Finite Group Databasebeta

← #14453518

Subgroups — #14453518

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D60C211yesmaximal, characteristic, complemented
2C3×#65886C211yesmaximal, characteristic, complemented
3C22×#6658C211yesmaximal, characteristic, complemented
4C2×#91301C211yesmaximal, characteristic, complemented
5C5×#5011C211yesmaximal, characteristic, complemented
6#11748551C211yesmaximal, characteristic, complemented
7#11748542C211yesmaximal, characteristic, complemented
8#11748532C211yesmaximal, characteristic, complemented
9#11748524C211yesmaximal, characteristic, complemented
10#11748518C211yesmaximal, characteristic, complemented
11#11748513C211yesmaximal, characteristic, complemented
12#11747064C211yesmaximal, characteristic, complemented
13#11747054C211yesmaximal, characteristic, complemented
14#11747044C211yesmaximal, characteristic, complemented
15#11747036C211yesmaximal, characteristic, complemented
16#10611225—31nomaximal, Hall
17C2×D4×D15—21no—
18C22×D60C2211yescharacteristic
19C22×D60C2211yescharacteristic
20C2×C3×#709C2211yescharacteristic, complemented
21C22×C3×Dic10C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic
23#91819C2211yescharacteristic
24#91819C2211yescharacteristic
25#91784—21no—
26#91771—21no—
27#91771—21no—
28#91763C2211yescharacteristic
29C4×D60C2211yescharacteristic
30C2×C5×#208C2211yescharacteristic, complemented
31C22×C5×C3⋊C8C2211yescharacteristic, complemented
32C3×#4085—21no—
33C3×#4076C2211yescharacteristic, complemented
34C3×#4070C2211yescharacteristic, complemented
35C3×#4042—21no—
36C3×#4031—21no—
37C3×#4027—21no—
38C3×#4021C2211yescharacteristic, complemented
39C3×C4×Dic10C2211yescharacteristic, complemented
40C2×#6658—24no—
41C2×#6658C2211yescharacteristic
42C2×#6658C2211yescharacteristic
43C2×#6658C2211yescharacteristic, complemented
44C2×#6658C2211yescharacteristic, complemented
45C2×#6658C2211yescharacteristic, complemented
46C2×#6658C2211yescharacteristic, complemented
47#91301—24no—
48C2×#6653C2211yescharacteristic
49C2×#6653C2211yescharacteristic, complemented
50C2×#6653C2211yescharacteristic, complemented
51C5×#830C2211yescharacteristic, complemented
52C5×#830C2211yescharacteristic, complemented
53C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54C5×#803C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90971C2211yescharacteristic, complemented
57#90971C2211yescharacteristic, complemented
58#90968C2211yescharacteristic
59#90968C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63C2×#4054—31no—
64C22×#677—31no—
65#65886D311yescharacteristic, complemented
66D4×D20—31no—
67C5×#435—31no—
68#65423—31no—
69#65404—31no—
70#65137—31no—
71#65133—31no—
72#65027—31no—
73#65023—31no—
74#65021—31no—
75#65020—31no—
76#65001—31no—
77#64999—31no—
78C23×D15—21no—
79C23×D15—21no—
80C2×C3×C5×D4D411yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C2×#1220—21no—
84C2×#1220—21no—
85D4×D15—44no—
86C2×D60—22no—
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—21no—
90C2×D60—21no—
91C2×D60—21no—
92C2×D60—41no—
93C2×D60—41no—
94C2×D60C2311yescharacteristic
95C2×D60C2311yescharacteristic
96C2×D60C2311yescharacteristic
97C2×C4×D15—21no—
98C2×C3×C22⋊D5—21no—
99C2×C3×C22⋊D5—21no—
100C22×C3×Dic5—21no—
101C3×#709—22no—
102C3×#709—41no—
103C2×C3×D20C2311yescharacteristic
104C2×C3×C4×D5—21no—
105C2×C3×Dic10—22no—
106C2×C3×Dic10—21no—
107C2×C3×Dic10—41no—
108C2×C3×Dic10C2311yescharacteristic
109C2×C3×Dic10C2311yescharacteristic
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C22⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C42×C5C2311yescharacteristic
114#6714—21no—
115#6714—21no—
116#6714—21no—
117C4⋊Dic15C2311yescharacteristic
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×C4⋊Dic5C2311yescharacteristic
129C3×#683—21no—
130C3×#683—21no—
131C3×C4×Dic5—21no—
132#6658—22no—
133#6658—22no—
134#6658—22no—
135#6658—22no—
136#6658—41no—
137#6658D414yescomplemented
138#6653—22no—
139#6653—22no—
140#6653—41no—
141C3×#548—51no—
142C2×#949—51no—
143C22×#215—51no—
144D4×D12—51no—
145#5238—51no—
146#5227—51no—
147#5058—51no—
148#5057—51no—
149#5049—51no—
150#5046—51no—
151#5038—51no—
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011D511yescharacteristic, complemented
156C2×D4×D5—61no—
157C2×#709C2×D311yescharacteristic, complemented
158C22×D20—31no—
159C22×D20—31no—
160C22×Dic10C2×D311yescharacteristic, complemented
161C2×C5×M16—31no—
162C22×C5×C8—31no—
163C4×C5×D4C2×D311yescharacteristic
164#4085—21no—
165#4076—31no—
166#4076—31no—
167#4076C2×D311yescharacteristic, complemented
168#4070C2×D311yescharacteristic, complemented
169#4054—64no—
170C2×D40—31no—
171C2×D40—31no—
172C2×D40—31no—
173C2×#677—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179C2×#677—64no—
180#4042—21no—
181#4041—61no—
182#4031—21no—
183#4028—61no—
184#4028—61no—
185#4027—21no—
186#4021C2×D311yescharacteristic, complemented
187#4020—31no—
188C4×D20—31no—
189C4×Dic10C2×D311yescharacteristic, complemented
190C5×C4⋊C8—31no—
191C5×C22⋊C8—31no—
192C5×C22⋊C8—31no—
193C5×#97—31no—
194#3953—31no—
195#3953—31no—
196#3953—31no—
197#3953—31no—
198#3950—31no—
199#3948—31no—
200#3948—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15—42no—
208C22×D15—42no—
209C22×D15—42no—
210C22×D15—42no—
211C22×D15—81no—
212C22×D15—81no—
213C22×C3×D5—21no—
214C3×C5×D4—22no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5C2×D411yescharacteristic
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2411yescharacteristic
224#1220—42no—
225#1220—42no—
226C2×Dic15—21no—
227D60—21no—
228D60—21no—
229D60—21no—
230D60—21no—
231D60—21no—
232D60—42no—
233D60—42no—
234D60—42no—
235D60—81no—
236D60C2×D412yes—
237C4×D15—42no—
238C3×C22⋊D5—42no—
239C3×C22⋊D5—42no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—42no—
244C3×D20—21no—
245C3×D20—21no—
246C3×C4×D5—42no—
247C3×Dic10—21no—
248C3×Dic10—21no—
249C3×Dic10—21no—
250C3×Dic10—42no—
251C3×Dic10C2×D412yescomplemented
252C5×C3⋊C8—21no—
253C5×C3⋊C8—21no—
254C5×C3⋊C8—21no—
255C5×C3⋊C8C2×D412yescomplemented
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C2×D3×D4—101no—
259C22×D12—51no—
260C22×D12—51no—
261C3×#124—51no—
262C3×#124—101no—
263C3×C22⋊Q8—51no—
264C3×C22⋊Q8—101no—
265C3×#121—51no—
266C3×#121—101no—
267C3×C4×Q8—51no—
268C3×C4×D4—101no—
269C3×C4×D4C2×D511yescharacteristic
270#949—104no—
271C2×#215—51no—
272C2×#215—51no—
273C2×#215—51no—
274C2×#215—51no—
275C2×#215—51no—
276C2×#215—51no—
277C2×#215—104no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930—51no—
282#930—51no—
283C2×#208C2×D511yescharacteristic, complemented
284C22×C3⋊C8C2×D511yescharacteristic, complemented
285#895—101no—
286#882—101no—
287#882—101no—
288#874—51no—
289C4×D12—51no—
290#835—51no—
291#835—51no—
292#832—51no—
293#830C2×D511yescharacteristic, complemented
294#830C2×D511yescharacteristic, complemented
295#809—51no—
296#809—51no—
297#809—51no—
298#807—51no—
299C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
300#803C2×D511yescharacteristic, complemented
301C23×D5—61no—
302C23×D5—61no—
303C2×C5×D4#6711yescharacteristic
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C2×C22⋊D5—21no—
307C2×C22⋊D5—21no—
308C2×C22⋊D5—61no—
309C2×C22⋊D5—61no—
310C22×Dic5—21no—
311D4×D5—124no—
312#709—22no—
313#709—41no—
314C2×D20—31no—
315C2×D20—31no—
316C2×D20—31no—
317C2×D20—62no—
318C2×D20—62no—
319C2×D20—61no—
320C2×D20—61no—
321C2×D20—61no—
322C2×D20—61no—
323C2×D20—121no—
324C2×D20—121no—
325C2×D20C22×D311yescharacteristic
326C2×C4×D5—21no—
327C2×C4×D5—61no—
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C22×D311yescharacteristic
332C2×Dic10C22×D311yescharacteristic
333C5×M16—62no—
334C2×C5×C8—31no—
335C2×C5×C8—31no—
336C2×C5×C8—31no—
337C2×C5×C8—31no—
338C2×C5×C8—62no—
339C5×C4⋊C4#6711yescharacteristic
340C5×C22⋊C4#6711yescharacteristic
341C5×C22⋊C4#6711yescharacteristic
342C42×C5C22×D311yescharacteristic
343C22⋊Dic5—21no—
344#685—21no—
345#685—21no—
346#685—21no—
347#685—61no—
348#685—61no—
349#685—61no—
350C4⋊Dic5—31no—
351C4⋊Dic5C22×D311yescharacteristic
352#683—21no—
353#683—21no—
354C4×Dic5—21no—
355D40—62no—
356D40—62no—
357D40—121no—
358#677—34no—
359#677—62no—
360#677—62no—
361#677—62no—
362#677—62no—
363#677—121no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—151no—
366#548—51no—
367D42—151no—
368#496—151no—
369#468—151no—
370#466—151no—
371#463—151no—
372#460—151no—
373#450—151no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—31no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5AGL(1,ℤ/8)12yescomplemented
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×D15—84no—
396C2×D15—84no—
397C2×C3×D5—41no—
398C2×C3×D5—41no—
399C2×C3×D5—41no—
400C3×C4×C5—21no—
401C3×C4×C5—21no—
402C3×C4×C5—21no—
403C3×C4×C5—21no—
404C3×C4×C5C22×D411yescharacteristic
405C3×C4×C5H(5,𝔽2)11yescharacteristic
406Dic15—41no—
407C3×Dic5—22no—
408C3×Dic5—41no—
409C3×Dic5—41no—
410C23×D3—101no—
411C23×D3—101no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—51no—
416C2×C3×Q8—102no—
417C2×C3×Q8—101no—
418C2×C3×Q8—201no—
419C2×C3×D4—51no—
420C2×C3×D4—101no—
421C2×C3×D4—101no—
422C2×C3×D4D2011yescharacteristic
423C22×C3×C4—101no—
424C22×C3×C4—101no—
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—101no—
428C2×#67—101no—
429D3×D4—204no—
430C2×D12—51no—
431C2×D12—51no—
432C2×D12—51no—
433C2×D12—102no—
434C2×D12—102no—
435C2×D12—101no—
436C2×D12—101no—
437C2×D12—101no—
438C2×D12—101no—
439C2×D12—201no—
440C2×D12—201no—
441C2×C4×D3—101no—
442C3×C4⋊C4—51no—
443C3×C4⋊C4—101no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4D2011yescharacteristic
446C3×C22⋊C4—101no—
447C3×C22⋊C4—101no—
448C3×C22⋊C4—101no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4D2011yescharacteristic
451C3×C22⋊C4D2011yescharacteristic
452C3×C42—101no—
453C3×C42C22×D511yescharacteristic
454#215—54no—
455#215—102no—
456#215—102no—
457#215—102no—
458#215—102no—
459#215—201no—
460#213—102no—
461#213—102no—
462#213—201no—
463(C2×D3)⋊C4—101no—
464(C2×D3)⋊C4—101no—
465(C2×D3)⋊C4—101no—
466C4⋊Dic3—51no—
467#208—22no—
468C2×C3⋊C8—22no—
469C2×C3⋊C8C22×D511yescharacteristic
470C2×C3⋊C8C22×D511yescharacteristic
471C2×C3⋊C8C22×D511yescharacteristic
472C2×C3⋊C8C22×D511yescharacteristic
473C23×C5C2×#6711yescharacteristic
474C23×C5C2×#6711yescharacteristic
475C22×D5—21no—
476C22×D5—61no—
477C22×D5—61no—
478C22×D5—61no—
479C22×D5—122no—
480C22×D5—122no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5—241no—
485C5×D4—22no—
486C2×C4×C5—21no—
487C2×C4×C5—21no—
488C2×C4×C5—21no—
489C2×C4×C5—21no—
490C2×C4×C5C2×#6711yescharacteristic
491C2×C4×C5C2×#6711yescharacteristic
492C2×C4×C5C2×#6711yescharacteristic
493C2×C4×C5C2×#6711yescharacteristic
494C2×C4×C5C23×D311yescharacteristic
495C22⋊D5—42no—
496C22⋊D5—42no—
497C22⋊D5—122no—
498C22⋊D5—122no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—42no—
503C2×Dic5—61no—
504D20—21no—
505D20—21no—
506D20—32no—
507D20—61no—
508D20—61no—
509D20—61no—
510D20—61no—
511D20—61no—
512D20—122no—
513D20—122no—
514D20—122no—
515D20—241no—
516C4×D5—42no—
517C4×D5—122no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10D3×D412yescomplemented
523C5×C8—32no—
524C5×C8—61no—
525C5×C8—61no—
526C5×C8—61no—
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—151no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—151no—
534C2×SD16—151no—
535C2×SD16—151no—
536C2×SD16—151no—
537C2×SD16—151no—
538C2×SD16—151no—
539C2×SD16—304no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—31no—
544C22×C8—31no—
545#127—151no—
546#124—51no—
547#124—101no—
548C22⋊Q8—51no—
549C22⋊Q8—101no—
550#121—51no—
551#121—101no—
552#121—151no—
553#121—151no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—51no—
558C4×D4—101no—
559C4×D4—151no—
560C4×D4D3×D511yescharacteristic
561#107—151no—
562C4⋊C8—31no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—31no—
570C22⋊C8—31no—
571#97—31no—
572C2×C3×C5—22no—
573C2×C3×C5—41no—
574C2×C3×C5D4211yescharacteristic
575C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
576C2×C3×C5#57711yescharacteristic
577D15—42no—
578D15—81no—
579D15—81no—
580C3×D5—81no—
581C23×C3—101no—
582C23×C3C2×D2011yescharacteristic
583C23×C3C2×D2011yescharacteristic
584C22×D3—101no—
585C22×D3—101no—
586C22×D3—101no—
587C22×D3—202no—
588C22×D3—202no—
589C22×D3—202no—
590C22×D3—202no—
591C22×D3—401no—
592C22×D3—401no—
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—22no—
599C3×D4—101no—
600C3×D4—101no—
601C3×D4—202no—
602C3×D4—202no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—202no—
611C2×C3×C4—202no—
612C2×C3×C4C2×D2011yescharacteristic
613C2×C3×C4C2×D2011yescharacteristic
614C2×C3×C4C2×D2011yescharacteristic
615C2×C3×C4C2×D2011yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—202no—
618#67—202no—
619C2×Dic3—101no—
620D12—52no—
621D12—101no—
622D12—101no—
623D12—101no—
624D12—101no—
625D12—101no—
626D12—202no—
627D12—202no—
628D12—202no—
629D12—401no—
630C4×D3—202no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C3⋊C8—21no—
634C3⋊C8D4×D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—21no—
639C22×C5—21no—
640C22×C5#94912yescomplemented
641C22×C5C22×#6711yescharacteristic
642C2×D5—41no—
643C2×D5—41no—
644C2×D5—41no—
645C2×D5—62no—
646C2×D5—121no—
647C2×D5—121no—
648C2×D5—121no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—21no—
658C4×C5—21no—
659C4×C5—21no—
660C4×C5C2×D3×D411yescharacteristic
661C4×C5#100411yescharacteristic
662Dic5—22no—
663Dic5—41no—
664Dic5—41no—
665Dic5—121no—
666C24—301no—
667C24—301no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—51no—
676C2×D4—101no—
677C2×D4—101no—
678C2×D4—151no—
679C2×D4—151no—
680C2×D4—151no—
681C2×D4—302no—
682C2×D4—302no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—301no—
689C2×D4—601no—
690C2×D4—601no—
691C2×D4—604no—
692C2×D4#120211yescharacteristic
693C22×C4—101no—
694C22×C4—101no—
695C22×C4—301no—
696C22×C4C2×D3×D511yescharacteristic
697C22×C4C2×D3×D511yescharacteristic
698SD16—154no—
699SD16—302no—
700SD16—302no—
701SD16—302no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—62no—
713C4⋊C4—51no—
714C4⋊C4—101no—
715C4⋊C4—101no—
716C4⋊C4—151no—
717C4⋊C4#120211yescharacteristic
718C22⋊C4—101no—
719C22⋊C4—101no—
720C22⋊C4—101no—
721C22⋊C4—101no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4#120211yescharacteristic
726C22⋊C4#120211yescharacteristic
727C42—101no—
728C42C2×D3×D511yescharacteristic
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—201no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3#405412yescomplemented
739C22×C3C22×D2011yescharacteristic
740C2×D3—102no—
741C2×D3—201no—
742C2×D3—201no—
743C2×D3—201no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—404no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—102no—
756C3×C4—201no—
757C3×C4—201no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414911yescharacteristic
760Dic3—201no—
761C2×C5—22no—
762C2×C5—41no—
763C2×C5D4×#6711yescharacteristic
764C2×C5C2×#94911yescharacteristic
765C2×C5#583711yescharacteristic
766D5—81no—
767D5—122no—
768D5—241no—
769D5—241no—
770C23—101no—
771C23—301no—
772C23—301no—
773C23—301no—
774C23—602no—
775C23—602no—
776C23—602no—
777C23—602no—
778C23—1201no—
779C23—1201no—
780C23C2×#120211yescharacteristic
781C23C2×#120211yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—22no—
788D4—101no—
789D4—101no—
790D4—152no—
791D4—202no—
792D4—202no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—301no—
797D4—301no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—202no—
812C2×C4—202no—
813C2×C4—301no—
814C2×C4—602no—
815C2×C4C2×#120211yescharacteristic
816C2×C4C2×#120211yescharacteristic
817C2×C4C2×#120211yescharacteristic
818C2×C4C2×#120211yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—32no—
821C8—61no—
822C8—61no—
823C8—61no—
824C2×C3—22no—
825C2×C3—41no—
826C2×C3—401no—
827C2×C3D4×D2011yescharacteristic
828C2×C3C2×#405411yescharacteristic
829C2×C3#6608511yescharacteristic
830D3—202no—
831D3—401no—
832D3—401no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—201no—
840C22—201no—
841C22—201no—
842C22—302no—
843C22—601no—
844C22—601no—
845C22—601no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—1204no—
852C22—1204no—
853C22#9130112yescomplemented
854C22C22×#120211yescharacteristic
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—102no—
860C4—201no—
861C4—201no—
862C4—601no—
863C4D3×D4×D511yescharacteristic
864C4#9202611yescharacteristic
865C3#1061122511yescharacteristic, complemented, Sylow
866C2—22no—
867C2—41no—
868C2—401no—
869C2—602no—
870C2—1201no—
871C2—1201no—
872C2C2×#9130111yescharacteristic
873C2D4×#120211yescharacteristic
874C2#1175531011yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3265
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×D60C2semidirect
2. C3×#65886C2semidirect
3. C22×#6658C2semidirect
4. C2×#91301C2semidirect
5. C5×#5011C2semidirect
6. #11748551C2semidirect
7. #11748542C2semidirect
8. #11748532C2semidirect
9. #11748524C2semidirect
10. #11748518C2semidirect
11. #11748513C2semidirect
12. #11747064C2semidirect
13. #11747054C2semidirect
14. #11747044C2semidirect
15. #11747036C2semidirect
20. C2×C3×#709C22semidirect
21. C22×C3×Dic10C22semidirect
30. C2×C5×#208C22semidirect
31. C22×C5×C3⋊C8C22semidirect
33. C3×#4076C22semidirect
34. C3×#4070C22semidirect
38. C3×#4021C22semidirect
39. C3×C4×Dic10C22semidirect
43. C2×#6658C22semidirect
44. C2×#6658C22semidirect
45. C2×#6658C22semidirect
46. C2×#6658C22semidirect
49. C2×#6653C22semidirect
50. C2×#6653C22semidirect
51. C5×#830C22semidirect
52. C5×#830C22semidirect
53. C5×C4⋊(C3⋊C8)C22semidirect
54. C5×#803C22semidirect
55. #90990C22semidirect
56. #90971C22semidirect
57. #90971C22semidirect
59. #90968C22semidirect
60. #90968C22semidirect
61. #90965C22semidirect
65. #65886D3semidirect
137. #6658D4semidirect
155. #5011D5semidirect
157. C2×#709C2×D3semidirect
160. C22×Dic10C2×D3semidirect
167. #4076C2×D3semidirect
168. #4070C2×D3semidirect
186. #4021C2×D3semidirect
189. C4×Dic10C2×D3semidirect
251. C3×Dic10C2×D4semidirect
255. C5×C3⋊C8C2×D4semidirect
283. C2×#208C2×D5semidirect
284. C22×C3⋊C8C2×D5semidirect
293. #830C2×D5semidirect
294. #830C2×D5semidirect
299. C4⋊(C3⋊C8)C2×D5semidirect
300. #803C2×D5semidirect
384. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10D3×D4semidirect
634. C3⋊C8D4×D5semidirect
640. C22×C5#949semidirect
729. C3×C5#3265semidirect
738. C22×C3#4054semidirect
833. C5#83542semidirect
853. C22#91301semidirect
865. C3#10611225semidirect

Maximal subgroups

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

subgroupindex
D4×D602
C3×#658862
C22×#66582
C2×#913012
C5×#50112
#117485512
#117485422
#117485322
#117485242
#117485182
#117485132
#117470642
#117470542
#117470442
#117470362
#106112253
#835425