Finite Group Databasebeta

← #14453773

Subgroups — #14453773

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
1#11756309C211yesmaximal, characteristic
2C3×D4×Dic10C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic, complemented
4C22×#6658C211yesmaximal, characteristic, complemented
5C5×#5011C211yesmaximal, characteristic, complemented
6#11748560C211yesmaximal, characteristic, complemented
7#11748556C211yesmaximal, characteristic, complemented
8#11748552C211yesmaximal, characteristic, complemented
9#11748551C211yesmaximal, characteristic, complemented
10#11748542C211yesmaximal, characteristic, complemented
11#11748532C211yesmaximal, characteristic, complemented
12#11747085C211yesmaximal, characteristic, complemented
13#11747076C211yesmaximal, characteristic, complemented
14#11747065C211yesmaximal, characteristic, complemented
15#11747054C211yesmaximal, characteristic, complemented
16#10611226—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22#91826—21no—
23#91819C2211yescharacteristic
24#91813C2211yescharacteristic
25#91783—21no—
26#91773—21no—
27C22⋊C4×D15—21no—
28#91764C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C2×C5×#208C2211yescharacteristic, complemented
31C22×C5×C3⋊C8C2211yescharacteristic
32C3×D4×Dic5—21no—
33C3×#4070C2211yescharacteristic
34C3×#4070C2211yescharacteristic, complemented
35C3×#4034—21no—
36C3×#4024—21no—
37C3×#4024—21no—
38C3×#4015C2211yescharacteristic, complemented
39C3×C4×Dic10C2211yescharacteristic, complemented
40C2×#6662C2211yescharacteristic, complemented
41C2×#6662C2211yescharacteristic, complemented
42C2×#6662C2211yescharacteristic, complemented
43#91315—24no—
44C2×#6658—24no—
45C2×#6658C2211yescharacteristic
46C2×#6658C2211yescharacteristic
47C2×#6658C2211yescharacteristic
48C2×#6658C2211yescharacteristic
49C2×#6658C2211yescharacteristic
50C2×#6658C2211yescharacteristic
51C5×#830C2211yescharacteristic
52C5×#830C2211yescharacteristic, complemented
53C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54C5×#803C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90971C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90968C2211yescharacteristic
61#90968C2211yescharacteristic
62#83559—51nomaximal, Hall
63C2×#4055—31no—
64C22×#677—31no—
65#65884—31no—
66D4×Dic10D311yescharacteristic, complemented
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×D15—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84#6817—22no—
85#6817—41no—
86C2×D60—22no—
87C2×D60—21no—
88C2×D60—41no—
89C2×D60C2311yescharacteristic
90C2×D60C2311yescharacteristic
91C2×C4×D15—21no—
92C2×C4×D15—21no—
93C2×Dic30C2311yescharacteristic
94C22×C3×Dic5—21no—
95C22×C3×Dic5—21no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10—22no—
98C2×C3×Dic10—21no—
99C2×C3×Dic10—21no—
100C2×C3×Dic10—41no—
101C2×C3×Dic10—41no—
102C2×C3×Dic10C2311yescharacteristic
103C2×C3×Dic10C2311yescharacteristic
104C2×C3×Dic10C2311yescharacteristic
105C3×C5×C4⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C5×C22⋊C4D411yescharacteristic
108C3×C42×C5C2311yescharacteristic
109#6719—21no—
110#6714—21no—
111#6714—21no—
112#6714—21no—
113#6714—21no—
114C4⋊Dic15C2311yescharacteristic
115#6712—21no—
116C5×#208—22no—
117C2×C5×C3⋊C8—22no—
118C2×C5×C3⋊C8C2311yescharacteristic
119C2×C5×C3⋊C8C2311yescharacteristic
120C2×C5×C3⋊C8C2311yescharacteristic
121C2×C5×C3⋊C8C2311yescharacteristic
122C3×C22⋊Dic5—21no—
123C3×C22⋊Dic5—21no—
124C3×C4⋊Dic5—21no—
125C3×C4⋊Dic5—21no—
126C3×C4⋊Dic5C2311yescharacteristic
127C3×#683—21no—
128C3×#683—21no—
129C3×#683—21no—
130C3×C4×Dic5—21no—
131#6662—22no—
132#6662—22no—
133#6662—41no—
134#6658—22no—
135#6658—22no—
136#6658—22no—
137#6658—22no—
138#6658—41no—
139#6658D414yescomplemented
140C3×D4×Q8—51no—
141C2×#942—51no—
142C22×#215—51no—
143#5550—51no—
144#5228—51no—
145#5227—51no—
146#5086—51no—
147#5083—51no—
148#5051—51no—
149#5049—51no—
150#5047—51no—
151#5046—51no—
152#5028—51no—
153#5026—51no—
154#5011D511yescharacteristic, complemented
155C2×#709—31no—
156C22×D20—31no—
157C22×Dic10C2×D311yescharacteristic
158C22×Dic10C2×D311yescharacteristic, complemented
159C2×C5×M16—31no—
160C22×C5×C8—31no—
161C4×C5×D4C2×D311yescharacteristic
162#4083—61no—
163D4×Dic5—21no—
164#4076—31no—
165#4070—31no—
166#4070C2×D311yescharacteristic
167#4070C2×D311yescharacteristic, complemented
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—61no—
180#4034—21no—
181#4030—61no—
182D5×C22⋊C4—61no—
183#4024—21no—
184#4024—21no—
185#4021—31no—
186C4×D20—31no—
187#4015C2×D311yescharacteristic, complemented
188C4×Dic10C2×D311yescharacteristic, complemented
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×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—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
218#1220—42no—
219#1220—81no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224D60—21no—
225D60—42no—
226D60C2×D412yes—
227C4×D15—42no—
228C4×D15—81no—
229Dic30—21no—
230Dic30—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—42no—
236C2×C3×Dic5—42no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241C3×Dic10—21no—
242C3×Dic10—42no—
243C3×Dic10—42no—
244C3×Dic10C2×D412yes—
245C5×C3⋊C8—21no—
246C5×C3⋊C8—21no—
247C5×C3⋊C8—21no—
248C5×C3⋊C8C2×D412yes—
249C22×C3×Q8—51no—
250C22×C3×Q8—51no—
251C2×#235—51no—
252C22×D12—51no—
253C3×C4⋊Q8—51no—
254C3×C4⋊Q8—101no—
255C3×C22⋊Q8—51no—
256C3×C22⋊Q8—51no—
257C3×C22⋊Q8—101no—
258C3×C22⋊Q8—101no—
259C3×C4×Q8—51no—
260C3×C4×D4—101no—
261C3×C4×D4C2×D511yescharacteristic
262C2×#216—51no—
263C2×#216—51no—
264C2×#216—51no—
265#942—104no—
266C2×#215—51no—
267C2×#215—51no—
268C2×#215—51no—
269C2×#215—51no—
270C2×#215—51no—
271C2×#215—51no—
272C2×#215—104no—
273#937—101no—
274#930—51no—
275#924—51no—
276C2×#208C2×D511yescharacteristic, complemented
277C22×C3⋊C8C2×D511yescharacteristic
278#894—101no—
279#884—101no—
280D3×C22⋊C4—101no—
281#875—51no—
282C4×D12—51no—
283#835—51no—
284#835—51no—
285#835—51no—
286#830C2×D511yescharacteristic
287#830C2×D511yescharacteristic, complemented
288#810—51no—
289#809—51no—
290#809—51no—
291#807—51no—
292C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
293#803C2×D511yescharacteristic, complemented
294C23×D5—61no—
295C2×C5×D4#6711yescharacteristic
296C22×C4×C5C22×D311yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C2×C22⋊D5—61no—
299C2×C22⋊D5—61no—
300C22×Dic5—21no—
301C22×Dic5—21no—
302#709—62no—
303#709—121no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20—62no—
307C2×D20—61no—
308C2×D20—121no—
309C2×C4×D5—61no—
310C2×C4×D5—61no—
311C2×Dic10—22no—
312C2×Dic10—22no—
313C2×Dic10—21no—
314C2×Dic10—21no—
315C2×Dic10—31no—
316C2×Dic10—41no—
317C2×Dic10—41no—
318C2×Dic10C22×D311yescharacteristic
319C2×Dic10C22×D311yescharacteristic
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—21no—
333C22⋊Dic5—61no—
334#685—61no—
335#685—61no—
336#685—61no—
337#685—61no—
338C4⋊Dic5—21no—
339C4⋊Dic5—21no—
340C4⋊Dic5—31no—
341C4⋊Dic5C22×D311yescharacteristic
342#683—21no—
343#683—21no—
344#683—21no—
345#683—61no—
346C4×Dic5—21no—
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—51no—
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—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×D15—22no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—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—41no—
392Dic15—41no—
393C3×Dic5—22no—
394C3×Dic5—41no—
395C3×Dic5—41no—
396C3×Dic5—41no—
397C23×D3—101no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×Q8—51no—
401C2×C3×Q8—102no—
402C2×C3×Q8—102no—
403C2×C3×Q8—101no—
404C2×C3×Q8—101no—
405C2×C3×Q8—201no—
406C2×C3×Q8—201no—
407C2×C3×D4D2011yescharacteristic
408C22×C3×C4—101no—
409C22×C3×C4—101no—
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C2×#67—101no—
413C2×#67—101no—
414#235—102no—
415#235—201no—
416C2×D12—51no—
417C2×D12—51no—
418C2×D12—102no—
419C2×D12—101no—
420C2×D12—201no—
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×Dic6—51no—
424C3×C4⋊C4—51no—
425C3×C4⋊C4—101no—
426C3×C4⋊C4—101no—
427C3×C4⋊C4—101no—
428C3×C4⋊C4—101no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4D2011yescharacteristic
431C3×C22⋊C4—101no—
432C3×C22⋊C4—101no—
433C3×C22⋊C4D2011yescharacteristic
434C3×C22⋊C4D2011yescharacteristic
435C3×C42—101no—
436C3×C42C22×D511yescharacteristic
437#217—101no—
438#216—102no—
439#216—102no—
440#216—201no—
441#215—54no—
442#215—102no—
443#215—102no—
444#215—102no—
445#215—102no—
446#215—201no—
447(C2×D3)⋊C4—101no—
448(C2×D3)⋊C4—101no—
449(C2×D3)⋊C4—101no—
450(C2×D3)⋊C4—101no—
451C4⋊Dic3—51no—
452Dic3⋊C4—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—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
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—122no—
477C22⋊D5—241no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—21no—
482C2×Dic5—42no—
483C2×Dic5—42no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486D20—32no—
487D20—61no—
488D20—61no—
489D20—61no—
490D20—122no—
491C4×D5—122no—
492C4×D5—241no—
493Dic10—21no—
494Dic10—21no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—42no—
499Dic10—42no—
500Dic10—61no—
501Dic10—61no—
502Dic10D3×D412yes—
503C5×C8—32no—
504C5×C8—61no—
505C5×C8—61no—
506C5×C8—61no—
507C2×#41—151no—
508C22×Q8—51no—
509C22×Q8—51no—
510C22×D4—151no—
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—51no—
525C4⋊Q8—101no—
526#124—151no—
527#123—301no—
528C22⋊Q8—51no—
529C22⋊Q8—51no—
530C22⋊Q8—101no—
531C22⋊Q8—101no—
532C22⋊Q8—151no—
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—51no—
537C4×D4—101no—
538C4×D4—151no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—301no—
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
557D15—42no—
558D15—81no—
559C23×C3C2×D2011yescharacteristic
560C23×C3C2×D2011yescharacteristic
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×Q8—52no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×Q8—101no—
571C3×Q8—101no—
572C3×Q8—202no—
573C3×Q8—202no—
574C3×D4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—101no—
580C2×C3×C4—101no—
581C2×C3×C4—101no—
582C2×C3×C4—101no—
583C2×C3×C4—202no—
584C2×C3×C4—202no—
585C2×C3×C4C2×D2011yescharacteristic
586C2×C3×C4C2×D2011yescharacteristic
587C2×C3×C4C2×D2011yescharacteristic
588C2×C3×C4C2×D2011yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—202no—
591#67—401no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594D12—52no—
595D12—101no—
596D12—101no—
597D12—101no—
598D12—202no—
599C4×D3—202no—
600C4×D3—401no—
601Dic6—101no—
602Dic6—101no—
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#94212yescomplemented
613C22×C5C22×#6711yescharacteristic
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5C2×D3×D411yescharacteristic
626C4×C5#100411yescharacteristic
627Dic5—22no—
628Dic5—41no—
629Dic5—41no—
630Dic5—41no—
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—51no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—102no—
640C2×Q8—102no—
641C2×Q8—101no—
642C2×Q8—101no—
643C2×Q8—151no—
644C2×Q8—201no—
645C2×Q8—201no—
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—302no—
649C2×D4—301no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—601no—
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—101no—
678C4⋊C4—101no—
679C4⋊C4—101no—
680C4⋊C4—101no—
681C4⋊C4—151no—
682C4⋊C4—301no—
683C4⋊C4#120211yescharacteristic
684C22⋊C4—101no—
685C22⋊C4—101no—
686C22⋊C4—301no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#120211yescharacteristic
692C22⋊C4#120211yescharacteristic
693C42—101no—
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#405512yescomplemented
702C22×C3C22×D2011yescharacteristic
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—102no—
715C3×C4—201no—
716C3×C4—201no—
717C3×C4—201no—
718C3×C4C2×D4×D511yescharacteristic
719C3×C4#414911yescharacteristic
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5D4×#6711yescharacteristic
725C2×C5C2×#94211yescharacteristic
726C2×C5#583711yescharacteristic
727D5—122no—
728D5—241no—
729C23—301no—
730C23—301no—
731C23—602no—
732C23—602no—
733C23—1201no—
734C23C2×#120211yescharacteristic
735C23C2×#120211yescharacteristic
736Q8—52no—
737Q8—101no—
738Q8—101no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—202no—
743Q8—202no—
744Q8—301no—
745Q8—301no—
746D4—22no—
747D4—152no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—602no—
767C2×C4—1201no—
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×C3D4×D2011yescharacteristic
780C2×C3C2×#405511yescharacteristic
781C2×C3#6608511yescharacteristic
782D3—202no—
783D3—401no—
784C5#8355911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—302no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9131512yescomplemented
798C22C22×#120211yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—102no—
804C4—201no—
805C4—201no—
806C4—201no—
807C4—601no—
808C4—601no—
809C4D3×D4×D511yescharacteristic
810C4#9202611yescharacteristic
811C3#1061122611yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—602no—
815C2—1201no—
816C2C2×#9131511yescharacteristic
817C2D4×#120211yescharacteristic
818C2#1175531011yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11756309C2
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
2. C3×D4×Dic10C2semidirect
3. C2×#91315C2semidirect
4. C22×#6658C2semidirect
5. C5×#5011C2semidirect
6. #11748560C2semidirect
7. #11748556C2semidirect
8. #11748552C2semidirect
9. #11748551C2semidirect
10. #11748542C2semidirect
11. #11748532C2semidirect
12. #11747085C2semidirect
13. #11747076C2semidirect
14. #11747065C2semidirect
15. #11747054C2semidirect
20. C22×C3×Dic10C22semidirect
30. C2×C5×#208C22semidirect
34. C3×#4070C22semidirect
38. C3×#4015C22semidirect
39. C3×C4×Dic10C22semidirect
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. #90971C22semidirect
58. #90971C22semidirect
59. #90971C22semidirect
66. D4×Dic10D3semidirect
139. #6658D4semidirect
154. #5011D5semidirect
158. C22×Dic10C2×D3semidirect
167. #4070C2×D3semidirect
187. #4015C2×D3semidirect
188. C4×Dic10C2×D3semidirect
276. C2×#208C2×D5semidirect
287. #830C2×D5semidirect
292. C4⋊(C3⋊C8)C2×D5semidirect
293. #803C2×D5semidirect
376. C22×C3×C5#137semidirect
612. C22×C5#942semidirect
695. C3×C5#3266semidirect
701. C22×C3#4055semidirect
784. C5#83559semidirect
797. C22#91315semidirect
811. C3#10611226semidirect

Maximal subgroups

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

subgroupindex
#117563092
C3×D4×Dic102
C2×#913152
C22×#66582
C5×#50112
#117485602
#117485562
#117485522
#117485512
#117485422
#117485322
#117470852
#117470762
#117470652
#117470542
#106112263
#835595