Finite Group Databasebeta

← #14453739

Subgroups — #14453739

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×Q8×#67C211yesmaximal, characteristic, complemented
2C2×C3×#4088C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#11754638C211yesmaximal, characteristic
5#11751328C211yesmaximal, characteristic, complemented
6#11749398C211yesmaximal, characteristic, complemented
7#11749326C211yesmaximal, characteristic, complemented
8#11749324C211yesmaximal, characteristic, complemented
9#11749304C211yesmaximal, characteristic, complemented
10#11749296C211yesmaximal, characteristic, complemented
11#11749234C211yesmaximal, characteristic, complemented
12#11749227C211yesmaximal, characteristic, complemented
13#11748528C211yesmaximal, characteristic, complemented
14#11748484C211yesmaximal, characteristic, complemented
15#11748456C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×#709C2211yescharacteristic
20C2×D3×D20C2211yescharacteristic
21C2×#6717C2211yescharacteristic
22C2×#6717C2211yescharacteristic
23#91819C2211yescharacteristic
24C5×#946—21no—
25C5×#946C2211yescharacteristic
26C5×Q8×Dic3C2211yescharacteristic, complemented
27C5×#944—21no—
28C5×#944C2211yescharacteristic, complemented
29C4×C5×#67—21no—
30C4×C5×#67C2211yescharacteristic
31C5×#924—21no—
32C5×#924C2211yescharacteristic, complemented
33C2×C3×#689C2211yescharacteristic, complemented
34C2×C3×#689C2211yescharacteristic, complemented
35C3×#4088—24no—
36C2×C3×#688C2211yescharacteristic
37C2×C3×#688C2211yescharacteristic
38C2×C3×#681C2211yescharacteristic, complemented
39#91577—21no—
40#91550—21no—
41D3×#688—24no—
42D5×(C2×D3)⋊C4—21no—
43Dic3×D20C2211yescharacteristic
44#91374C2211yescharacteristic
45#91369C2211yescharacteristic
46#91348—21no—
47C2×#6661C2211yescharacteristic, complemented
48C2×#6660C2211yescharacteristic
49C2×#6655C2211yescharacteristic
50C2×D3×#168C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90973C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90964C2211yescharacteristic
60(C2×D3)⋊#168C2211yescharacteristic
61#90953C2211yescharacteristic, complemented
62#83987—51nomaximal, Hall
63C5×D4×Q8—31no—
64C2×#4088D311yescharacteristic, complemented
65C22×#688—31no—
66#65884—31no—
67#65517—31no—
68#65516—31no—
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—
87C2×D60C2311yescharacteristic
88C2×C5×#67D411yescharacteristic
89C5×D3×Q8—22no—
90C5×D3×Q8—41no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C5×Dic6—21no—
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C3×#709—22no—
97C3×#709—41no—
98C2×C3×D20C2311yescharacteristic
99C2×C3×C4×D5—21no—
100C2×C3×Dic10C2311yescharacteristic
101C2×#1202—21no—
102C2×D5×Dic3—21no—
103D3×D20—22no—
104D3×D20—41no—
105#6717—22no—
106#6717—41no—
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111C5×#217—21no—
112C5×#217D411yescharacteristic
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4D411yescharacteristic
115C5×C4⋊Dic3—21no—
116C5×C4⋊Dic3C2311yescharacteristic
117C5×Dic3⋊C4—21no—
118C5×Dic3⋊C4—21no—
119C5×Dic3⋊C4—21no—
120C5×Dic3⋊C4—21no—
121C5×Dic3⋊C4D411yescharacteristic
122C4×C5×Dic3—21no—
123C4×C5×Dic3C2311yescharacteristic
124C3×#689—22no—
125C3×#689—22no—
126C3×#688—22no—
127C3×#688D414yescomplemented
128C3×#681—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6669—21no—
132#6667—21no—
133#6667—21no—
134(C2×D3)⋊Dic5—21no—
135#6665—21no—
136#6661—41no—
137#6660—22no—
138#6655—22no—
139D3×#168—22no—
140C2×C3×#137—51no—
141#5829—51no—
142Q8×#67D511yescharacteristic, complemented
143C2×D3×SD16—51no—
144#5239—51no—
145#5227—51no—
146#5190—51no—
147#5188—51no—
148#5186—51no—
149#5185—51no—
150#5169—51no—
151#5164—51no—
152#5162—51no—
153#5134—51no—
154#5127—51no—
155C22×C5×Q8—31no—
156C22×C5×Q8C2×D311yescharacteristic, complemented
157C2×#709C2×D311yescharacteristic
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×#689C2×D311yescharacteristic, complemented
170C2×#689C2×D311yescharacteristic, complemented
171#4088—24no—
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#4076—31no—
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#3967—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
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—81no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224C5×#67—22no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
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—42no—
236C3×C22⋊D5—42no—
237C2×C3×Dic5—21no—
238C3×D20—21no—
239C3×D20C2×D412yes—
240C3×C4×D5—42no—
241C3×Dic10—21no—
242C3×Dic10—21no—
243#1202—42no—
244D5×Dic3—81no—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3×#168—21no—
248C3×#168C2×D412yes—
249C2×C3×#41—51no—
250C22×C3×Q8C2×D511yescharacteristic, complemented
251C2×D3×Q8C2×D511yescharacteristic
252C2×D3×D4—51no—
253C3×#137—104no—
254C2×C3×Q16—51no—
255C2×C3×Q16—51no—
256C2×C3×SD16—51no—
257C2×C3×SD16—51no—
258C2×C3×M16—51no—
259#947—51no—
260#946—21no—
261#946—51no—
262#946C2×D511yescharacteristic
263Q8×Dic3C2×D511yescharacteristic, complemented
264#944—21no—
265#944C2×D511yescharacteristic, complemented
266C2×#216—51no—
267C2×#215—51no—
268C2×#215—51no—
269#939—101no—
270#937—101no—
271D4×Dic3—51no—
272C2×#214—51no—
273#930—51no—
274#929—101no—
275C4×#67—21no—
276C4×#67C2×D511yescharacteristic
277C2×(C2×D3)⋊C4—101no—
278#924—21no—
279#924C2×D511yescharacteristic, complemented
280D3×SD16—104no—
281C2×#204—51no—
282C2×D3×C8—51no—
283#835—51no—
284#835—51no—
285#835—51no—
286#832—51no—
287#830—51no—
288#821—51no—
289(C2×D3)⋊C8—51no—
290#818—51no—
291#816—51no—
292#815—51no—
293Dic3⋊C8—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—22no—
312#709—41no—
313C2×D20—31no—
314C2×D20—62no—
315C2×D20—61no—
316C2×D20—121no—
317C2×D20C22×D311yescharacteristic
318C2×C4×D5—21no—
319C2×C4×D5—61no—
320C2×Dic10C22×D311yescharacteristic
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—22no—
336#689—22no—
337#689—121no—
338#688—22no—
339#688—62no—
340#688—62no—
341#688—62no—
342#688—121no—
343#688#6714yescomplemented
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5—31no—
349#683—61no—
350#681—22no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—62no—
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—51no—
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—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—41no—
376C2×D15—41no—
377C2×D15—41no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C2×C5×D3#13712yescomplemented
381C2×C3×D5—22no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384D3×D5—84no—
385C3×C4×C5—21no—
386C3×C4×C5—22no—
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—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—21no—
401C2×C3×Q8—22no—
402C2×C3×Q8—41no—
403C2×C3×Q8—51no—
404C2×C3×Q8C22×D511yescharacteristic
405C2×C3×Q8C22×D511yescharacteristic
406C2×C3×D4—51no—
407C2×C3×D4—101no—
408C22×C3×C4—21no—
409C22×C3×C4—101no—
410C22×C3×C4C22×D511yescharacteristic
411C2×#67—101no—
412C2×#67—101no—
413C2×#67C22⋊D511yescharacteristic
414C22×Dic3—101no—
415D3×Q8—22no—
416D3×Q8—41no—
417D3×D4—102no—
418D3×D4—201no—
419C2×D12—51no—
420C2×C4×D3—21no—
421C2×C4×D3C22×D511yescharacteristic
422C2×Dic6—21no—
423C2×Dic6C22×D511yescharacteristic
424C3×Q16—102no—
425C3×Q16—102no—
426C3×SD16—54no—
427C3×SD16—102no—
428C3×M16—102no—
429C2×C3×C8—51no—
430C2×C3×C8—51no—
431#217—21no—
432#217—101no—
433#217C22⋊D511yescharacteristic
434#216—201no—
435#215—102no—
436#215—201no—
437#214—102no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4C22⋊D511yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3—51no—
446C4⋊Dic3C22×D511yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—21no—
449Dic3⋊C4—21no—
450Dic3⋊C4—21no—
451Dic3⋊C4—101no—
452Dic3⋊C4C22⋊D511yescharacteristic
453C4×Dic3—21no—
454C4×Dic3C22×D511yescharacteristic
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
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×Q8C2×#6712yes—
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—42no—
491C22⋊D5—241no—
492C2×Dic5—21no—
493C2×Dic5—61no—
494D20—21no—
495D20—61no—
496D20—61no—
497D20—122no—
498D20C2×#6712yes—
499C4×D5—42no—
500C4×D5—241no—
501Dic10—21no—
502Dic10—21no—
503#168—21no—
504#168—61no—
505#168—61no—
506#168C2×#6712yes—
507C2×#41—51no—
508C22×Q8—31no—
509C22×Q8D3×D511yescharacteristic, complemented
510C22×D4—151no—
511#137—104no—
512C2×Q16—51no—
513C2×Q16—51no—
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—51no—
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—151no—
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—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
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—81no—
557C3×D5—42no—
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×Q8—101no—
571C3×Q8—101no—
572C3×Q8D4×D512yes—
573C3×D4—52no—
574C3×D4—101no—
575C3×D4—202no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—42no—
581C2×C3×C4—101no—
582C2×C3×C4—202no—
583C2×C3×C4C2×C22⋊D511yescharacteristic
584C2×C3×C4C23×D511yescharacteristic
585#67—22no—
586#67—202no—
587#67—401no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—101no—
591C2×Dic3—401no—
592C2×Dic3C2×C22⋊D511yescharacteristic
593C2×Dic3C2×C22⋊D511yescharacteristic
594C2×Dic3C2×C22⋊D511yescharacteristic
595D12—101no—
596D12—101no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—42no—
600Dic6—21no—
601Dic6—21no—
602Dic6—42no—
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—22no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—121no—
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×C5#100411yescharacteristic
630C4×C5C22×#6711yescharacteristic
631Dic5—41no—
632Dic5—121no—
633C24—301no—
634#41—102no—
635#41—201no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—31no—
639C2×Q8—41no—
640C2×Q8—51no—
641C2×Q8—61no—
642C2×Q8—62no—
643C2×Q8—121no—
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—101no—
658C22×C4—301no—
659C22×C4C2×D3×D511yescharacteristic
660Q16—102no—
661Q16—102no—
662Q16—601no—
663SD16—54no—
664SD16—102no—
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—31no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—151no—
683C4⋊C4—301no—
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—301no—
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—102no—
700C22×C3—201no—
701C22×C3—201no—
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—201no—
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×C5D3×#13711yescharacteristic
725C2×C5#577811yescharacteristic
726C2×C5D4×#6711yescharacteristic
727D5—42no—
728D5—241no—
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—101no—
743Q8—101no—
744Q8—122no—
745Q8D5×#6712yes—
746D4—52no—
747D4—62no—
748D4—101no—
749D4—202no—
750D4—301no—
751D4—301no—
752D4—602no—
753D4—1201no—
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—202no—
769C2×C4—301no—
770C2×C4—1201no—
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—52no—
774C8—101no—
775C8—301no—
776C8—301no—
777C2×C3—41no—
778C2×C3—202no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#408811yescharacteristic
781C2×C3#6617111yescharacteristic
782D3—22no—
783D3—401no—
784C5#8398711yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—32no—
789C22—61no—
790C22—61no—
791C22—102no—
792C22—201no—
793C22—201no—
794C22—601no—
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×D5×#6711yescharacteristic
810C4#9204911yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—41no—
813C2—62no—
814C2—202no—
815C2—1201no—
816C2D3×#408811yescharacteristic
817C2#1175509211yescharacteristic
818C2#67×C22⋊D511yescharacteristic
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#11754638C2
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×Q8×#67C2semidirect
2. C2×C3×#4088C2semidirect
3. C2×D3×#688C2semidirect
5. #11751328C2semidirect
6. #11749398C2semidirect
7. #11749326C2semidirect
8. #11749324C2semidirect
9. #11749304C2semidirect
10. #11749296C2semidirect
11. #11749234C2semidirect
12. #11749227C2semidirect
13. #11748528C2semidirect
14. #11748484C2semidirect
15. #11748456C2semidirect
17. C22×C3×C5×Q8C22semidirect
26. C5×Q8×Dic3C22semidirect
28. C5×#944C22semidirect
32. C5×#924C22semidirect
33. C2×C3×#689C22semidirect
34. C2×C3×#689C22semidirect
38. C2×C3×#681C22semidirect
47. C2×#6661C22semidirect
51. #91119C22semidirect
52. #91119C22semidirect
53. #91114C22semidirect
54. #90988C22semidirect
55. Dic3⋊#168C22semidirect
56. #90973C22semidirect
57. #90970C22semidirect
61. #90953C22semidirect
64. C2×#4088D3semidirect
127. C3×#688D4semidirect
142. Q8×#67D5semidirect
156. C22×C5×Q8C2×D3semidirect
169. C2×#689C2×D3semidirect
170. C2×#689C2×D3semidirect
182. C2×#681C2×D3semidirect
250. C22×C3×Q8C2×D5semidirect
263. Q8×Dic3C2×D5semidirect
265. #944C2×D5semidirect
279. #924C2×D5semidirect
343. #688#67semidirect
380. C2×C5×D3#137semidirect
509. C22×Q8D3×D5semidirect
695. C3×C5#3266semidirect
709. C2×D3#4088semidirect
784. C5#83987semidirect
811. C3#10615290semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×#672
C2×C3×#40882
C2×D3×#6882
#117546382
#117513282
#117493982
#117493262
#117493242
#117493042
#117492962
#117492342
#117492272
#117485282
#117484842
#117484562
#106152903
#839875