Finite Group Databasebeta

← #14453774

Subgroups — #14453774

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
2C3×#65884C211yesmaximal, characteristic
3C2×#91313C211yesmaximal, characteristic, complemented
4C22×#6657C211yesmaximal, characteristic, complemented
5C5×#5011C211yesmaximal, characteristic, complemented
6#11748564C211yesmaximal, characteristic, complemented
7#11748560C211yesmaximal, characteristic, complemented
8#11748549C211yesmaximal, characteristic, complemented
9#11748540C211yesmaximal, characteristic, complemented
10#11748531C211yesmaximal, characteristic, complemented
11#11748530C211yesmaximal, characteristic, complemented
12#11747084C211yesmaximal, characteristic, complemented
13#11747074C211yesmaximal, characteristic, complemented
14#11747062C211yesmaximal, characteristic, complemented
15#11747052C211yesmaximal, characteristic, complemented
16#10611226—31nomaximal, Hall
17C22×Dic30C2211yescharacteristic
18C22×Dic30C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
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
30C2×C5×#208C2211yescharacteristic, complemented
31C22×C5×C3⋊C8C2211yescharacteristic
32C3×#4083—21no—
33C3×#4076C2211yescharacteristic
34C3×#4070C2211yescharacteristic
35C3×#4040—21no—
36C3×#4030—21no—
37C3×D5×C22⋊C4—21no—
38C3×#4021C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C2×#6662C2211yescharacteristic, complemented
41C2×#6662C2211yescharacteristic, complemented
42C2×#6662C2211yescharacteristic, complemented
43#91313—24no—
44C2×#6657—24no—
45C2×#6657C2211yescharacteristic
46C2×#6657C2211yescharacteristic
47C2×#6657C2211yescharacteristic
48C2×#6657C2211yescharacteristic
49C2×#6657C2211yescharacteristic
50C2×#6657C2211yescharacteristic
51C5×#830C2211yescharacteristic
52C5×#830C2211yescharacteristic, complemented
53C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54C5×#803C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90974C2211yescharacteristic, complemented
58#90974C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90965C2211yescharacteristic
61#90965C2211yescharacteristic
62#83506—51nomaximal, Hall
63C2×#4055—31no—
64C22×#677—31no—
65#65884D311yescharacteristic
66D4×Dic10—31no—
67C5×#435—31no—
68#65423—31no—
69#65405—31no—
70#65134—31no—
71#65130—31no—
72#65028—31no—
73#65027—31no—
74#65022—31no—
75#65020—31no—
76#65004—31no—
77#64999—31no—
78C23×C3×D5—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×C3×C22⋊D5—21no—
94C2×C3×C22⋊D5—21no—
95C3×#709—22no—
96C3×#709—41no—
97C2×C3×D20—22no—
98C2×C3×D20—21no—
99C2×C3×D20—41no—
100C2×C3×D20C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×C4×D5—21no—
103C2×C3×C4×D5—21no—
104C2×C3×Dic10C2311yescharacteristic
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×#208—22no—
119C2×C5×C3⋊C8—22no—
120C2×C5×C3⋊C8C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C3×C22⋊Dic5—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×C4⋊Dic5C2311yescharacteristic
130C3×#683—21no—
131#6662—22no—
132#6662—22no—
133#6662—41no—
134#6657—22no—
135#6657—22no—
136#6657—22no—
137#6657—22no—
138#6657—41no—
139#6657D414yescomplemented
140C3×#546—51no—
141C2×#951—51no—
142C22×#214—51no—
143D4×Dic6—51no—
144#5239—51no—
145#5218—51no—
146#5060—51no—
147#5054—51no—
148#5051—51no—
149#5050—51no—
150#5042—51no—
151#5040—51no—
152#5019—51no—
153#5018—51no—
154#5011D511yescharacteristic, complemented
155C2×#709C2×D311yescharacteristic
156C22×D20C2×D311yescharacteristic
157C22×Dic10—31no—
158C22×Dic10—31no—
159C2×C5×M16—31no—
160C22×C5×C8—31no—
161C4×C5×D4C2×D311yescharacteristic
162#4083—21no—
163D4×Dic5—61no—
164#4076C2×D311yescharacteristic
165#4070—31no—
166#4070—31no—
167#4070C2×D311yescharacteristic
168#4055—64no—
169C2×Dic20—31no—
170C2×Dic20—31no—
171C2×Dic20—31no—
172C2×#677—31no—
173C2×#677—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—64no—
179#4040—21no—
180#4034—61no—
181#4030—21no—
182D5×C22⋊C4—21no—
183#4024—61no—
184#4024—61no—
185#4021C2×D311yescharacteristic
186C4×D20C2×D311yescharacteristic
187#4015—31no—
188C4×Dic10—31no—
189C5×C4⋊C8—31no—
190C5×C22⋊C8—31no—
191C5×C22⋊C8—31no—
192C5×#97—31no—
193#3953—31no—
194#3953—31no—
195#3950—31no—
196#3948—31no—
197#3948—31no—
198#3948—31no—
199#3948—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—42no—
206C22×C3×D5—42no—
207C22×C3×D5—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—
232C3×C22⋊D5—42no—
233C3×C22⋊D5—81no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C3×D20—21no—
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×D20C2×D412yes—
241C3×C4×D5—42no—
242C3×C4×D5—81no—
243C3×Dic10—21no—
244C3×Dic10—21no—
245C5×C3⋊C8—21no—
246C5×C3⋊C8—21no—
247C5×C3⋊C8—21no—
248C5×C3⋊C8C2×D412yes—
249C2×C3×#41—51no—
250C22×C3×D4—51no—
251C22×Dic6—51no—
252C22×Dic6—51no—
253C3×#124—51no—
254C3×#123—101no—
255C3×C22⋊Q8—51no—
256C3×#121—51no—
257C3×#121—101no—
258C3×#120—101no—
259C3×C4×D4—51no—
260C3×C4×D4C2×D511yescharacteristic
261C2×C3×C22⋊C4—101no—
262#951—104no—
263C2×#216—51no—
264C2×#216—51no—
265C2×#216—51no—
266D4×Dic3—101no—
267C2×#214—51no—
268C2×#214—51no—
269C2×#214—51no—
270C2×#214—51no—
271C2×#214—51no—
272C2×#214—51no—
273C2×#214—104no—
274#924—51no—
275#924—51no—
276C2×#208C2×D511yescharacteristic, complemented
277C22×C3⋊C8C2×D511yescharacteristic
278#888—101no—
279#878—101no—
280#878—101no—
281#869—51no—
282C4×Dic6—51no—
283#835—51no—
284#832—51no—
285#832—51no—
286#830C2×D511yescharacteristic
287#830C2×D511yescharacteristic, complemented
288#810—51no—
289#810—51no—
290#810—51no—
291#807—51no—
292C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
293#803C2×D511yescharacteristic, complemented
294C23×D5—21no—
295C2×C5×D4#6711yescharacteristic
296C22×C4×C5C22×D311yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C2×C22⋊D5—21no—
299C2×C22⋊D5—21no—
300C22×Dic5—61no—
301C22×Dic5—61no—
302#709—22no—
303#709—41no—
304C2×D20—22no—
305C2×D20—21no—
306C2×D20—41no—
307C2×D20C22×D311yescharacteristic
308C2×D20C22×D311yescharacteristic
309C2×C4×D5—21no—
310C2×C4×D5—21no—
311C2×Dic10—31no—
312C2×Dic10—31no—
313C2×Dic10—31no—
314C2×Dic10—62no—
315C2×Dic10—62no—
316C2×Dic10—61no—
317C2×Dic10—61no—
318C2×Dic10—121no—
319C2×Dic10—121no—
320C2×Dic10C22×D311yescharacteristic
321C5×M16—62no—
322C2×C5×C8—31no—
323C2×C5×C8—31no—
324C2×C5×C8—31no—
325C2×C5×C8—31no—
326C2×C5×C8—62no—
327C5×C4⋊C4#6711yescharacteristic
328C5×C22⋊C4#6711yescharacteristic
329C5×C22⋊C4#6711yescharacteristic
330C42×C5C22×D311yescharacteristic
331C22⋊Dic5—21no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#685—21no—
335#685—21no—
336#685—21no—
337#685—21no—
338C4⋊Dic5—31no—
339C4⋊Dic5—61no—
340C4⋊Dic5—61no—
341C4⋊Dic5C22×D311yescharacteristic
342#683—21no—
343#683—61no—
344#683—61no—
345#683—61no—
346C4×Dic5—61no—
347Dic20—62no—
348Dic20—62no—
349Dic20—121no—
350#677—34no—
351#677—62no—
352#677—62no—
353#677—62no—
354#677—62no—
355#677—121no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546—51no—
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—31no—
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×C3×D5—22no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C2×C3×D5—41no—
383C2×C3×D5—41no—
384C2×C3×D5—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—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C24×C3—101no—
398C3×#41—102no—
399C3×#41—201no—
400C2×C3×Q8—51no—
401C2×C3×D4—51no—
402C2×C3×D4—51no—
403C2×C3×D4—102no—
404C2×C3×D4—101no—
405C2×C3×D4—101no—
406C2×C3×D4—101no—
407C2×C3×D4—201no—
408C2×C3×D4D2011yescharacteristic
409C22×C3×C4—101no—
410C22×C3×C4—101no—
411C22×C3×C4C22×D511yescharacteristic
412C22×C3×C4C22×D511yescharacteristic
413C22×Dic3—101no—
414C22×Dic3—101no—
415C2×Dic6—51no—
416C2×Dic6—51no—
417C2×Dic6—51no—
418C2×Dic6—102no—
419C2×Dic6—102no—
420C2×Dic6—101no—
421C2×Dic6—101no—
422C2×Dic6—201no—
423C2×Dic6—201no—
424C3×C4⋊C4—51no—
425C3×C4⋊C4—101no—
426C3×C4⋊C4D2011yescharacteristic
427C3×C22⋊C4—101no—
428C3×C22⋊C4—101no—
429C3×C22⋊C4—101no—
430C3×C22⋊C4—101no—
431C3×C22⋊C4—101no—
432C3×C22⋊C4D2011yescharacteristic
433C3×C22⋊C4D2011yescharacteristic
434C3×C42C22×D511yescharacteristic
435#217—101no—
436#217—101no—
437#216—102no—
438#216—102no—
439#216—201no—
440#214—54no—
441#214—102no—
442#214—102no—
443#214—102no—
444#214—102no—
445#214—201no—
446C4⋊Dic3—51no—
447C4⋊Dic3—101no—
448C4⋊Dic3—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452C4×Dic3—101no—
453#208—22no—
454C2×C3⋊C8—22no—
455C2×C3⋊C8C22×D511yescharacteristic
456C2×C3⋊C8C22×D511yescharacteristic
457C2×C3⋊C8C22×D511yescharacteristic
458C2×C3⋊C8C22×D511yescharacteristic
459C23×C5C2×#6711yescharacteristic
460C23×C5C2×#6711yescharacteristic
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—42no—
464C22×D5—42no—
465C22×D5—81no—
466C5×D4—22no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5C2×#6711yescharacteristic
472C2×C4×C5C2×#6711yescharacteristic
473C2×C4×C5C2×#6711yescharacteristic
474C2×C4×C5C2×#6711yescharacteristic
475C2×C4×C5C23×D311yescharacteristic
476C22⋊D5—42no—
477C22⋊D5—81no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—122no—
485C2×Dic5—122no—
486D20—21no—
487D20—21no—
488D20—21no—
489D20—42no—
490D20D3×D412yes—
491C4×D5—42no—
492C4×D5—81no—
493Dic10—21no—
494Dic10—21no—
495Dic10—32no—
496Dic10—61no—
497Dic10—61no—
498Dic10—61no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10—122no—
503C5×C8—32no—
504C5×C8—61no—
505C5×C8—61no—
506C5×C8—61no—
507C2×#41—51no—
508C22×Q8—151no—
509C22×Q8—151no—
510C22×D4—51no—
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—31no—
523C22×C8—31no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—51no—
527#123—101no—
528C22⋊Q8—51no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—51no—
534#121—101no—
535#120—101no—
536C4×Q8—151no—
537C4×D4—51no—
538C4×D4—301no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—101no—
541#107—151no—
542C4⋊C8—31no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—31no—
550C22⋊C8—31no—
551#97—31no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557C3×D5—42no—
558C3×D5—81no—
559C23×C3—101no—
560C23×C3—101no—
561C23×C3—202no—
562C23×C3—202no—
563C23×C3—401no—
564C23×C3C2×D2011yescharacteristic
565C23×C3C2×D2011yescharacteristic
566C3×Q8—101no—
567C3×Q8—101no—
568C3×D4—22no—
569C3×D4—52no—
570C3×D4—101no—
571C3×D4—101no—
572C3×D4—101no—
573C3×D4—202no—
574C3×D4—202no—
575C3×D4—401no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—202no—
583C2×C3×C4—401no—
584C2×C3×C4C2×D2011yescharacteristic
585C2×C3×C4C2×D2011yescharacteristic
586C2×C3×C4C2×D2011yescharacteristic
587C2×C3×C4C2×D2011yescharacteristic
588C2×C3×C4C23×D511yescharacteristic
589C2×Dic3—101no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—202no—
594C2×Dic3—202no—
595Dic6—52no—
596Dic6—101no—
597Dic6—101no—
598Dic6—101no—
599Dic6—101no—
600Dic6—101no—
601Dic6—202no—
602Dic6—202no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8D4×D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5#95112yescomplemented
613C22×C5C22×#6711yescharacteristic
614C2×D5—22no—
615C2×D5—41no—
616C2×D5—41no—
617C2×D5—41no—
618C2×D5—41no—
619C2×D5—41no—
620C2×D5—84no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5C2×D3×D411yescharacteristic
626C4×C5#100411yescharacteristic
627Dic5—41no—
628Dic5—41no—
629Dic5—62no—
630Dic5—121no—
631Dic5—121no—
632Dic5—121no—
633C24—101no—
634#41—102no—
635#41—201no—
636C2×Q8—51no—
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—51no—
647C2×D4—51no—
648C2×D4—102no—
649C2×D4—101no—
650C2×D4—101no—
651C2×D4—101no—
652C2×D4—201no—
653C2×D4#120211yescharacteristic
654C22×C4—101no—
655C22×C4—101no—
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—62no—
670C2×C8—31no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—31no—
674C2×C8—62no—
675C4⋊C4—51no—
676C4⋊C4—101no—
677C4⋊C4—151no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4#120211yescharacteristic
684C22⋊C4—101no—
685C22⋊C4—101no—
686C22⋊C4—101no—
687C22⋊C4—101no—
688C22⋊C4—101no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#120211yescharacteristic
692C22⋊C4#120211yescharacteristic
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—102no—
702C22×C3—201no—
703C22×C3—201no—
704C22×C3—201no—
705C22×C3—201no—
706C22×C3—201no—
707C22×C3—404no—
708C22×C3#405512yescomplemented
709C22×C3C22×D2011yescharacteristic
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—201no—
715C3×C4—201no—
716C3×C4C2×D4×D511yescharacteristic
717C3×C4#414911yescharacteristic
718Dic3—102no—
719Dic3—201no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5D4×#6711yescharacteristic
725C2×C5C2×#95111yescharacteristic
726C2×C5#583611yescharacteristic
727D5—42no—
728D5—81no—
729C23—101no—
730C23—101no—
731C23—202no—
732C23—202no—
733C23—401no—
734C23C2×#120211yescharacteristic
735C23C2×#120211yescharacteristic
736Q8—101no—
737Q8—101no—
738Q8—152no—
739Q8—301no—
740Q8—301no—
741Q8—301no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8—602no—
746D4—22no—
747D4—52no—
748D4—101no—
749D4—101no—
750D4—101no—
751D4—202no—
752D4—202no—
753D4—401no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—202no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—301no—
765C2×C4—401no—
766C2×C4—602no—
767C2×C4—602no—
768C2×C4C2×#120211yescharacteristic
769C2×C4C2×#120211yescharacteristic
770C2×C4C2×#120211yescharacteristic
771C2×C4C2×#120211yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—32no—
774C8—61no—
775C8—61no—
776C8—61no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3—202no—
780C2×C3—401no—
781C2×C3D4×D2011yescharacteristic
782C2×C3C2×#405511yescharacteristic
783C2×C3#6608511yescharacteristic
784C5#8350611yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—102no—
791C22—201no—
792C22—201no—
793C22—201no—
794C22—201no—
795C22—201no—
796C22—404no—
797C22#9131312yescomplemented
798C22C22×#120211yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—201no—
804C4—201no—
805C4—302no—
806C4—601no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202611yescharacteristic
811C3#1061122611yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—202no—
815C2—401no—
816C2C2×#9131311yescharacteristic
817C2D4×#120211yescharacteristic
818C2#1175530911yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65884C2
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×#91313C2semidirect
4. C22×#6657C2semidirect
5. C5×#5011C2semidirect
6. #11748564C2semidirect
7. #11748560C2semidirect
8. #11748549C2semidirect
9. #11748540C2semidirect
10. #11748531C2semidirect
11. #11748530C2semidirect
12. #11747084C2semidirect
13. #11747074C2semidirect
14. #11747062C2semidirect
15. #11747052C2semidirect
18. C22×Dic30C22semidirect
24. #91813C22semidirect
28. #91758C22semidirect
29. C4×Dic30C22semidirect
30. C2×C5×#208C22semidirect
40. C2×#6662C22semidirect
41. C2×#6662C22semidirect
42. C2×#6662C22semidirect
52. C5×#830C22semidirect
53. C5×C4⋊(C3⋊C8)C22semidirect
54. C5×#803C22semidirect
55. #90990C22semidirect
56. #90974C22semidirect
57. #90974C22semidirect
58. #90974C22semidirect
59. #90971C22semidirect
139. #6657D4semidirect
154. #5011D5semidirect
276. C2×#208C2×D5semidirect
287. #830C2×D5semidirect
292. C4⋊(C3⋊C8)C2×D5semidirect
293. #803C2×D5semidirect
376. C22×C3×C5#137semidirect
612. C22×C5#951semidirect
695. C3×C5#3266semidirect
708. C22×C3#4055semidirect
784. C5#83506semidirect
797. C22#91313semidirect
811. C3#10611226semidirect

Maximal subgroups

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

subgroupindex
D4×Dic302
C3×#658842
C2×#913132
C22×#66572
C5×#50112
#117485642
#117485602
#117485492
#117485402
#117485312
#117485302
#117470842
#117470742
#117470622
#117470522
#106112263
#835065