Finite Group Databasebeta

← #14453523

Subgroups — #14453523

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
1C22×C5×#204C211yesmaximal, characteristic, complemented
2D12×C22⋊D5C211yesmaximal, characteristic, complemented
3#11754544C211yesmaximal, characteristic, complemented
4C2×#91249C211yesmaximal, characteristic, complemented
5#11751216C211yesmaximal, characteristic, complemented
6C3×#65400C211yesmaximal, characteristic, complemented
7#11748544C211yesmaximal, characteristic, complemented
8#11748520C211yesmaximal, characteristic, complemented
9#11748114C211yesmaximal, characteristic, complemented
10#11747997C211yesmaximal, characteristic, complemented
11#11747902C211yesmaximal, characteristic, complemented
12#11747900C211yesmaximal, characteristic, complemented
13#11747842C211yesmaximal, characteristic, complemented
14#11747770C211yesmaximal, characteristic, complemented
15#11747769C211yesmaximal, characteristic, complemented
16#10615595—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic, complemented
19C2×D3×C22⋊D5—21no—
20C2×D5×D12C2211yescharacteristic
21C2×#6773C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic, complemented
23#91819C2211yescharacteristic
24#91819C2211yescharacteristic, complemented
25C2×D120C2211yescharacteristic, complemented
26C2×C5×#204—24no—
27C2×C5×#204C2211yescharacteristic
28C2×C5×#204C2211yescharacteristic
29C2×C5×#204C2211yescharacteristic, complemented
30C2×C5×#204C2211yescharacteristic, complemented
31C3×C4×C22⋊D5C2211yescharacteristic
32C2×C3×#676C2211yescharacteristic, complemented
33#91570—21no—
34#91569—21no—
35#91556—21no—
36#91475—21no—
37#91455—21no—
38#91451C2211yescharacteristic
39#91449C2211yescharacteristic
40#91424—21no—
41#91416—21no—
42Dic5×D12C2211yescharacteristic
43#91375C2211yescharacteristic, complemented
44#91359C2211yescharacteristic, complemented
45Dic5×Dic6C2211yescharacteristic, complemented
46C2×#6660C2211yescharacteristic, complemented
47C2×#6660C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic
49C2×#6654C2211yescharacteristic, complemented
50#91249—24no—
51#91105C2211yescharacteristic, complemented
52#91105C2211yescharacteristic, complemented
53#91102C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×#3952C2211yescharacteristic, complemented
56C3×#3947C2211yescharacteristic, complemented
57C3×#3946C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90967C2211yescharacteristic
61#90967C2211yescharacteristic, complemented
62#79494—51nomaximal, Hall
63C22×C5×SD16—31no—
64#66151—31no—
65D4×C22⋊D5—31no—
66C2×#4060—31no—
67#65516—31no—
68#65506—31no—
69#65465—31no—
70#65463—31no—
71#65461—31no—
72#65458—31no—
73#65454—31no—
74#65453—31no—
75#65452—31no—
76#65404—31no—
77#65400D311yescharacteristic, complemented
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C22×C3×C4×C5C2311yescharacteristic
81C2×#1220—21no—
82C2×#1220—21no—
83C2×D60C2311yescharacteristic
84C2×D60C2311yescharacteristic
85C22×C5×Dic3—21no—
86C2×C5×D12—22no—
87C2×C5×D12—21no—
88C2×C5×D12—41no—
89C2×C5×D12C2311yescharacteristic
90C2×C5×D12C2311yescharacteristic
91C2×C5×Dic6—22no—
92C2×C5×Dic6—21no—
93C2×C5×Dic6—41no—
94C2×C5×Dic6C2311yescharacteristic
95C2×C5×Dic6C2311yescharacteristic
96C2×C3×C22⋊D5D411yescharacteristic
97C2×C3×C4×D5C2311yescharacteristic
98D3×C22⋊D5—44no—
99C2×#1203—21no—
100C2×#1203—21no—
101C2×#1203—21no—
102C2×#1202—21no—
103C2×#1201—21no—
104C2×#1200—21no—
105C2×D3×Dic5—21no—
106D5×D12—22no—
107D5×D12—41no—
108#6773—22no—
109#6773—41no—
110C2×C3×C5×C8—22no—
111C2×C3×C5×C8C2311yescharacteristic
112C2×C3×C5×C8C2311yescharacteristic
113#6714—21no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116C4⋊Dic15C2311yescharacteristic
117D120—22no—
118C5×#204—22no—
119C5×#204—22no—
120C5×#204—22no—
121C5×#204D414yescomplemented
122C3×C22⋊Dic5D411yescharacteristic
123C3×#685D411yescharacteristic
124C3×#683D411yescharacteristic
125C3×C4×Dic5C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128C3×#676—22no—
129Dic3⋊Dic5—21no—
130#6669—21no—
131#6667—21no—
132#6667—21no—
133(C2×D3)⋊Dic5—21no—
134(C2×D3)⋊Dic5—21no—
135#6665—21no—
136Dic3×Dic5—21no—
137#6660—22no—
138#6660—41no—
139#6654—22no—
140#6654—41no—
141C2×#908—51no—
142C22×#204D511yescharacteristic, complemented
143#5552—51no—
144D4×D12—51no—
145C3×#435—51no—
146#5134—51no—
147#5115—51no—
148#4848—51no—
149#4844—51no—
150#4738—51no—
151#4734—51no—
152#4732—51no—
153#4731—51no—
154#4712—51no—
155#4710—51no—
156C22×C5×Q8—31no—
157C22×C5×D4—31no—
158C22×C22⋊D5—61no—
159C2×#713—31no—
160C2×D4×D5—31no—
161C2×C5×SD16—31no—
162C2×C5×SD16—31no—
163C2×C5×SD16—31no—
164C2×C5×SD16—31no—
165C2×C5×SD16—64no—
166C22×C5×C8C2×D311yescharacteristic, complemented
167#4099—61no—
168#4093—31no—
169#4093—61no—
170#4092—31no—
171#4092—61no—
172Q8×Dic5—31no—
173C2×#688—31no—
174C2×#688—31no—
175#4086—31no—
176#4085—61no—
177#4084—31no—
178#4083—61no—
179D4×Dic5—31no—
180C2×#686—31no—
181C2×#686—31no—
182#4076—31no—
183#4076—31no—
184#4076—61no—
185C4×C22⋊D5—61no—
186C4×C22⋊D5C2×D311yescharacteristic
187#4060—64no—
188C2×D40—31no—
189C2×#676C2×D311yescharacteristic, complemented
190#3967—31no—
191#3967—31no—
192#3964—31no—
193#3964—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3953—31no—
196#3953—31no—
197#3952C2×D311yescharacteristic, complemented
198#3950—31no—
199#3947C2×D311yescharacteristic, complemented
200#3946C2×D311yescharacteristic, complemented
201#3265—151noSylow
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
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×D5C2×D411yescharacteristic
211C2×D3×D5—42no—
212C2×D3×D5—42no—
213C2×D3×D5—81no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—42no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222D60—21no—
223D60—21no—
224D60—21no—
225D60—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—42no—
229C5×D12—21no—
230C5×D12—21no—
231C5×D12—21no—
232C5×D12—42no—
233C5×D12C2×D412yes—
234C5×Dic6—21no—
235C5×Dic6—21no—
236C5×Dic6—21no—
237C5×Dic6—42no—
238C5×Dic6C2×D412yescomplemented
239C3×C22⋊D5—22no—
240C2×C3×Dic5C2×D411yescharacteristic
241C2×C3×Dic5C2×D411yescharacteristic
242C2×C3×Dic5C2×D411yescharacteristic
243C3×C4×D5—21no—
244C3×C4×D5—21no—
245#1203—42no—
246#1203—42no—
247#1203—81no—
248#1202—42no—
249#1201—42no—
250#1200—42no—
251D3×Dic5—42no—
252C3×C5×C8—21no—
253C3×C5×C8C2×D412yescomplemented
254C3×#168—21no—
255C3×#168—21no—
256C2×D3×D4—101no—
257C2×#235—51no—
258C22×D12—51no—
259C22×D12C2×D511yescharacteristic
260C22×Dic6C2×D511yescharacteristic, complemented
261C2×C3×M16—51no—
262C22×C3×C8C2×D511yescharacteristic, complemented
263C3×C4×D4—51no—
264#939—101no—
265#930—51no—
266#930—51no—
267#930—51no—
268#924—51no—
269#908—104no—
270C2×D24—51no—
271C2×D24—51no—
272C2×D24—51no—
273C2×#204—24no—
274C2×#204—51no—
275C2×#204—51no—
276C2×#204C2×D511yescharacteristic
277C2×#204C2×D511yescharacteristic
278C2×#204C2×D511yescharacteristic, complemented
279C2×#204C2×D511yescharacteristic, complemented
280#896—101no—
281#895—101no—
282#885—101no—
283#882—101no—
284#882—101no—
285#67⋊C4—101no—
286#875—51no—
287#874—51no—
288C4×D12—51no—
289C4×Dic6—51no—
290C3×C4⋊C8—51no—
291C3×C22⋊C8—51no—
292C3×C22⋊C8—51no—
293C3×#97—51no—
294#821—51no—
295#821—51no—
296#821—51no—
297#821—51no—
298#818—51no—
299#816—51no—
300#816—51no—
301C24×C5—61no—
302C23×D5—61no—
303C2×C5×Q8—31no—
304C2×C5×Q8—31no—
305C2×C5×Q8—62no—
306C2×C5×Q8—61no—
307C2×C5×Q8—121no—
308C2×C5×D4—31no—
309C2×C5×D4—31no—
310C2×C5×D4—62no—
311C2×C5×D4—61no—
312C2×C5×D4—121no—
313C22×C4×C5—61no—
314C22×C4×C5C22×D311yescharacteristic
315C2×C22⋊D5—61no—
316C2×C22⋊D5—61no—
317C2×C22⋊D5—61no—
318C2×C22⋊D5—61no—
319C2×C22⋊D5—61no—
320C2×C22⋊D5—61no—
321C2×C22⋊D5—124no—
322C2×C22⋊D5D1211yescharacteristic
323C22×Dic5—61no—
324#713—62no—
325#713—121no—
326D4×D5—62no—
327D4×D5—121no—
328C2×D20—31no—
329C2×D20—31no—
330C2×D20—61no—
331C2×C4×D5—61no—
332C2×C4×D5C22×D311yescharacteristic
333C5×SD16—34no—
334C5×SD16—62no—
335C5×SD16—62no—
336C5×SD16—62no—
337C2×C5×C8—22no—
338C2×C5×C8C22×D311yescharacteristic
339C2×C5×C8C22×D311yescharacteristic
340C22⋊Dic5—61no—
341C22⋊Dic5—61no—
342C22⋊Dic5D1211yescharacteristic
343#688—62no—
344#688—121no—
345#686—62no—
346#686—121no—
347#685—61no—
348#685—61no—
349#685—61no—
350#685—61no—
351#685—61no—
352#685D1211yescharacteristic
353C4⋊Dic5—31no—
354C4⋊Dic5—31no—
355C4⋊Dic5—61no—
356#683—61no—
357#683D1211yescharacteristic
358C4×Dic5—61no—
359C4×Dic5C22×D311yescharacteristic
360C2×#168C22×D311yescharacteristic
361C2×#168C22×D311yescharacteristic
362D40—62no—
363#676—22no—
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—31no—
366#548—151no—
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—51no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5AGL(1,ℤ/8)12yescomplemented
382C22×C3×C5C22×D411yescharacteristic
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—22no—
390C2×C5×D3—41no—
391C2×C5×D3—41no—
392C2×C5×D3—41no—
393C2×C5×D3—41no—
394C2×C5×D3—41no—
395C2×C5×D3—84no—
396C2×C3×D5—21no—
397C2×C3×D5—21no—
398C2×C3×D5—21no—
399D3×D5—84no—
400C3×C4×C5—21no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403Dic15—41no—
404Dic15—41no—
405C3×Dic5—21no—
406C3×Dic5—21no—
407C3×Dic5—21no—
408C5×Dic3—22no—
409C5×Dic3—41no—
410C23×D3—21no—
411C23×D3—101no—
412C2×C3×D4—51no—
413C22×C3×C4—51no—
414C22×C3×C4C22×D511yescharacteristic
415C2×#67—101no—
416C2×#67—101no—
417C2×#67—101no—
418C2×#67—101no—
419C22×Dic3—21no—
420D3×D4—204no—
421#235—102no—
422#235—201no—
423C2×D12—22no—
424C2×D12—21no—
425C2×D12—41no—
426C2×D12—51no—
427C2×D12—51no—
428C2×D12—102no—
429C2×D12—101no—
430C2×D12—101no—
431C2×D12—101no—
432C2×D12—201no—
433C2×D12C22×D511yescharacteristic
434C2×D12C22×D511yescharacteristic
435C2×C4×D3—101no—
436C2×C4×D3—101no—
437C2×Dic6—22no—
438C2×Dic6—21no—
439C2×Dic6—41no—
440C2×Dic6C22×D511yescharacteristic
441C2×Dic6C22×D511yescharacteristic
442C3×M16—102no—
443C2×C3×C8—22no—
444C2×C3×C8—51no—
445C2×C3×C8—51no—
446C2×C3×C8C22×D511yescharacteristic
447C2×C3×C8C22×D511yescharacteristic
448C3×C4⋊C4—51no—
449C3×C22⋊C4—51no—
450C3×C22⋊C4—51no—
451C3×C42—51no—
452#217—101no—
453(C2×D3)⋊C4—101no—
454(C2×D3)⋊C4—101no—
455(C2×D3)⋊C4—101no—
456(C2×D3)⋊C4—101no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459C4⋊Dic3—51no—
460C4⋊Dic3—51no—
461Dic3⋊C4—101no—
462Dic3⋊C4—101no—
463C4×Dic3—101no—
464D24—102no—
465D24—102no—
466D24—201no—
467#204—22no—
468#204—22no—
469#204—22no—
470#204—102no—
471#204—201no—
472#204C22⋊D514yescomplemented
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—122no—
476C23×C5—122no—
477C23×C5—241no—
478C23×C5C2×D1211yescharacteristic
479C22×D5—61no—
480C22×D5—61no—
481C22×D5—122no—
482C22×D5—122no—
483C22×D5—241no—
484C22×D5C2×D1211yescharacteristic
485C5×Q8—32no—
486C5×Q8—61no—
487C5×Q8—61no—
488C5×Q8—61no—
489C5×Q8—122no—
490C5×D4—32no—
491C5×D4—61no—
492C5×D4—61no—
493C5×D4—61no—
494C5×D4—122no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—61no—
498C2×C4×C5—61no—
499C2×C4×C5—122no—
500C2×C4×C5C2×D1211yescharacteristic
501C2×C4×C5C23×D311yescharacteristic
502C22⋊D5—22no—
503C22⋊D5—122no—
504C22⋊D5—122no—
505C22⋊D5—122no—
506C22⋊D5—122no—
507C22⋊D5—122no—
508C22⋊D5—241no—
509C2×Dic5—61no—
510C2×Dic5—61no—
511C2×Dic5—122no—
512C2×Dic5C2×D1211yescharacteristic
513C2×Dic5C2×D1211yescharacteristic
514C2×Dic5C2×D1211yescharacteristic
515D20—61no—
516D20—61no—
517D20—61no—
518D20—61no—
519D20—122no—
520C4×D5—21no—
521C4×D5—21no—
522C4×D5—122no—
523C5×C8—21no—
524C5×C8D3×D412yescomplemented
525#168—21no—
526#168—21no—
527C2×#41—151no—
528C22×Q8—31no—
529C22×D4—31no—
530C22×D4—151no—
531C22×D4—301no—
532AGL(1,ℤ/8)—304no—
533C2×SD16—31no—
534C2×SD16—31no—
535C2×SD16—31no—
536C2×SD16—31no—
537C2×SD16—64no—
538C2×SD16—151no—
539C2×SD16—151no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—51no—
544C22×C8D3×D511yescharacteristic, complemented
545#127—151no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—151no—
551#121—151no—
552#121—151no—
553#121—301no—
554#121—301no—
555#120—301no—
556#120—301no—
557C4×Q8—151no—
558C4×D4—51no—
559C4×D4—151no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—51no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—51no—
570C22⋊C8—51no—
571#97—51no—
572C2×C3×C5—22no—
573C2×C3×C5D4211yescharacteristic
574C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
575C2×C3×C5#57711yescharacteristic
576D15—81no—
577D15—81no—
578C3×D5—41no—
579C5×D3—42no—
580C5×D3—81no—
581C23×C3—51no—
582C23×C3D4×D511yescharacteristic
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—42no—
586C22×D3—42no—
587C22×D3—81no—
588C22×D3—101no—
589C22×D3—101no—
590C22×D3—202no—
591C22×D3—202no—
592C22×D3—401no—
593C3×D4—102no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—51no—
597C2×C3×C4—51no—
598C2×C3×C4—51no—
599C2×C3×C4—101no—
600C2×C3×C4—101no—
601C2×C3×C4D4×D511yescharacteristic
602C2×C3×C4C23×D511yescharacteristic
603#67—202no—
604#67—202no—
605#67—202no—
606#67—202no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—42no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—42no—
616D12—101no—
617D12—101no—
618D12—101no—
619D12—101no—
620D12—202no—
621D12—202no—
622D12—401no—
623D12C2×C22⋊D512yes—
624C4×D3—202no—
625C4×D3—202no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630Dic6C2×C22⋊D512yescomplemented
631C3×C8—21no—
632C3×C8—101no—
633C3×C8—101no—
634C3×C8C2×C22⋊D512yescomplemented
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—62no—
638C22×C5—121no—
639C22×C5—121no—
640C22×C5—121no—
641C22×C5—121no—
642C22×C5—121no—
643C22×C5—244no—
644C22×C5#90812yescomplemented
645C22×C5C22×D1211yescharacteristic
646C2×D5—21no—
647C2×D5—21no—
648C2×D5—21no—
649C2×D5—121no—
650C2×D5—121no—
651C2×D5—121no—
652C2×D5—121no—
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—244no—
656C4×C5—21no—
657C4×C5—62no—
658C4×C5—121no—
659C4×C5C2×D3×D411yescharacteristic
660C4×C5#100911yescharacteristic
661Dic5—21no—
662Dic5—21no—
663Dic5—21no—
664Dic5—121no—
665Dic5—121no—
666C24—61no—
667C24—301no—
668#41—302no—
669#41—601no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×Q8—62no—
673C2×Q8—61no—
674C2×Q8—121no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—51no—
678C2×D4—62no—
679C2×D4—61no—
680C2×D4—121no—
681C2×D4—151no—
682C2×D4—151no—
683C2×D4—301no—
684C2×D4—301no—
685C2×D4—301no—
686C2×D4—301no—
687C2×D4—302no—
688C2×D4—301no—
689C2×D4—301no—
690C2×D4—301no—
691C2×D4—601no—
692C2×D4—604no—
693C22×C4—51no—
694C22×C4—61no—
695C22×C4—301no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—34no—
699SD16—62no—
700SD16—62no—
701SD16—62no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—102no—
708C2×C8—22no—
709C2×C8—51no—
710C2×C8—51no—
711C2×C8C2×D3×D511yescharacteristic
712C2×C8C2×D3×D511yescharacteristic
713C4⋊C4—51no—
714C4⋊C4—151no—
715C4⋊C4—151no—
716C4⋊C4—301no—
717C4⋊C4—301no—
718C22⋊C4—51no—
719C22⋊C4—51no—
720C22⋊C4—301no—
721C22⋊C4—301no—
722C22⋊C4—301no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—51no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—101no—
733C22×C3—101no—
734C22×C3—101no—
735C22×C3#406012yescomplemented
736C22×C3C2×D4×D511yescharacteristic
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—84no—
744C2×D3—201no—
745C2×D3—201no—
746C2×D3—201no—
747C2×D3—201no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—404no—
751C3×C4—21no—
752C3×C4—101no—
753C3×C4—101no—
754C3×C4—101no—
755C3×C4#414411yescharacteristic
756C3×C4C22×C22⋊D511yescharacteristic
757Dic3—22no—
758Dic3—41no—
759Dic3—201no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—122no—
763C2×C5—241no—
764C2×C5D4×D1211yescharacteristic
765C2×C5C2×#90811yescharacteristic
766C2×C5#575111yescharacteristic
767D5—41no—
768D5—241no—
769D5—241no—
770C23—51no—
771C23—61no—
772C23—61no—
773C23—122no—
774C23—122no—
775C23—241no—
776C23—301no—
777C23—301no—
778C23—602no—
779C23—602no—
780C23—1201no—
781C23D5×D1211yescharacteristic
782Q8—32no—
783Q8—61no—
784Q8—61no—
785Q8—61no—
786Q8—122no—
787D4—32no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—102no—
792D4—122no—
793D4—301no—
794D4—301no—
795D4—301no—
796D4—301no—
797D4—602no—
798D4—602no—
799D4—602no—
800D4—602no—
801D4—602no—
802D4—602no—
803D4—1201no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—51no—
807C2×C4—51no—
808C2×C4—51no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—122no—
814C2×C4—301no—
815C2×C4—301no—
816C2×C4—602no—
817C2×C4—602no—
818C2×C4D5×D1211yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—21no—
821C8—101no—
822C8—101no—
823C8D3×C22⋊D512yescomplemented
824C2×C3—22no—
825C2×C3—201no—
826C2×C3C2×#406011yescharacteristic
827C2×C3#6609611yescharacteristic
828C2×C3D4×C22⋊D511yescharacteristic
829D3—42no—
830D3—81no—
831D3—401no—
832D3—401no—
833C5#7949411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—62no—
837C22—101no—
838C22—101no—
839C22—101no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—244no—
846C22—601no—
847C22—601no—
848C22—601no—
849C22—601no—
850C22—601no—
851C22—601no—
852C22—1204no—
853C22#9124912yescomplemented
854C22C2×D5×D1211yescharacteristic
855C4—21no—
856C4—62no—
857C4—101no—
858C4—101no—
859C4—101no—
860C4—121no—
861C4—601no—
862C4—601no—
863C4#9201811yescharacteristic
864C4C2×D3×C22⋊D511yescharacteristic
865C3#1061559511yescharacteristic, complemented, Sylow
866C2—22no—
867C2—122no—
868C2—201no—
869C2—241no—
870C2—1201no—
871C2—1201no—
872C2C2×#9124911yescharacteristic
873C2#1175396011yescharacteristic
874C2D12×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C5×#204C2semidirect
2. D12×C22⋊D5C2semidirect
3. #11754544C2semidirect
4. C2×#91249C2semidirect
5. #11751216C2semidirect
6. C3×#65400C2semidirect
7. #11748544C2semidirect
8. #11748520C2semidirect
9. #11748114C2semidirect
10. #11747997C2semidirect
11. #11747902C2semidirect
12. #11747900C2semidirect
13. #11747842C2semidirect
14. #11747770C2semidirect
15. #11747769C2semidirect
18. C22×C5×Dic6C22semidirect
21. C2×#6773C22semidirect
22. C22×C3×C5×C8C22semidirect
24. #91819C22semidirect
25. C2×D120C22semidirect
29. C2×C5×#204C22semidirect
30. C2×C5×#204C22semidirect
32. C2×C3×#676C22semidirect
43. #91375C22semidirect
44. #91359C22semidirect
45. Dic5×Dic6C22semidirect
46. C2×#6660C22semidirect
47. C2×#6660C22semidirect
49. C2×#6654C22semidirect
51. #91105C22semidirect
52. #91105C22semidirect
53. #91102C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×#3952C22semidirect
56. C3×#3947C22semidirect
57. C3×#3946C22semidirect
58. #90973C22semidirect
59. #90973C22semidirect
61. #90967C22semidirect
77. #65400D3semidirect
121. C5×#204D4semidirect
142. C22×#204D5semidirect
166. C22×C5×C8C2×D3semidirect
189. C2×#676C2×D3semidirect
194. C22⋊#168C2×D3semidirect
197. #3952C2×D3semidirect
199. #3947C2×D3semidirect
200. #3946C2×D3semidirect
238. C5×Dic6C2×D4semidirect
253. C3×C5×C8C2×D4semidirect
260. C22×Dic6C2×D5semidirect
262. C22×C3×C8C2×D5semidirect
278. C2×#204C2×D5semidirect
279. C2×#204C2×D5semidirect
381. C22×C3×C5AGL(1,ℤ/8)semidirect
472. #204C22⋊D5semidirect
524. C5×C8D3×D4semidirect
544. C22×C8D3×D5semidirect
630. Dic6C2×C22⋊D5semidirect
634. C3×C8C2×C22⋊D5semidirect
644. C22×C5#908semidirect
729. C3×C5#3265semidirect
735. C22×C3#4060semidirect
823. C8D3×C22⋊D5semidirect
833. C5#79494semidirect
853. C22#91249semidirect
865. C3#10615595semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2042
D12×C22⋊D52
#117545442
C2×#912492
#117512162
C3×#654002
#117485442
#117485202
#117481142
#117479972
#117479022
#117479002
#117478422
#117477702
#117477692
#106155953
#794945