Finite Group Databasebeta

← #14453231

Subgroups — #14453231

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#949C211yesmaximal, characteristic, complemented
2C3×#66163C211yesmaximal, characteristic, complemented
3C2×D5×#213C211yesmaximal, characteristic, complemented
4D12×C22⋊D5C211yesmaximal, characteristic, complemented
5#11751339C211yesmaximal, characteristic, complemented
6#11749397C211yesmaximal, characteristic, complemented
7#11749365C211yesmaximal, characteristic, complemented
8#11749340C211yesmaximal, characteristic, complemented
9#11749224C211yesmaximal, characteristic, complemented
10#11749092C211yesmaximal, characteristic, complemented
11#11749021C211yesmaximal, characteristic, complemented
12#11748977C211yesmaximal, characteristic, complemented
13#11748519C211yesmaximal, characteristic, complemented
14#11748516C211yesmaximal, characteristic, complemented
15#11748488C211yesmaximal, characteristic, complemented
16#10615683—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic, complemented
18C22×C5×D12C2211yescharacteristic, complemented
19C2×C3×D4×D5C2211yescharacteristic, complemented
20C2×D3×C22⋊D5—21no—
21C2×D5×D12C2211yescharacteristic
22C2×#6717C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic, complemented
25C5×#949—24no—
26C2×C5×#215C2211yescharacteristic, complemented
27C2×C5×#215C2211yescharacteristic, complemented
28C2×C5×#213C2211yescharacteristic
29C2×C5×#213C2211yescharacteristic, complemented
30C2×C5×#208C2211yescharacteristic, complemented
31C3×#4093C2211yescharacteristic, complemented
32C3×#4092C2211yescharacteristic, complemented
33C3×#4085—21no—
34C3×#4083—21no—
35C3×D4×Dic5C2211yescharacteristic, complemented
36C3×#4076C2211yescharacteristic, complemented
37C3×#4075—21no—
38C3×C4×C22⋊D5C2211yescharacteristic
39C2×C3×#685—21no—
40#91570—21no—
41D5×#213—24no—
42#91475—21no—
43#91451C2211yescharacteristic, complemented
44#91449C2211yescharacteristic
45#91416—21no—
46Dic5×D12C2211yescharacteristic, complemented
47C2×#6653C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D5×C3⋊C8C2211yescharacteristic, complemented
51#91119C2211yescharacteristic, complemented
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90982C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90966C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90965C2211yescharacteristic, complemented
60#90955C2211yescharacteristic, complemented
61#90952C2211yescharacteristic, complemented
62#83502—51nomaximal, Hall
63C2×C5×AGL(1,ℤ/8)—31no—
64#66163D311yescharacteristic, complemented
65D4×C22⋊D5—31no—
66C2×D5×D8—31no—
67#65527—31no—
68#65506—31no—
69#65465—31no—
70#65460—31no—
71#65458—31no—
72#65454—31no—
73#65445—31no—
74#65441—31no—
75#65439—31no—
76#65424—31no—
77#65416—31no—
78C23×C5×D3—21no—
79C23×C3×D5—21no—
80C22×D3×D5—21no—
81C3×C5×#41—22no—
82C3×C5×#41—41no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4C2311yescharacteristic
86C22×C3×C4×C5—21no—
87C22×C3×C4×C5C2311yescharacteristic
88C2×#1220—21no—
89C2×D60C2311yescharacteristic
90C2×C5×D12—22no—
91C2×C5×D12—21no—
92C2×C5×D12—41no—
93C2×C5×D12C2311yescharacteristic
94C2×C5×D12C2311yescharacteristic
95C2×C3×C22⋊D5—21no—
96C2×C3×C22⋊D5—21no—
97C2×C3×C22⋊D5D411yescharacteristic
98C22×C3×Dic5—21no—
99C3×D4×D5—22no—
100C3×D4×D5—41no—
101C2×C3×D20C2311yescharacteristic
102C2×C3×C4×D5C2311yescharacteristic
103D3×C22⋊D5—44no—
104C2×#1203—21no—
105C2×#1203—21no—
106C2×#1203—21no—
107C2×#1201—21no—
108C2×D3×Dic5—21no—
109D5×D12—22no—
110D5×D12—41no—
111#6717—41no—
112#6715—22no—
113#6714—21no—
114C4⋊Dic15C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C2×C3⋊#168C2311yescharacteristic
117C5×#215—22no—
118C5×#215—22no—
119C5×#213—22no—
120C5×#213D414yescomplemented
121C5×#208—22no—
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C3×C22⋊Dic5—21no—
125C3×C22⋊Dic5D411yescharacteristic
126C3×#685—21no—
127C3×#685—21no—
128C3×#685—21no—
129C3×#685—21no—
130C3×#685D411yescharacteristic
131C3×C4⋊Dic5C2311yescharacteristic
132C3×#683—21no—
133C3×#683D411yescharacteristic
134C3×C4×Dic5C2311yescharacteristic
135(C2×D3)⋊Dic5—21no—
136(C2×D3)⋊Dic5—21no—
137#6653—22no—
138#6652—22no—
139#6652—41no—
140D5×C3⋊C8—22no—
141C3×#546—51no—
142C2×#949D511yescharacteristic, complemented
143C22×#213—51no—
144D4×D12—51no—
145#5238—51no—
146#5217—51no—
147#5058—51no—
148#5057—51no—
149#5048—51no—
150#5046—51no—
151#5039—51no—
152#5036—51no—
153#5015—51no—
154#5014—51no—
155#5011—51no—
156C2×C5×#41C2×D311yescharacteristic, complemented
157C22×C5×D4—31no—
158C22×C22⋊D5—61no—
159C2×D4×D5—31no—
160C2×D4×D5C2×D311yescharacteristic, complemented
161C5×AGL(1,ℤ/8)—64no—
162C2×C5×SD16—31no—
163C2×C5×SD16—31no—
164C2×C5×D8—31no—
165C2×C5×D8—31no—
166C2×C5×M16—31no—
167#4099—61no—
168#4093C2×D311yescharacteristic, complemented
169#4092C2×D311yescharacteristic, complemented
170C2×#688—31no—
171#4086—31no—
172#4085—21no—
173#4085—61no—
174#4084—31no—
175#4083—21no—
176#4083—61no—
177D4×Dic5—31no—
178D4×Dic5C2×D311yescharacteristic, complemented
179C2×#686—31no—
180C2×#686—31no—
181C2×#686—31no—
182#4076—31no—
183#4076C2×D311yescharacteristic, complemented
184#4075—21no—
185C4×C22⋊D5C2×D311yescharacteristic
186C2×#685—21no—
187D5×D8—64no—
188C2×D40—31no—
189C2×C8×D5—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193#3964—31no—
194C22⋊#168—31no—
195#3953—31no—
196#3953—31no—
197#3952—31no—
198#3949—31no—
199#3947—31no—
200#3946—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5C2×D411yescharacteristic
204C22×D15—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3—81no—
210C22×C3×D5—21no—
211C22×C3×D5—42no—
212C22×C3×D5—42no—
213C22×C3×D5—81no—
214C22×C3×D5C2×D411yescharacteristic
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—42no—
222C3×C5×D4C2×D412yescomplemented
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2411yescharacteristic
229#1220—42no—
230C2×Dic15—21no—
231D60—21no—
232D60—21no—
233C5×D12—21no—
234C5×D12—21no—
235C5×D12—21no—
236C5×D12—42no—
237C5×D12C2×D412yes—
238C3×C22⋊D5—22no—
239C3×C22⋊D5—42no—
240C3×C22⋊D5—81no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—81no—
243C2×C3×Dic5C2×D411yescharacteristic
244C2×C3×Dic5C2×D411yescharacteristic
245C2×C3×Dic5C2×D411yescharacteristic
246C3×D20—21no—
247C3×D20—21no—
248C3×C4×D5—21no—
249C3×C4×D5—21no—
250#1203—42no—
251#1203—42no—
252#1203—81no—
253#1201—42no—
254D3×Dic5—42no—
255C3⋊#168—21no—
256C3⋊#168—21no—
257C5×C3⋊C8—21no—
258C5×C3⋊C8C2×D412yescomplemented
259C2×C3×#41C2×D511yescharacteristic, complemented
260C22×C3×D4—51no—
261C2×D3×D4—101no—
262C22×D12—51no—
263C22×D12C2×D511yescharacteristic, complemented
264C3×#124—51no—
265C3×#123—101no—
266C3×C22⋊Q8—51no—
267C3×#121—51no—
268C3×#121—101no—
269C3×#120—101no—
270C3×C4×D4—51no—
271C3×C4×D4—51no—
272C2×C3×C22⋊C4—101no—
273#949—24no—
274C2×#215—51no—
275C2×#215C2×D511yescharacteristic, complemented
276C2×#215C2×D511yescharacteristic, complemented
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—51no—
280C2×#213—51no—
281C2×#213—104no—
282C2×#213C2×D511yescharacteristic
283C2×#213C2×D511yescharacteristic, complemented
284#930—51no—
285#930—51no—
286C2×#208C2×D511yescharacteristic, complemented
287C22×C3⋊C8—51no—
288#895—101no—
289#882—101no—
290#882—101no—
291#874—51no—
292C4×D12—51no—
293#835—51no—
294#832—51no—
295#832—51no—
296#830—51no—
297#830—51no—
298#809—51no—
299#809—51no—
300#809—51no—
301#808—51no—
302C4⋊(C3⋊C8)—51no—
303#803—51no—
304C24×C5—61no—
305C23×D5—21no—
306C23×D5—61no—
307C5×#41—22no—
308C5×#41—41no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—21no—
311C2×C5×D4—31no—
312C2×C5×D4—31no—
313C2×C5×D4—62no—
314C2×C5×D4—61no—
315C2×C5×D4—121no—
316C2×C5×D4C22×D311yescharacteristic
317C22×C4×C5—21no—
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—21no—
320C2×C22⋊D5—21no—
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324C2×C22⋊D5—61no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5—124no—
327C2×C22⋊D5#6711yescharacteristic
328C22×Dic5—21no—
329C22×Dic5—61no—
330D4×D5—22no—
331D4×D5—41no—
332D4×D5—62no—
333D4×D5—121no—
334C2×D20—31no—
335C2×D20C22×D311yescharacteristic
336C2×C4×D5C22×D311yescharacteristic
337C5×SD16—62no—
338C5×SD16—62no—
339C5×D8—34no—
340C5×D8—62no—
341C5×M16—62no—
342C2×C5×C8—31no—
343C2×C5×C8—31no—
344C22⋊Dic5—21no—
345C22⋊Dic5—61no—
346C22⋊Dic5—61no—
347C22⋊Dic5#6711yescharacteristic
348#688—121no—
349#686—62no—
350#686—62no—
351#686—121no—
352#685—21no—
353#685—21no—
354#685—21no—
355#685—21no—
356#685—61no—
357#685#6711yescharacteristic
358C4⋊Dic5—31no—
359C4⋊Dic5C22×D311yescharacteristic
360#683—21no—
361#683#6711yescharacteristic
362C4×Dic5C22×D311yescharacteristic
363C2×#168—31no—
364C2×#168—31no—
365D40—62no—
366C8×D5—62no—
367C2×AGL(1,ℤ/8)—31no—
368C22×D8—151no—
369#546—51no—
370D42—151no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—22no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—21no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—22no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—84no—
399C2×C3×D5—21no—
400C2×C3×D5—21no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—84no—
405C2×C3×D5AGL(1,ℤ/8)12yescomplemented
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411Dic15—41no—
412C3×Dic5—21no—
413C3×Dic5—21no—
414C3×Dic5—21no—
415C3×Dic5—41no—
416C24×C3—101no—
417C23×D3—21no—
418C23×D3—101no—
419C3×#41—22no—
420C3×#41—41no—
421C2×C3×Q8C22×D511yescharacteristic
422C2×C3×D4—21no—
423C2×C3×D4—51no—
424C2×C3×D4—51no—
425C2×C3×D4—101no—
426C2×C3×D4—102no—
427C2×C3×D4—101no—
428C2×C3×D4—201no—
429C2×C3×D4C22×D511yescharacteristic
430C22×C3×C4—21no—
431C22×C3×C4—51no—
432C22×C3×C4—101no—
433C22×C3×C4C22×D511yescharacteristic
434C2×#67—101no—
435C2×#67—101no—
436D3×D4—204no—
437C2×D12—22no—
438C2×D12—21no—
439C2×D12—41no—
440C2×D12—51no—
441C2×D12—102no—
442C2×D12—101no—
443C2×D12—101no—
444C2×D12—101no—
445C2×D12—201no—
446C2×D12C22×D511yescharacteristic
447C2×D12C22×D511yescharacteristic
448C2×C4×D3—101no—
449C3×C4⋊C4—51no—
450C3×C4⋊C4—51no—
451C3×C4⋊C4—101no—
452C3×C22⋊C4—51no—
453C3×C22⋊C4—51no—
454C3×C22⋊C4—101no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C22⋊C4—101no—
458C3×C22⋊C4—101no—
459C3×C42—51no—
460#215—22no—
461#215—22no—
462#215—201no—
463#213—22no—
464#213—102no—
465#213—102no—
466#213—102no—
467#213—201no—
468#213C22⋊D514yescomplemented
469(C2×D3)⋊C4—101no—
470(C2×D3)⋊C4—101no—
471(C2×D3)⋊C4—101no—
472C4⋊Dic3—51no—
473#208—22no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476C2×C3⋊C8—102no—
477C2×C3⋊C8C22×D511yescharacteristic
478C2×C3⋊C8C22×D511yescharacteristic
479C23×C5—21no—
480C23×C5—61no—
481C23×C5—61no—
482C23×C5—122no—
483C23×C5—122no—
484C23×C5—241no—
485C23×C5C2×#6711yescharacteristic
486C22×D5—21no—
487C22×D5—42no—
488C22×D5—42no—
489C22×D5—61no—
490C22×D5—81no—
491C22×D5—122no—
492C22×D5—122no—
493C22×D5—241no—
494C22×D5C2×#6711yescharacteristic
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—32no—
499C5×D4—42no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—61no—
503C5×D4—122no—
504C5×D4D3×D412yescomplemented
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—42no—
509C2×C4×C5C2×#6711yescharacteristic
510C2×C4×C5C23×D311yescharacteristic
511C22⋊D5—22no—
512C22⋊D5—42no—
513C22⋊D5—81no—
514C22⋊D5—122no—
515C22⋊D5—122no—
516C22⋊D5—122no—
517C22⋊D5—122no—
518C22⋊D5—241no—
519C2×Dic5—21no—
520C2×Dic5—61no—
521C2×Dic5—81no—
522C2×Dic5—122no—
523C2×Dic5C2×#6711yescharacteristic
524C2×Dic5C2×#6711yescharacteristic
525C2×Dic5C2×#6711yescharacteristic
526D20—21no—
527D20—21no—
528D20—61no—
529D20—61no—
530C4×D5—21no—
531C4×D5—21no—
532C5×C8—32no—
533C5×C8—61no—
534#168—61no—
535#168—61no—
536C2×#41D3×D511yescharacteristic, complemented
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—64no—
542C2×SD16—31no—
543C2×SD16—31no—
544C2×SD16—151no—
545C2×D8—31no—
546C2×D8—31no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—31no—
553C22×C8—151no—
554#127—151no—
555#124—51no—
556#123—101no—
557C22⋊Q8—51no—
558#121—51no—
559#121—101no—
560#121—151no—
561#121—151no—
562#121—301no—
563#120—101no—
564#120—301no—
565#120—301no—
566C4×D4—51no—
567C4×D4—51no—
568C4×D4—151no—
569C2×C22⋊C4—101no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—151no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—42no—
582C2×C3×C5—41no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586D15—81no—
587C3×D5—22no—
588C3×D5—81no—
589C5×D3—42no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—51no—
593C23×C3—101no—
594C23×C3—202no—
595C23×C3—202no—
596C23×C3—401no—
597C23×C3D4×D511yescharacteristic
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—42no—
601C22×D3—42no—
602C22×D3—81no—
603C22×D3—101no—
604C22×D3—202no—
605C22×D3—202no—
606C22×D3—401no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—42no—
611C3×D4—102no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—202no—
615C3×D4—401no—
616C3×D4C2×C22⋊D512yescomplemented
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—42no—
621C2×C3×C4—51no—
622C2×C3×C4—51no—
623C2×C3×C4—51no—
624C2×C3×C4—101no—
625C2×C3×C4—101no—
626C2×C3×C4—101no—
627C2×C3×C4—401no—
628C2×C3×C4D4×D511yescharacteristic
629C2×C3×C4C23×D511yescharacteristic
630#67—202no—
631#67—202no—
632C2×Dic3—101no—
633D12—21no—
634D12—21no—
635D12—21no—
636D12—42no—
637D12—101no—
638D12—101no—
639D12—202no—
640D12—202no—
641D12—401no—
642D12C2×C22⋊D512yes—
643C4×D3—202no—
644C3⋊C8—21no—
645C3⋊C8—101no—
646C3⋊C8—101no—
647C3⋊C8C2×C22⋊D512yescomplemented
648C22×C5—22no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—21no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—62no—
655C22×C5—121no—
656C22×C5—121no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—244no—
661C22×C5C22×#6711yescharacteristic
662C2×D5—21no—
663C2×D5—21no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—84no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—244no—
672C2×D5#94912yescomplemented
673C4×C5—21no—
674C4×C5—41no—
675C4×C5C2×D3×D411yescharacteristic
676C4×C5#100411yescharacteristic
677Dic5—21no—
678Dic5—21no—
679Dic5—21no—
680Dic5—41no—
681Dic5—121no—
682C24—61no—
683C24—101no—
684C24—301no—
685#41—22no—
686#41—41no—
687C2×Q8C2×D3×D511yescharacteristic
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—101no—
696C2×D4—102no—
697C2×D4—101no—
698C2×D4—121no—
699C2×D4—151no—
700C2×D4—201no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—302no—
705C2×D4—301no—
706C2×D4—301no—
707C2×D4—601no—
708C2×D4—604no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—51no—
712C22×C4—101no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—62no—
716SD16—62no—
717SD16—601no—
718D8—34no—
719D8—62no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—62no—
725C2×C8—31no—
726C2×C8—31no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—51no—
731C4⋊C4—51no—
732C4⋊C4—101no—
733C4⋊C4—151no—
734C22⋊C4—51no—
735C22⋊C4—51no—
736C22⋊C4—101no—
737C22⋊C4—101no—
738C22⋊C4—101no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—51no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—52no—
753C22×C3—101no—
754C22×C3—101no—
755C22×C3—201no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—404no—
759C22×C3C2×D4×D511yescharacteristic
760C2×D3—22no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—84no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—201no—
770C2×D3—404no—
771C3×C4—21no—
772C3×C4—41no—
773C3×C4—101no—
774C3×C4—101no—
775C3×C4—101no—
776C3×C4—201no—
777C3×C4#414411yescharacteristic
778C3×C4C22×C22⋊D511yescharacteristic
779Dic3—201no—
780C2×C5—42no—
781C2×C5—41no—
782C2×C5—122no—
783C2×C5—241no—
784C2×C5D4×#6711yescharacteristic
785C2×C5C2×#94911yescharacteristic
786C2×C5#583511yescharacteristic
787D5—22no—
788D5—81no—
789D5—241no—
790C23—21no—
791C23—51no—
792C23—61no—
793C23—61no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—202no—
798C23—202no—
799C23—241no—
800C23—301no—
801C23—401no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23D5×#6711yescharacteristic
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—32no—
810D4—42no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—102no—
815D4—101no—
816D4—101no—
817D4—122no—
818D4—202no—
819D4—301no—
820D4—301no—
821D4—401no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4D3×C22⋊D512yescomplemented
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—42no—
832C2×C4—51no—
833C2×C4—51no—
834C2×C4—51no—
835C2×C4—101no—
836C2×C4—101no—
837C2×C4—101no—
838C2×C4—301no—
839C2×C4—401no—
840C2×C4—602no—
841C2×C4D5×#6711yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—32no—
844C8—61no—
845C8—301no—
846C8—301no—
847C2×C3—41no—
848C2×C3—42no—
849C2×C3—102no—
850C2×C3—401no—
851C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
852C2×C3#6610811yescharacteristic
853C2×C3D4×C22⋊D511yescharacteristic
854D3—42no—
855D3—81no—
856D3—401no—
857C5#8350211yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—22no—
862C22—41no—
863C22—41no—
864C22—52no—
865C22—62no—
866C22—101no—
867C22—101no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—404no—
878C22—601no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D5×#6711yescharacteristic
883C4—21no—
884C4—41no—
885C4—101no—
886C4—101no—
887C4—101no—
888C4—201no—
889C4—601no—
890C4C2×D3×C22⋊D511yescharacteristic
891C4#9204911yescharacteristic
892C3#1061568311yescharacteristic, complemented, Sylow
893C2—41no—
894C2—42no—
895C2—102no—
896C2—122no—
897C2—241no—
898C2—401no—
899C2—1201no—
900C2D5×#94911yescharacteristic
901C2#1175531611yescharacteristic
902C2#67×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#949C2semidirect
2. C3×#66163C2semidirect
3. C2×D5×#213C2semidirect
4. D12×C22⋊D5C2semidirect
5. #11751339C2semidirect
6. #11749397C2semidirect
7. #11749365C2semidirect
8. #11749340C2semidirect
9. #11749224C2semidirect
10. #11749092C2semidirect
11. #11749021C2semidirect
12. #11748977C2semidirect
13. #11748519C2semidirect
14. #11748516C2semidirect
15. #11748488C2semidirect
17. C2×C3×C5×#41C22semidirect
18. C22×C5×D12C22semidirect
19. C2×C3×D4×D5C22semidirect
22. C2×#6717C22semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
26. C2×C5×#215C22semidirect
27. C2×C5×#215C22semidirect
29. C2×C5×#213C22semidirect
30. C2×C5×#208C22semidirect
31. C3×#4093C22semidirect
32. C3×#4092C22semidirect
35. C3×D4×Dic5C22semidirect
36. C3×#4076C22semidirect
43. #91451C22semidirect
46. Dic5×D12C22semidirect
47. C2×#6653C22semidirect
49. C2×#6652C22semidirect
50. C2×D5×C3⋊C8C22semidirect
51. #91119C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90987C22semidirect
55. #90982C22semidirect
56. #90968C22semidirect
57. #90966C22semidirect
58. #90966C22semidirect
59. #90965C22semidirect
60. #90955C22semidirect
61. #90952C22semidirect
64. #66163D3semidirect
120. C5×#213D4semidirect
142. C2×#949D5semidirect
156. C2×C5×#41C2×D3semidirect
160. C2×D4×D5C2×D3semidirect
168. #4093C2×D3semidirect
169. #4092C2×D3semidirect
178. D4×Dic5C2×D3semidirect
183. #4076C2×D3semidirect
222. C3×C5×D4C2×D4semidirect
258. C5×C3⋊C8C2×D4semidirect
259. C2×C3×#41C2×D5semidirect
263. C22×D12C2×D5semidirect
275. C2×#215C2×D5semidirect
276. C2×#215C2×D5semidirect
283. C2×#213C2×D5semidirect
286. C2×#208C2×D5semidirect
405. C2×C3×D5AGL(1,ℤ/8)semidirect
468. #213C22⋊D5semidirect
504. C5×D4D3×D4semidirect
536. C2×#41D3×D5semidirect
616. C3×D4C2×C22⋊D5semidirect
647. C3⋊C8C2×C22⋊D5semidirect
672. C2×D5#949semidirect
745. C3×C5#3264semidirect
827. D4D3×C22⋊D5semidirect
857. C5#83502semidirect
892. C3#10615683semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9492
C3×#661632
C2×D5×#2132
D12×C22⋊D52
#117513392
#117493972
#117493652
#117493402
#117492242
#117490922
#117490212
#117489772
#117485192
#117485162
#117484882
#106156833
#835025