Finite Group Databasebeta

← #14453588

Subgroups — #14453588

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
1C3×#65967C211yesmaximal, characteristic, complemented
2C2×D5×#215C211yesmaximal, characteristic, complemented
3D12×C22⋊D5C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic, complemented
5#11751150C211yesmaximal, characteristic, complemented
6C5×#5046C211yesmaximal, characteristic, complemented
7#11749340C211yesmaximal, characteristic, complemented
8#11749267C211yesmaximal, characteristic, complemented
9#11749224C211yesmaximal, characteristic, complemented
10#11748513C211yesmaximal, characteristic, complemented
11#11748494C211yesmaximal, characteristic, complemented
12#11747480C211yesmaximal, characteristic, complemented
13#11747400C211yesmaximal, characteristic, complemented
14#11747307C211yesmaximal, characteristic, complemented
15#11747217C211yesmaximal, characteristic, complemented
16#10611887—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic, complemented
19C2×C3×#709C2211yescharacteristic, complemented
20C2×D3×C22⋊D5—21no—
21C2×D5×D12C2211yescharacteristic
22C3×C5×C22⋊Q8C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic, complemented
24#91819C2211yescharacteristic
25C2×#6710C2211yescharacteristic, complemented
26C2×C5×#215C2211yescharacteristic
27C2×C5×#215C2211yescharacteristic, complemented
28C3×#4093C2211yescharacteristic, complemented
29C3×C4×C22⋊D5C2211yescharacteristic
30C3×#4042—21no—
31C3×#4041C2211yescharacteristic, complemented
32C3×#4039—21no—
33C3×#4033C2211yescharacteristic, complemented
34C3×#4031—21no—
35C3×#4030—21no—
36#91570—21no—
37D5×#215—24no—
38#91475—21no—
39#91451C2211yescharacteristic
40#91449C2211yescharacteristic
41#91416—21no—
42Dic5×D12C2211yescharacteristic
43C2×#6658C2211yescharacteristic, complemented
44C2×#6656C2211yescharacteristic
45C2×#6656C2211yescharacteristic, complemented
46C2×#6653C2211yescharacteristic, complemented
47#91299—24no—
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D5×C3⋊C8C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53#91091C2211yescharacteristic, complemented
54C5×#830C2211yescharacteristic, complemented
55C5×#809C2211yescharacteristic
56C5×#809C2211yescharacteristic, complemented
57#90982C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83542—51nomaximal, Hall
63D4×C22⋊D5—31no—
64C2×#4078—31no—
65C2×D5×SD16—31no—
66#65967D311yescharacteristic, complemented
67C5×#450—31no—
68#65465—31no—
69#65459—31no—
70#65454—31no—
71#65338—31no—
72#65064—31no—
73#65062—31no—
74#65051—31no—
75#65046—31no—
76#65023—31no—
77#65017—31no—
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C2×C3×C5×Q8C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×D60C2311yescharacteristic
84C2×C5×D12—22no—
85C2×C5×D12—21no—
86C2×C5×D12—41no—
87C2×C5×D12C2311yescharacteristic
88C2×C5×D12C2311yescharacteristic
89C2×C3×C22⋊D5—21no—
90C2×C3×C22⋊D5D411yescharacteristic
91C3×Q8×D5—22no—
92C3×Q8×D5—41no—
93C3×#709—22no—
94C3×#709—41no—
95C2×C3×D20—21no—
96C2×C3×D20C2311yescharacteristic
97C2×C3×C4×D5—21no—
98C2×C3×C4×D5—21no—
99C2×C3×C4×D5C2311yescharacteristic
100C2×C3×Dic10—21no—
101C2×C3×Dic10C2311yescharacteristic
102D3×C22⋊D5—44no—
103C2×#1203—21no—
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1201—21no—
107C2×D3×Dic5—21no—
108D5×D12—22no—
109D5×D12—41no—
110C3×C5×C4⋊C4—21no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113#6717—22no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116#6710—22no—
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×#215—22no—
120C5×#215—41no—
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C3×C22⋊Dic5D411yescharacteristic
124C3×#685—21no—
125C3×#685—21no—
126C3×#685—21no—
127C3×#685D411yescharacteristic
128C3×#683—21no—
129C3×#683D411yescharacteristic
130C3×C4×Dic5—21no—
131C3×C4×Dic5C2311yescharacteristic
132(C2×D3)⋊Dic5—21no—
133(C2×D3)⋊Dic5—21no—
134#6658—22no—
135#6656—22no—
136#6656D414yescomplemented
137#6653—41no—
138#6652—22no—
139#6652—22no—
140D5×C3⋊C8—22no—
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#5046D511yescharacteristic, complemented
151#5038—51no—
152#5036—51no—
153#5027—51no—
154#5026—51no—
155#5011—51no—
156C22×C5×D4—31no—
157C22×C22⋊D5—61no—
158C2×Q8×D5C2×D311yescharacteristic, complemented
159C2×D4×D5—31no—
160C2×#709C2×D311yescharacteristic, complemented
161C2×C5×SD16—31no—
162C2×C5×SD16—31no—
163C5×C22⋊Q8C2×D311yescharacteristic, complemented
164#4099—61no—
165#4093C2×D311yescharacteristic, complemented
166C2×#688—31no—
167#4086—31no—
168#4085—61no—
169#4084—31no—
170#4083—61no—
171D4×Dic5—31no—
172C2×#687—31no—
173C2×#687—31no—
174#4078—64no—
175C2×#686—31no—
176C2×#686—31no—
177#4076—31no—
178C4×C22⋊D5C2×D311yescharacteristic
179C2×#681—31no—
180D5×SD16—64no—
181C2×D40—31no—
182C2×#677—31no—
183C2×C8×D5—31no—
184#4042—21no—
185#4041C2×D311yescharacteristic, complemented
186#4039—21no—
187#4033C2×D311yescharacteristic, complemented
188#4031—21no—
189#4030—21no—
190C5×#102—31no—
191C5×#102—31no—
192C5×C22⋊C8—31no—
193#3967—31no—
194#3953—31no—
195#3952—31no—
196#3948—31no—
197#3947—31no—
198#3946—31no—
199#3941—31no—
200#3939—31no—
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—81no—
209C22×C3×D5—21no—
210C22×C3×D5C2×D411yescharacteristic
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C3×C5×Q8—21no—
215C3×C5×Q8—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5C2×D411yescharacteristic
221C2×C3×C4×C5C2411yescharacteristic
222#1220—42no—
223C2×Dic15—21no—
224D60—21no—
225D60—21no—
226C5×D12—21no—
227C5×D12—21no—
228C5×D12—21no—
229C5×D12—42no—
230C5×D12C2×D412yes—
231C3×C22⋊D5—22no—
232C3×C22⋊D5—42no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5C2×D411yescharacteristic
235C2×C3×Dic5C2×D411yescharacteristic
236C2×C3×Dic5C2×D411yescharacteristic
237C3×D20—21no—
238C3×D20—21no—
239C3×D20—42no—
240C3×C4×D5—21no—
241C3×C4×D5—21no—
242C3×C4×D5—42no—
243C3×C4×D5—42no—
244C3×Dic10—21no—
245C3×Dic10—42no—
246C3×Dic10C2×D412yescomplemented
247#1203—42no—
248#1203—42no—
249#1203—81no—
250#1201—42no—
251D3×Dic5—42no—
252C3⋊#168—21no—
253C3⋊#168C2×D412yescomplemented
254C5×C3⋊C8—21no—
255C5×C3⋊C8—21no—
256C2×C3×#41—51no—
257C22×C3×Q8—51no—
258C2×D3×D4—101no—
259C22×D12—51no—
260C22×D12C2×D511yescharacteristic
261C3×#124—51no—
262C3×#124—101no—
263C3×C22⋊Q8—101no—
264C3×C22⋊Q8C2×D511yescharacteristic, complemented
265C3×#121—51no—
266C3×#121—101no—
267C3×C4×Q8—51no—
268C3×C4×D4—51no—
269C3×C4×D4—101no—
270#949—104no—
271C2×#215—51no—
272C2×#215—51no—
273C2×#215—51no—
274C2×#215—51no—
275C2×#215—104no—
276C2×#215C2×D511yescharacteristic
277C2×#215C2×D511yescharacteristic, complemented
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281#930—51no—
282#930—51no—
283C2×#208—51no—
284C22×C3⋊C8—51no—
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#830—51no—
294#830C2×D511yescharacteristic, complemented
295#809—51no—
296#809C2×D511yescharacteristic
297#809C2×D511yescharacteristic, complemented
298#807—51no—
299C4⋊(C3⋊C8)—51no—
300#803—51no—
301C24×C5—61no—
302C23×D5—61no—
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4—31no—
305C2×C5×D4—31no—
306C2×C5×D4—62no—
307C2×C5×D4—61no—
308C2×C5×D4—121no—
309C22×C4×C5C22×D311yescharacteristic
310C2×C22⋊D5—21no—
311C2×C22⋊D5—61no—
312C2×C22⋊D5—61no—
313C2×C22⋊D5—61no—
314C2×C22⋊D5—61no—
315C2×C22⋊D5—61no—
316C2×C22⋊D5—124no—
317C2×C22⋊D5#6711yescharacteristic
318C22×Dic5—61no—
319Q8×D5—22no—
320Q8×D5—41no—
321D4×D5—62no—
322D4×D5—121no—
323#709—22no—
324#709—41no—
325C2×D20—21no—
326C2×D20—31no—
327C2×D20C22×D311yescharacteristic
328C2×C4×D5—21no—
329C2×C4×D5—21no—
330C2×C4×D5C22×D311yescharacteristic
331C2×Dic10—21no—
332C2×Dic10C22×D311yescharacteristic
333C5×SD16—62no—
334C5×SD16—121no—
335C2×C5×C8—31no—
336C2×C5×C8—31no—
337C5×C4⋊C4—21no—
338C5×C4⋊C4C22×D311yescharacteristic
339C5×C22⋊C4—21no—
340C22⋊Dic5—61no—
341C22⋊Dic5—61no—
342C22⋊Dic5#6711yescharacteristic
343#688—62no—
344#687—34no—
345#687—62no—
346#686—62no—
347#686—62no—
348#685—21no—
349#685—21no—
350#685—21no—
351#685—61no—
352#685#6711yescharacteristic
353C4⋊Dic5—31no—
354#683—21no—
355#683#6711yescharacteristic
356C4×Dic5—21no—
357C4×Dic5C22×D311yescharacteristic
358#681—62no—
359C2×#168—31no—
360C2×#168—31no—
361D40—121no—
362#677—62no—
363C8×D5—62no—
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—31no—
374#449—151no—
375#448—151no—
376#447—151no—
377#440—151no—
378#435—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—21no—
382C22×C3×C5C22×D411yescharacteristic
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×C5×D3—22no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C5×D3—41no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—84no—
393C2×C3×D5—21no—
394C2×C3×D5—21no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5—41no—
398C2×C3×D5AGL(1,ℤ/8)12yescomplemented
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403C3×C4×C5C22×D411yescharacteristic
404C3×C4×C5H(5,𝔽2)11yescharacteristic
405Dic15—41no—
406C3×Dic5—21no—
407C3×Dic5—22no—
408C3×Dic5—21no—
409C3×Dic5—21no—
410C23×D3—21no—
411C23×D3—101no—
412C3×#41—102no—
413C3×#41—201no—
414C2×C3×Q8—51no—
415C2×C3×Q8—101no—
416C2×C3×Q8—102no—
417C2×C3×Q8—201no—
418C2×C3×Q8C22×D511yescharacteristic
419C2×C3×D4—51no—
420C2×C3×D4—51no—
421C2×C3×D4—101no—
422C2×C3×D4—101no—
423C22×C3×C4—51no—
424C22×C3×C4—101no—
425C22×C3×C4—101no—
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—101no—
428C2×#67—101no—
429D3×D4—204no—
430C2×D12—22no—
431C2×D12—21no—
432C2×D12—41no—
433C2×D12—51no—
434C2×D12—102no—
435C2×D12—101no—
436C2×D12—101no—
437C2×D12—101no—
438C2×D12—201no—
439C2×D12C22×D511yescharacteristic
440C2×D12C22×D511yescharacteristic
441C2×C4×D3—101no—
442C3×C4⋊C4—21no—
443C3×C4⋊C4—51no—
444C3×C4⋊C4—101no—
445C3×C4⋊C4C22×D511yescharacteristic
446C3×C22⋊C4—21no—
447C3×C22⋊C4—51no—
448C3×C22⋊C4—51no—
449C3×C22⋊C4—101no—
450C3×C22⋊C4—101no—
451C3×C22⋊C4—101no—
452C3×C42—51no—
453C3×C42—101no—
454#215—22no—
455#215—41no—
456#215—54no—
457#215—102no—
458#215—102no—
459#215—102no—
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—102no—
468C2×C3⋊C8—51no—
469C2×C3⋊C8—51no—
470C2×C3⋊C8—102no—
471C2×C3⋊C8C22×D511yescharacteristic
472C2×C3⋊C8C22×D511yescharacteristic
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—122no—
476C23×C5—122no—
477C23×C5—241no—
478C23×C5C2×#6711yescharacteristic
479C22×D5—21no—
480C22×D5—61no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5C2×#6711yescharacteristic
485C5×Q8—21no—
486C5×Q8—21no—
487C5×D4—32no—
488C5×D4—61no—
489C5×D4—61no—
490C5×D4—61no—
491C5×D4—122no—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5C2×#6711yescharacteristic
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—22no—
499C22⋊D5—42no—
500C22⋊D5—122no—
501C22⋊D5—122no—
502C22⋊D5—122no—
503C22⋊D5—122no—
504C22⋊D5—241no—
505C2×Dic5—21no—
506C2×Dic5—61no—
507C2×Dic5—122no—
508C2×Dic5C2×#6711yescharacteristic
509C2×Dic5C2×#6711yescharacteristic
510C2×Dic5C2×#6711yescharacteristic
511D20—21no—
512D20—21no—
513D20—42no—
514D20—61no—
515D20—61no—
516C4×D5—21no—
517C4×D5—21no—
518C4×D5—42no—
519C4×D5—42no—
520Dic10—21no—
521Dic10—42no—
522Dic10D3×D412yescomplemented
523C5×C8—61no—
524C5×C8—61no—
525#168—32no—
526#168—61no—
527C2×#41—51no—
528C22×Q8—51no—
529C22×D4—31no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—31no—
534C2×SD16—31no—
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—151no—
544C22×C8—151no—
545#127—151no—
546#124—51no—
547#124—101no—
548C22⋊Q8—101no—
549C22⋊Q8D3×D511yescharacteristic, complemented
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—51no—
559C4×D4—101no—
560C4×D4—151no—
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—31no—
566#102—31no—
567#102—151no—
568#102—151no—
569C22⋊C8—31no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—41no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—81no—
577C3×D5—22no—
578C3×D5—81no—
579C5×D3—42no—
580C5×D3—81no—
581C23×C3—51no—
582C23×C3—101no—
583C23×C3D4×D511yescharacteristic
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—42no—
587C22×D3—42no—
588C22×D3—81no—
589C22×D3—101no—
590C22×D3—202no—
591C22×D3—202no—
592C22×D3—401no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—52no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—102no—
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—51no—
608C2×C3×C4—51no—
609C2×C3×C4—51no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—202no—
614C2×C3×C4—202no—
615C2×C3×C4D4×D511yescharacteristic
616C2×C3×C4C23×D511yescharacteristic
617#67—202no—
618#67—202no—
619C2×Dic3—101no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624D12—101no—
625D12—101no—
626D12—202no—
627D12—202no—
628D12—401no—
629D12D4×D512yes—
630C4×D3—202no—
631C3⋊C8—21no—
632C3⋊C8—21no—
633C3⋊C8—52no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—21no—
638C22×C5—62no—
639C22×C5—121no—
640C22×C5—121no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5—121no—
644C22×C5—244no—
645C22×C5C22×#6711yescharacteristic
646C2×D5—21no—
647C2×D5—21no—
648C2×D5—41no—
649C2×D5—41no—
650C2×D5—41no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—244no—
655C2×D5#94912yescomplemented
656C4×C5—21no—
657C4×C5—41no—
658C4×C5—41no—
659C4×C5C2×D3×D411yescharacteristic
660C4×C5#100411yescharacteristic
661Dic5—22no—
662Dic5—21no—
663Dic5—21no—
664Dic5—21no—
665Dic5—121no—
666C24—61no—
667C24—301no—
668#41—102no—
669#41—201no—
670C2×Q8—51no—
671C2×Q8—101no—
672C2×Q8—102no—
673C2×Q8—201no—
674C2×Q8C2×D3×D511yescharacteristic
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—51no—
678C2×D4—51no—
679C2×D4—62no—
680C2×D4—61no—
681C2×D4—101no—
682C2×D4—101no—
683C2×D4—121no—
684C2×D4—151no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—301no—
688C2×D4—302no—
689C2×D4—301no—
690C2×D4—301no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—51no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—62no—
699SD16—121no—
700SD16—154no—
701SD16—302no—
702SD16—302no—
703SD16—302no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—151no—
711C2×C8—151no—
712C2×C8—302no—
713C4⋊C4—21no—
714C4⋊C4—51no—
715C4⋊C4—101no—
716C4⋊C4—151no—
717C4⋊C4C2×D3×D511yescharacteristic
718C22⋊C4—21no—
719C22⋊C4—51no—
720C22⋊C4—51no—
721C22⋊C4—101no—
722C22⋊C4—101no—
723C22⋊C4—101no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—51no—
728C42—101no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—52no—
734C22×C3—101no—
735C22×C3—101no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3—201no—
739C22×C3C2×D4×D511yescharacteristic
740C2×D3—22no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—84no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—101no—
755C3×C4—101no—
756C3×C4—101no—
757C3×C4—102no—
758C3×C4C2×D4×D511yescharacteristic
759C3×C4#414411yescharacteristic
760Dic3—201no—
761C2×C5—41no—
762C2×C5—122no—
763C2×C5—241no—
764C2×C5D4×#6711yescharacteristic
765C2×C5C2×#94911yescharacteristic
766C2×C5#583711yescharacteristic
767D5—22no—
768D5—81no—
769D5—241no—
770C23—51no—
771C23—61no—
772C23—61no—
773C23—101no—
774C23—122no—
775C23—122no—
776C23—241no—
777C23—301no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23D5×#6711yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—52no—
785Q8—101no—
786Q8—202no—
787D4—32no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—102no—
792D4—101no—
793D4—101no—
794D4—122no—
795D4—202no—
796D4—202no—
797D4—301no—
798D4—301no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—51no—
809C2×C4—51no—
810C2×C4—51no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—202no—
815C2×C4—202no—
816C2×C4—301no—
817C2×C4—602no—
818C2×C4D5×#6711yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—61no—
821C8—61no—
822C8—152no—
823C8—301no—
824C2×C3—41no—
825C2×C3—102no—
826C2×C3—401no—
827C2×C3#6592411yescharacteristic
828C2×C3#6609611yescharacteristic
829C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
830D3—42no—
831D3—81no—
832D3—401no—
833C5#8354211yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—21no—
837C22—52no—
838C22—62no—
839C22—101no—
840C22—101no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—201no—
847C22—201no—
848C22—201no—
849C22—244no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22—1204no—
854C22C2×D5×#6711yescharacteristic
855C4—21no—
856C4—41no—
857C4—41no—
858C4—101no—
859C4—102no—
860C4—101no—
861C4—101no—
862C4—601no—
863C4D3×D4×D511yescharacteristic
864C4#9202511yescharacteristic
865C3#1061188711yescharacteristic, complemented, Sylow
866C2—41no—
867C2—102no—
868C2—122no—
869C2—241no—
870C2—401no—
871C2—1201no—
872C2#1175503111yescharacteristic
873C2#1175508511yescharacteristic
874C2D5×#94911yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3265
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. C3×#65967C2semidirect
2. C2×D5×#215C2semidirect
3. D12×C22⋊D5C2semidirect
4. C2×#91299C2semidirect
5. #11751150C2semidirect
6. C5×#5046C2semidirect
7. #11749340C2semidirect
8. #11749267C2semidirect
9. #11749224C2semidirect
10. #11748513C2semidirect
11. #11748494C2semidirect
12. #11747480C2semidirect
13. #11747400C2semidirect
14. #11747307C2semidirect
15. #11747217C2semidirect
18. C2×C3×Q8×D5C22semidirect
19. C2×C3×#709C22semidirect
22. C3×C5×C22⋊Q8C22semidirect
23. C2×#6717C22semidirect
25. C2×#6710C22semidirect
27. C2×C5×#215C22semidirect
28. C3×#4093C22semidirect
31. C3×#4041C22semidirect
33. C3×#4033C22semidirect
43. C2×#6658C22semidirect
45. C2×#6656C22semidirect
46. C2×#6653C22semidirect
49. C2×#6652C22semidirect
50. C2×D5×C3⋊C8C22semidirect
51. #91119C22semidirect
52. #91093C22semidirect
53. #91091C22semidirect
54. C5×#830C22semidirect
56. C5×#809C22semidirect
57. #90982C22semidirect
58. #90971C22semidirect
59. #90965C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
66. #65967D3semidirect
136. #6656D4semidirect
150. #5046D5semidirect
158. C2×Q8×D5C2×D3semidirect
160. C2×#709C2×D3semidirect
163. C5×C22⋊Q8C2×D3semidirect
165. #4093C2×D3semidirect
185. #4041C2×D3semidirect
187. #4033C2×D3semidirect
246. C3×Dic10C2×D4semidirect
253. C3⋊#168C2×D4semidirect
264. C3×C22⋊Q8C2×D5semidirect
277. C2×#215C2×D5semidirect
294. #830C2×D5semidirect
297. #809C2×D5semidirect
398. C2×C3×D5AGL(1,ℤ/8)semidirect
522. Dic10D3×D4semidirect
549. C22⋊Q8D3×D5semidirect
655. C2×D5#949semidirect
729. C3×C5#3265semidirect
833. C5#83542semidirect
865. C3#10611887semidirect

Maximal subgroups

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

subgroupindex
C3×#659672
C2×D5×#2152
D12×C22⋊D52
C2×#912992
#117511502
C5×#50462
#117493402
#117492672
#117492242
#117485132
#117484942
#117474802
#117474002
#117473072
#117472172
#106118873
#835425