Finite Group Databasebeta

← #14453746

Subgroups — #14453746

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×D12C211yesmaximal, characteristic, complemented
2C2×#91520C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4#11752749C211yesmaximal, characteristic
5#11751127C211yesmaximal, characteristic, complemented
6C3×#65317C211yesmaximal, characteristic, complemented
7#11749304C211yesmaximal, characteristic, complemented
8#11749278C211yesmaximal, characteristic, complemented
9#11747516C211yesmaximal, characteristic, complemented
10#11747483C211yesmaximal, characteristic, complemented
11#11747353C211yesmaximal, characteristic, complemented
12#11747323C211yesmaximal, characteristic, complemented
13#11747087C211yesmaximal, characteristic, complemented
14#11747080C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic, complemented
19C2×D3×D20C2211yescharacteristic
20C2×#6769C2211yescharacteristic
21C3×C4×C5×Q8C2211yescharacteristic, complemented
22C2×#6717C2211yescharacteristic
23C4×D60C2211yescharacteristic
24C5×#897—21no—
25C5×#897—21no—
26C5×#897C2211yescharacteristic
27C5×#897C2211yescharacteristic, complemented
28C4×C5×D12—21no—
29C4×C5×D12C2211yescharacteristic
30C5×#869—21no—
31C5×#869C2211yescharacteristic, complemented
32C2×C3×#689C2211yescharacteristic, complemented
33C2×C3×#688C2211yescharacteristic
34C3×#4021C2211yescharacteristic
35#91520—24no—
36D3×#688—24no—
37#91475—21no—
38#91473—21no—
39#91461—21no—
40#91456C2211yescharacteristic
41#91369C2211yescharacteristic
42#91356—21no—
43C2×#6661C2211yescharacteristic, complemented
44C2×#6661C2211yescharacteristic, complemented
45C2×#6660C2211yescharacteristic
46C2×#6660C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×#6655C2211yescharacteristic
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91093C2211yescharacteristic
53#91091C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80627—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#65338—31no—
73#65336—31no—
74#65335—31no—
75#65317D311yescharacteristic, complemented
76#65315—31no—
77#65300—31no—
78C22×D3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C5×D3×Q8—22no—
83C5×D3×Q8—22no—
84C5×D3×Q8—41no—
85C5×D3×Q8—41no—
86C2×C5×D12D411yescharacteristic
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3C2311yescharacteristic
90C2×C4×C5×D3C2311yescharacteristic
91C2×C5×Dic6—21no—
92C2×C5×Dic6—21no—
93C2×C5×Dic6C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×D20C2311yescharacteristic
96C2×C3×Dic10C2311yescharacteristic
97C2×#1203—21no—
98C2×#1202—21no—
99C2×#1201—21no—
100C2×#1200—21no—
101D3×D20—22no—
102D3×D20—41no—
103#6769—22no—
104#6769—41no—
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4C2311yescharacteristic
107C3×C42×C5—21no—
108C3×C42×C5C2311yescharacteristic
109#6717D414yescomplemented
110#6714—21no—
111C4⋊Dic15C2311yescharacteristic
112C2×C3⋊#168C2311yescharacteristic
113C2×C3⋊#168C2311yescharacteristic
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4D411yescharacteristic
117C5×(C2×D3)⋊C4D411yescharacteristic
118C5×C4⋊Dic3—21no—
119C5×C4⋊Dic3—21no—
120C5×C4⋊Dic3—21no—
121C5×C4⋊Dic3—21no—
122C5×C4⋊Dic3D411yescharacteristic
123C3×#689—22no—
124C3×#688—22no—
125C3×#685—21no—
126C3×#685—21no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6669—21no—
130(C2×D3)⋊Dic5—21no—
131#6665—21no—
132#6661—22no—
133#6661—41no—
134#6660—22no—
135#6660—22no—
136#6655—22no—
137#6655—41no—
138#6650—22no—
139D3×#168—22no—
140C2×#918—51no—
141C2×D3×SD16—51no—
142#5676—51no—
143Q8×D12D511yescharacteristic, complemented
144C3×#464—51no—
145#5186—51no—
146#5170—51no—
147#5060—51no—
148#5026—51no—
149#4841—51no—
150#4836—51no—
151#4813—51no—
152#4808—51no—
153#4780—51no—
154#4776—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—31no—
163C5×C22⋊Q8—61no—
164C5×C22⋊Q8—61no—
165C4×C5×Q8C2×D311yescharacteristic, complemented
166C4×C5×D4—31no—
167C4×C5×D4—61no—
168C2×#689—31no—
169C2×#689—31no—
170C2×#689C2×D311yescharacteristic, complemented
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#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021C2×D311yescharacteristic
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3967—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942C2×D311yescharacteristic, complemented
195#3941—31no—
196#3941C2×D311yescharacteristic
197#3939—31no—
198C4⋊#168C2×D311yescharacteristic, complemented
199#3935—31no—
200#3266—151noSylow
201C22×D15—21no—
202C22×C5×D3C2×D411yescharacteristic
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×Q8C2×D412yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2411yescharacteristic
215C2×Dic15—21no—
216D60—21no—
217D60C2×D412yes—
218C4×D15—81no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C2×D411yescharacteristic
222C2×C5×Dic3C2×D411yescharacteristic
223C5×D12—22no—
224C4×C5×D3—21no—
225C4×C5×D3—21no—
226C4×C5×D3—21no—
227C4×C5×D3—21no—
228C4×C5×D3—42no—
229C4×C5×D3—42no—
230C5×Dic6—21no—
231C5×Dic6—21no—
232C5×Dic6—21no—
233C5×Dic6—21no—
234C5×Dic6—42no—
235C5×Dic6—42no—
236C2×C3×Dic5—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241#1203—42no—
242#1202—42no—
243#1201—81no—
244#1200—42no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C2×#239—51no—
250C2×D3×Q8C2×D511yescharacteristic
251C2×D3×Q8C2×D511yescharacteristic, complemented
252C2×D3×D4—51no—
253C2×C3×Q16—51no—
254C2×C3×SD16—51no—
255C3×#124—51no—
256C3×C4×Q8C2×D511yescharacteristic, complemented
257#946—51no—
258C2×#216—51no—
259C2×#216—51no—
260C2×#215—51no—
261#938—51no—
262C2×#214—51no—
263C2×#214—51no—
264#918—104no—
265D3×SD16—104no—
266C2×#204—51no—
267C2×#204—51no—
268C2×ΓL(1,𝔽25)—51no—
269C2×D3×C8—51no—
270#897—21no—
271#897—21no—
272#897C2×D511yescharacteristic
273#897C2×D511yescharacteristic, complemented
274#884—101no—
275#883—101no—
276#882—101no—
277D3×C22⋊C4—101no—
278C4×D12—21no—
279C4×D12—51no—
280C4×D12C2×D511yescharacteristic
281#869—21no—
282#869C2×D511yescharacteristic, complemented
283C3×C4⋊C8—51no—
284C3×#103—51no—
285C3×#102—51no—
286#835—51no—
287(C2×D3)⋊C8—51no—
288(C2×D3)⋊C8—51no—
289#816—51no—
290#816—51no—
291#809—51no—
292#807—51no—
293#803—51no—
294C23×D5—61no—
295C2×C5×Q8—31no—
296C2×C5×Q8—31no—
297C2×C5×Q8—61no—
298C2×C5×Q8—61no—
299C2×C5×Q8—62no—
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—31no—
307C22×C4×C5—61no—
308C22×C4×C5—61no—
309C2×C22⋊D5—61no—
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×Dic10C22×D311yescharacteristic
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—31no—
329C5×C22⋊C4—31no—
330C5×C22⋊C4—61no—
331C5×C22⋊C4—61no—
332C42×C5—21no—
333C42×C5C22×D311yescharacteristic
334C22⋊Dic5—61no—
335#689—22no—
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—21no—
346#685—61no—
347#685—61no—
348C4⋊Dic5—31no—
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—51no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5C22×D411yescharacteristic
372C2×D15—22no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C5×D3—21no—
376C2×C5×D3—21no—
377C2×C5×D3—21no—
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—21no—
388C3×C4×C5—41no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391Dic15—41no—
392C3×Dic5—41no—
393C5×Dic3—21no—
394C5×Dic3—21no—
395C5×Dic3—41no—
396C5×Dic3—41no—
397C23×D3—101no—
398C2×C3×Q8—51no—
399C2×C3×Q8C22×D511yescharacteristic
400C2×C3×D4—51no—
401C2×#67—101no—
402C2×#67—101no—
403#239—102no—
404#239—201no—
405D3×Q8—22no—
406D3×Q8—22no—
407D3×Q8—41no—
408D3×Q8—41no—
409D3×D4—102no—
410D3×D4—201no—
411C2×D12—51no—
412C2×D12—101no—
413C2×D12C22⋊D511yescharacteristic
414C2×C4×D3—21no—
415C2×C4×D3—21no—
416C2×C4×D3—101no—
417C2×C4×D3—101no—
418C2×C4×D3C22×D511yescharacteristic
419C2×C4×D3C22×D511yescharacteristic
420C2×Dic6—21no—
421C2×Dic6—21no—
422C2×Dic6C22×D511yescharacteristic
423C2×Dic6C22×D511yescharacteristic
424C3×Q16—102no—
425C3×SD16—102no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4C22×D511yescharacteristic
430C3×C22⋊C4—101no—
431C3×C22⋊C4—101no—
432C3×C42—21no—
433C3×C42C22×D511yescharacteristic
434#217—101no—
435#216—102no—
436#216—201no—
437#215—54no—
438#214—102no—
439#214—201no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4C22⋊D511yescharacteristic
445(C2×D3)⋊C4C22⋊D511yescharacteristic
446C4⋊Dic3—21no—
447C4⋊Dic3—21no—
448C4⋊Dic3—21no—
449C4⋊Dic3—21no—
450C4⋊Dic3—51no—
451C4⋊Dic3C22⋊D511yescharacteristic
452Dic3⋊C4—101no—
453C2×C3⋊C8—51no—
454C2×C3⋊C8—51no—
455#204—102no—
456#204—102no—
457ΓL(1,𝔽25)—102no—
458D3×C8—102no—
459C23×C5—31no—
460C23×C5—31no—
461C22×D5—21no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—21no—
467C5×Q8—61no—
468C5×Q8—61no—
469C5×Q8—61no—
470C5×Q8—61no—
471C5×Q8—122no—
472C5×Q8—122no—
473C5×Q8D3×D412yes—
474C5×D4—62no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—31no—
478C2×C4×C5—31no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—61no—
485C2×C4×C5—122no—
486C2×C4×C5—122no—
487C2×C4×C5D3×D411yescharacteristic
488C2×C4×C5D3×D411yescharacteristic
489C2×C4×C5C23×D311yescharacteristic
490C22⋊D5—122no—
491C22⋊D5—241no—
492C2×Dic5—21no—
493C2×Dic5—61no—
494D20—21no—
495D20—21no—
496D20—32no—
497D20—61no—
498D20—122no—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—21no—
502Dic10—21no—
503#168—21no—
504#168—21no—
505#168—32no—
506#168—61no—
507C2×#41—151no—
508C22×Q8—31no—
509C22×Q8—31no—
510C22×D4—151no—
511#137—304no—
512C2×Q16—51no—
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—151no—
523C22×C8—151no—
524C4⋊Q8—31no—
525C4⋊Q8—61no—
526#124—51no—
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×Q8D3×D511yescharacteristic, complemented
537C4×D4—31no—
538C4×D4—61no—
539C4×D4—151no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—51no—
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×C5D4211yescharacteristic
553C2×C3×C5C2×#13711yescharacteristic
554C2×C3×C5#57711yescharacteristic
555D15—42no—
556C3×D5—81no—
557C5×D3—22no—
558C5×D3—41no—
559C23×C3—101no—
560C22×D3—101no—
561C22×D3—202no—
562C22×D3—202no—
563C22×D3—401no—
564C22×D3C2×C22⋊D511yescharacteristic
565C22×D3C2×C22⋊D511yescharacteristic
566C3×Q8—21no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8D4×D512yes—
570C3×D4—101no—
571C3×D4—101no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—101no—
575C2×C3×C4C2×C22⋊D511yescharacteristic
576C2×C3×C4C2×C22⋊D511yescharacteristic
577C2×C3×C4C23×D511yescharacteristic
578#67—202no—
579#67—401no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—101no—
583C2×Dic3C2×C22⋊D511yescharacteristic
584C2×Dic3C2×C22⋊D511yescharacteristic
585D12—22no—
586D12—52no—
587D12—101no—
588D12—202no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—42no—
594C4×D3—42no—
595C4×D3—202no—
596C4×D3—401no—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—42no—
602Dic6—42no—
603C3×C8—101no—
604C3×C8—101no—
605C3⋊C8—52no—
606C3⋊C8—101no—
607C22×C5—32no—
608C22×C5—61no—
609C22×C5—61no—
610C22×C5—61no—
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—21no—
623C4×C5—22no—
624C4×C5—41no—
625C4×C5—61no—
626C4×C5—61no—
627C4×C5—121no—
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—51no—
639C2×Q8—61no—
640C2×Q8—61no—
641C2×Q8—62no—
642C2×Q8—62no—
643C2×Q8—121no—
644C2×Q8—121no—
645C2×Q8C2×D3×D511yescharacteristic
646C2×D4—31no—
647C2×D4—51no—
648C2×D4—151no—
649C2×D4—301no—
650C2×D4—302no—
651C2×D4—301no—
652C2×D4—301no—
653C2×D4—601no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—301no—
659C22×C4—301no—
660Q16—102no—
661Q16—302no—
662Q16—601no—
663SD16—102no—
664SD16—154no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—151no—
682C4⋊C4—301no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—31no—
685C22⋊C4—31no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—101no—
689C22⋊C4—101no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—21no—
694C42C2×D3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—201no—
697C22×C3—201no—
698C22×C3—201no—
699C22×C3C22×C22⋊D511yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
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—21no—
713C3×C4—41no—
714C3×C4—201no—
715C3×C4C2×D4×D511yescharacteristic
716C3×C4#414411yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—41no—
721Dic3—201no—
722C2×C5—62no—
723C2×C5—121no—
724C2×C5#560911yescharacteristic
725C2×C5#577011yescharacteristic
726C2×C5D3×#13711yescharacteristic
727D5—81no—
728D5—122no—
729C23—31no—
730C23—31no—
731C23—101no—
732C23—301no—
733C23—602no—
734C23—602no—
735C23—1201no—
736Q8—21no—
737Q8—61no—
738Q8—61no—
739Q8—61no—
740Q8—61no—
741Q8—101no—
742Q8—101no—
743Q8—122no—
744Q8—122no—
745Q8#677712yes—
746D4—62no—
747D4—101no—
748D4—101no—
749D4—152no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—101no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—301no—
768C2×C4—602no—
769C2×C4—1201no—
770C2×C4D3×C22⋊D511yescharacteristic
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—101no—
774C8—101no—
775C8—152no—
776C8—301no—
777C2×C3—401no—
778C2×C3D4×C22⋊D511yescharacteristic
779C2×C3C2×#408811yescharacteristic
780C2×C3#6617111yescharacteristic
781D3—22no—
782D3—41no—
783D3—202no—
784C5#8062711yescharacteristic, complemented, Sylow
785C22—32no—
786C22—61no—
787C22—61no—
788C22—61no—
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—21no—
801C4—22no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—201no—
808C4—601no—
809C4C2×#677711yescharacteristic
810C4#9201811yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—62no—
813C2—121no—
814C2—401no—
815C2—602no—
816C2#1175465711yescharacteristic
817C2D3×#408811yescharacteristic
818C2#1175532611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752749C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C5×Q8×D12C2semidirect
2. C2×#91520C2semidirect
3. C2×D3×#688C2semidirect
5. #11751127C2semidirect
6. C3×#65317C2semidirect
7. #11749304C2semidirect
8. #11749278C2semidirect
9. #11747516C2semidirect
10. #11747483C2semidirect
11. #11747353C2semidirect
12. #11747323C2semidirect
13. #11747087C2semidirect
14. #11747080C2semidirect
15. #11746999C2semidirect
18. C2×C5×D3×Q8C22semidirect
21. C3×C4×C5×Q8C22semidirect
27. C5×#897C22semidirect
31. C5×#869C22semidirect
32. C2×C3×#689C22semidirect
43. C2×#6661C22semidirect
44. C2×#6661C22semidirect
49. C2×#6650C22semidirect
51. #91119C22semidirect
53. #91091C22semidirect
54. #91087C22semidirect
55. C3×#3942C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90973C22semidirect
59. #90973C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65317D3semidirect
109. #6717D4semidirect
143. Q8×D12D5semidirect
165. C4×C5×Q8C2×D3semidirect
170. C2×#689C2×D3semidirect
194. #3942C2×D3semidirect
198. C4⋊#168C2×D3semidirect
251. C2×D3×Q8C2×D5semidirect
256. C3×C4×Q8C2×D5semidirect
273. #897C2×D5semidirect
282. #869C2×D5semidirect
380. C2×C5×D3#137semidirect
536. C4×Q8D3×D5semidirect
695. C3×C5#3266semidirect
709. C2×D3#4088semidirect
784. C5#80627semidirect
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×D122
C2×#915202
C2×D3×#6882
#117527492
#117511272
C3×#653172
#117493042
#117492782
#117475162
#117474832
#117473532
#117473232
#117470872
#117470802
#117469992
#106152903
#806275