
1C2×#91831C211yesmaximal, characteristic, complemented
2C5×Q8×#67C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#11754667C211yesmaximal, characteristic
5C3×#65516C211yesmaximal, characteristic, complemented
6#11749398C211yesmaximal, characteristic, complemented
7#11749325C211yesmaximal, characteristic, complemented
8#11749319C211yesmaximal, characteristic, complemented
9#11749302C211yesmaximal, characteristic, complemented
10#11749301C211yesmaximal, characteristic, complemented
11#11749235C211yesmaximal, characteristic, complemented
12#11749233C211yesmaximal, characteristic, complemented
13#11748566C211yesmaximal, characteristic, complemented
14#11748546C211yesmaximal, characteristic, complemented
15#11748496C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×#6817C2211yescharacteristic
19C2×C5×D3×Q8C2211yescharacteristic
20C2×D3×D20C2211yescharacteristic
21C2×#6718C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23#91831—24no—
24C2×#6717C2211yescharacteristic
25C2×#6717C2211yescharacteristic
26C2×#6710C2211yescharacteristic, complemented
27C5×#946—21no—
28C5×#946C2211yescharacteristic
29C5×Q8×Dic3C2211yescharacteristic, complemented
30C5×#944—21no—
31C5×#944C2211yescharacteristic, complemented
32C4×C5×#67—21no—
33C4×C5×#67C2211yescharacteristic
34C5×#924—21no—
35C5×#924C2211yescharacteristic, complemented
36C2×C3×#688C2211yescharacteristic
37C2×C3×#688C2211yescharacteristic
38C3×#4076C2211yescharacteristic
39#91577—21no—
40#91533—21no—
41D3×#688—24no—
42#91473—21no—
43#91428C2211yescharacteristic
44#91365C2211yescharacteristic
45#91364C2211yescharacteristic
46#91354—21no—
47C2×#6663C2211yescharacteristic, complemented
48C2×#6660C2211yescharacteristic
49C2×#6655C2211yescharacteristic
50C2×D3×#168C2211yescharacteristic
51C3×#3967C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×C22⋊#168C2211yescharacteristic, complemented
54#90989C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90972C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90964C2211yescharacteristic
60(C2×D3)⋊#168C2211yescharacteristic
61#90953C2211yescharacteristic, complemented
62#80061—51nomaximal, Hall
63C5×D4×Q8—31no—
64C2×#4088—31no—
65C22×#688—31no—
66#65884—31no—
67#65517—31no—
68#65516D311yescharacteristic, complemented
69#65375—31no—
70#65372—31no—
71#65340—31no—
72#65338—31no—
73#65336—31no—
74#65335—31no—
75#65317—31no—
76#65315—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—22no—
81C2×C3×C5×Q8—41no—
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87#6817—22no—
88#6817—41no—
89C2×D60C2311yescharacteristic
90C2×C4×D15—21no—
91C2×Dic30C2311yescharacteristic
92C2×C5×#67D411yescharacteristic
93C5×D3×Q8—22no—
94C5×D3×Q8—41no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C5×Dic6—21no—
98C2×C5×Dic6C2311yescharacteristic
99C2×C3×C22⋊D5—21no—
100C2×C3×D20C2311yescharacteristic
101C2×#1202—21no—
102C2×#1200—21no—
103D3×D20—22no—
104D3×D20—41no—
105#6718—22no—
106#6718—22no—
107#6717—22no—
108#6717D414yescomplemented
109#6710—22no—
110C2×C3⋊#168C2311yescharacteristic
111C2×C3⋊#168C2311yescharacteristic
112C5×#217—21no—
113C5×#217D411yescharacteristic
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4D411yescharacteristic
116C5×C4⋊Dic3—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C5×Dic3⋊C4—21no—
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4—21no—
122C5×Dic3⋊C4D411yescharacteristic
123C4×C5×Dic3—21no—
124C4×C5×Dic3C2311yescharacteristic
125C3×#688—22no—
126C3×#688—41no—
127C3×#685—21no—
128C3×C4⋊Dic5C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6668—21no—
132#6667—21no—
133(C2×D3)⋊Dic5—21no—
134#6665—21no—
135#6665—21no—
136#6663—41no—
137#6660—22no—
138#6655—22no—
139D3×#168—22no—
140Q8×#67D511yescharacteristic, complemented
141C2×#942—51no—
142C2×D3×SD16—51no—
143#5612—51no—
144C3×#448—51no—
145#5169—51no—
146#5167—51no—
147#5166—51no—
148#5042—51no—
149#4818—51no—
150#4817—51no—
151#4813—51no—
152#4809—51no—
153#4733—51no—
154#4728—51no—
155C22×C5×Q8—31no—
156C22×C5×Q8C2×D311yescharacteristic, complemented
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8—31no—
160C5×C4⋊Q8—61no—
161C5×C22⋊Q8—31no—
162C5×C22⋊Q8—31no—
163C5×C22⋊Q8—61no—
164C5×C22⋊Q8—61no—
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—64no—
177C2×#688C2×D311yescharacteristic
178C2×#688C2×D311yescharacteristic
179#4083—61no—
180#4076C2×D311yescharacteristic
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967C2×D311yescharacteristic, complemented
191#3967C2×D311yescharacteristic, complemented
192C22⋊#168—31no—
193C22⋊#168C2×D311yescharacteristic, complemented
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3939—31no—
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—
210C3×C5×Q8—21no—
211C3×C5×Q8—42no—
212C3×C5×Q8C2×D412yes—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—42no—
218C2×C3×C4×C5C2×D411yescharacteristic
219C2×C3×C4×C5C2411yescharacteristic
220#1220—42no—
221C2×Dic15—21no—
222D60—21no—
223D60C2×D412yes—
224C4×D15—42no—
225Dic30—21no—
226Dic30—21no—
227C5×#67—22no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3C2×D411yescharacteristic
231C2×C5×Dic3C2×D411yescharacteristic
232C2×C5×Dic3C2×D411yescharacteristic
233C4×C5×D3—21no—
234C4×C5×D3—21no—
235C4×C5×D3—42no—
236C5×Dic6—21no—
237C5×Dic6—21no—
238C5×Dic6—42no—
239C3×C22⋊D5—81no—
240C2×C3×Dic5—21no—
241C3×D20—21no—
242C3×D20—21no—
243#1202—42no—
244#1200—81no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C22×C3×Q8C2×D511yescharacteristic, complemented
250C2×D3×Q8C2×D511yescharacteristic
251C2×D3×D4—51no—
252C2×#235—51no—
253C2×C3×SD16—51no—
254C2×C3×SD16—51no—
255C3×#121—51no—
256#946—21no—
257#946C2×D511yescharacteristic
258Q8×Dic3C2×D511yescharacteristic, complemented
259#944—21no—
260#944C2×D511yescharacteristic, complemented
261C2×#216—51no—
262C2×#216—51no—
263#942—104no—
264C2×#215—51no—
265C2×#215—51no—
266#938—101no—
267#937—101no—
268#936—51no—
269C2×#214—51no—
270C4×#67—21no—
271C4×#67C2×D511yescharacteristic
272#924—21no—
273#924C2×D511yescharacteristic, complemented
274C2×#208—51no—
275D3×SD16—104no—
276C2×Dic12—51no—
277C2×#204—51no—
278C2×D3×C8—51no—
279#897—51no—
280#893—51no—
281#883—101no—
282D3×C22⋊C4—101no—
283C3×#103—51no—
284C3×#103—51no—
285C3×C22⋊C8—51no—
286#832—51no—
287#821—51no—
288(C2×D3)⋊C8—51no—
289#816—51no—
290#815—51no—
291Dic3⋊C8—51no—
292#810—51no—
293#807—51no—
294C23×D5—61no—
295C2×C5×Q8—21no—
296C2×C5×Q8—22no—
297C2×C5×Q8—31no—
298C2×C5×Q8—41no—
299C2×C5×Q8—61no—
300C2×C5×Q8—62no—
301C2×C5×Q8—121no—
302C2×C5×Q8C22×D311yescharacteristic
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4—31no—
305C22×C4×C5—21no—
306C22×C4×C5—31no—
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—31no—
322C5×C4⋊C4—31no—
323C5×C4⋊C4—61no—
324C5×C4⋊C4—61no—
325C5×C4⋊C4—61no—
326C5×C4⋊C4—61no—
327C5×C4⋊C4—61no—
328C5×C22⋊C4—31no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—61no—
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—41no—
341#688—62no—
342#688—62no—
343#688—62no—
344#685—21no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5C22×D311yescharacteristic
349#683—61no—
350#681—62no—
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—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—51no—
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—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—41no—
391C3×Dic5—41no—
392C5×Dic3—21no—
393C5×Dic3—21no—
394C5×Dic3—21no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C23×D3—101no—
398C2×C3×Q8—21no—
399C2×C3×Q8—22no—
400C2×C3×Q8—41no—
401C2×C3×Q8C22×D511yescharacteristic
402C2×C3×Q8C22×D511yescharacteristic
403C2×C3×D4—51no—
404C2×C3×D4—101no—
405C22×C3×C4—21no—
406C22×C3×C4C22×D511yescharacteristic
407C2×#67—101no—
408C2×#67—101no—
409C2×#67C22⋊D511yescharacteristic
410D3×Q8—22no—
411D3×Q8—41no—
412D3×D4—102no—
413D3×D4—201no—
414#235—102no—
415#235—201no—
416C2×D12—51no—
417C2×C4×D3—21no—
418C2×C4×D3—101no—
419C2×C4×D3—101no—
420C2×C4×D3C22×D511yescharacteristic
421C2×Dic6—21no—
422C2×Dic6—51no—
423C2×Dic6C22×D511yescharacteristic
424C3×SD16—102no—
425C3×SD16—201no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C3×C4⋊C4—51no—
429C3×C22⋊C4—101no—
430#217—21no—
431#217—101no—
432#217—101no—
433#217C22⋊D511yescharacteristic
434#216—102no—
435#216—102no—
436#215—54no—
437#215—102no—
438#214—102no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4C22⋊D511yescharacteristic
443C4⋊Dic3—21no—
444C4⋊Dic3—101no—
445C4⋊Dic3C22×D511yescharacteristic
446Dic3⋊C4—21no—
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4—21no—
450Dic3⋊C4C22⋊D511yescharacteristic
451C4×Dic3—21no—
452C4×Dic3C22×D511yescharacteristic
453#208—102no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456Dic12—201no—
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—21no—
469C5×Q8—42no—
470C5×Q8—61no—
471C5×Q8—61no—
472C5×Q8—122no—
473C5×Q8D3×D412yes—
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—42no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—61no—
486C2×C4×C5—61no—
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—21no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—31no—
509C22×Q8D3×D511yescharacteristic, complemented
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—31no—
525C4⋊Q8—61no—
526#124—151no—
527#123—301no—
528C22⋊Q8—31no—
529C22⋊Q8—31no—
530C22⋊Q8—61no—
531C22⋊Q8—61no—
532C22⋊Q8—151no—
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—151no—
542C4⋊C8—151no—
543#103—51no—
544#103—51no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—51no—
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×Q8—21no—
569C3×Q8—42no—
570C3×Q8D4×D512yes—
571C3×D4—101no—
572C3×D4—101no—
573C3×D4—401no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—42no—
579C2×C3×C4—101no—
580C2×C3×C4C2×C22⋊D511yescharacteristic
581C2×C3×C4C23×D511yescharacteristic
582#67—22no—
583#67—202no—
584#67—202no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—101no—
588C2×Dic3C2×C22⋊D511yescharacteristic
589C2×Dic3C2×C22⋊D511yescharacteristic
590C2×Dic3C2×C22⋊D511yescharacteristic
591D12—52no—
592D12—101no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—42no—
596C4×D3—202no—
597C4×D3—401no—
598Dic6—21no—
599Dic6—21no—
600Dic6—42no—
601Dic6—101no—
602Dic6—101no—
603C3×C8—101no—
604C3×C8—101no—
605C3⋊C8—52no—
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—22no—
623C4×C5—41no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5—121no—
628C4×C5—121no—
629C4×C5C2×D3×D411yescharacteristic
630C4×C5#100411yescharacteristic
631Dic5—41no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—31no—
639C2×Q8—41no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—121no—
643C2×Q8—151no—
644C2×Q8C2×D3×D511yescharacteristic
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—21no—
655C22×C4—31no—
656C22×C4—61no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—102no—
664SD16—154no—
665SD16—201no—
666SD16—302no—
667SD16—302no—
668SD16—302no—
669M16—302no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—31no—
676C4⋊C4—31no—
677C4⋊C4—51no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—61no—
683C4⋊C4—301no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—61no—
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—22no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—201no—
714C3×C4C2×D4×D511yescharacteristic
715C3×C4#414411yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—41no—
721Dic3—201no—
722C2×C5—41no—
723C2×C5—62no—
724C2×C5#559011yescharacteristic
725C2×C5#576211yescharacteristic
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—21no—
739Q8—42no—
740Q8—61no—
741Q8—61no—
742Q8—122no—
743Q8—301no—
744Q8—301no—
745Q8#679012yes—
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—42no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—101no—
767C2×C4—122no—
768C2×C4—301no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—101no—
774C8—101no—
775C8—152no—
776C8—301no—
777C2×C3—41no—
778C2×C3—401no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#408811yescharacteristic
781C2×C3#6617111yescharacteristic
782D3—22no—
783D3—202no—
784C5#8006111yescharacteristic, 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—22no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—201no—
808C4—601no—
809C4C2×#679011yescharacteristic
810C4#9204911yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—41no—
813C2—62no—
814C2—401no—
815C2—602no—
816C2D3×#408811yescharacteristic
817C2#1175509111yescharacteristic
818C2#1175544011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×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. C2×#91831C2semidirect
2. C5×Q8×#67C2semidirect
3. C2×D3×#688C2semidirect
5. C3×#65516C2semidirect
6. #11749398C2semidirect
7. #11749325C2semidirect
8. #11749319C2semidirect
9. #11749302C2semidirect
10. #11749301C2semidirect
11. #11749235C2semidirect
12. #11749233C2semidirect
13. #11748566C2semidirect
14. #11748546C2semidirect
15. #11748496C2semidirect
17. C22×C3×C5×Q8C22semidirect
21. C2×#6718C22semidirect
22. C2×#6718C22semidirect
26. C2×#6710C22semidirect
29. C5×Q8×Dic3C22semidirect
31. C5×#944C22semidirect
35. C5×#924C22semidirect
47. C2×#6663C22semidirect
51. C3×#3967C22semidirect
52. C3×#3967C22semidirect
53. C3×C22⋊#168C22semidirect
54. #90989C22semidirect
55. Dic3⋊#168C22semidirect
56. #90975C22semidirect
57. #90972C22semidirect
61. #90953C22semidirect
68. #65516D3semidirect
108. #6717D4semidirect
140. Q8×#67D5semidirect
156. C22×C5×Q8C2×D3semidirect
190. #3967C2×D3semidirect
191. #3967C2×D3semidirect
193. C22⋊#168C2×D3semidirect
249. C22×C3×Q8C2×D5semidirect
258. Q8×Dic3C2×D5semidirect
260. #944C2×D5semidirect
273. #924C2×D5semidirect
380. C2×C5×D3#137semidirect
509. C22×Q8D3×D5semidirect
695. C3×C5#3266semidirect
709. C2×D3#4088semidirect
784. C5#80061semidirect
811. C3#10615290semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C5×Q8×#672
C2×D3×#6882
#117546672
C3×#655162
#117493982
#117493252
#117493192
#117493022
#117493012
#117492352
#117492332
#117485662
#117485462
#117484962
#106152903
#800615