Finite Group Databasebeta

← #14453544

Subgroups — #14453544

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
1C5×D4×#67C211yesmaximal, characteristic, complemented
2C22×C3×#687C211yesmaximal, characteristic, complemented
3C2×#91496C211yesmaximal, characteristic, complemented
4#11754321C211yesmaximal, characteristic, complemented
5#11751318C211yesmaximal, characteristic, complemented
6#11749162C211yesmaximal, characteristic, complemented
7#11749080C211yesmaximal, characteristic, complemented
8#11749076C211yesmaximal, characteristic, complemented
9#11749058C211yesmaximal, characteristic, complemented
10#11749051C211yesmaximal, characteristic, complemented
11#11749010C211yesmaximal, characteristic, complemented
12#11749005C211yesmaximal, characteristic, complemented
13#11748529C211yesmaximal, characteristic, complemented
14#11748514C211yesmaximal, characteristic, complemented
15#11748500C211yesmaximal, characteristic, complemented
16#10615222—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C5×#67—21no—
19C2×C5×D3×D4C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic, complemented
21C2×#6769C2211yescharacteristic, complemented
22C2×#6715C2211yescharacteristic
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic, complemented
25C5×#953—21no—
26C5×#940C2211yescharacteristic
27C5×#939—21no—
28C5×#938C2211yescharacteristic
29C5×#937—21no—
30C5×D4×Dic3C2211yescharacteristic
31C5×#930C2211yescharacteristic
32C4×C5×#67C2211yescharacteristic
33C2×C3×#687—24no—
34C2×C3×#687C2211yescharacteristic
35C2×C3×#687C2211yescharacteristic
36C2×C3×#687C2211yescharacteristic, complemented
37C2×C3×#687C2211yescharacteristic, complemented
38C22×C3×#168C2211yescharacteristic, complemented
39#91566—21no—
40#91552—21no—
41#91496—24no—
42#91411—21no—
43#91374C2211yescharacteristic, complemented
44#91369C2211yescharacteristic, complemented
45Dic3×Dic10C2211yescharacteristic, complemented
46#91326—21no—
47C2×#6656C2211yescharacteristic, complemented
48C2×#6656C2211yescharacteristic, complemented
49C2×#6654C2211yescharacteristic, complemented
50C2×#6650C2211yescharacteristic, complemented
51#91116C2211yescharacteristic
52#91116C2211yescharacteristic, complemented
53#91114C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55Dic3⋊#168C2211yescharacteristic, complemented
56#90970C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90969C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#83864—51nomaximal, Hall
63C5×D42—31no—
64C22×#687D311yescharacteristic, complemented
65C2×#4078—31no—
66#65886—31no—
67#65507—31no—
68#65506—31no—
69#65364—31no—
70#65363—31no—
71#65331—31no—
72#65329—31no—
73#65327—31no—
74#65326—31no—
75#65307—31no—
76#65305—31no—
77#65300—31no—
78C24×C3×C5—21no—
79C23×C5×D3—21no—
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4C2311yescharacteristic
84C2×C3×C5×D4C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87C2×D60C2311yescharacteristic
88C2×C5×#67—21no—
89C2×C5×#67—21no—
90C2×C5×#67—21no—
91C2×C5×#67—21no—
92C2×C5×#67—21no—
93C2×C5×#67—44no—
94C2×C5×#67D411yescharacteristic
95C22×C5×Dic3—21no—
96C5×D3×D4—22no—
97C5×D3×D4—41no—
98C2×C5×D12C2311yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C22×C3×Dic5—21no—
101C2×C3×Dic10—22no—
102C2×C3×Dic10—21no—
103C2×C3×Dic10—41no—
104C2×C3×Dic10C2311yescharacteristic
105C2×C3×Dic10C2311yescharacteristic
106C2×#1203—21no—
107C2×#1200—21no—
108#6769—22no—
109#6769—41no—
110#6715—22no—
111#6715—41no—
112#6714—21no—
113C4⋊Dic15C2311yescharacteristic
114C2×C3⋊#168C2311yescharacteristic
115C2×C3⋊#168C2311yescharacteristic
116C5×#217—21no—
117C5×#217—21no—
118C5×#217D411yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4D411yescharacteristic
121C5×C4⋊Dic3C2311yescharacteristic
122C5×Dic3⋊C4D411yescharacteristic
123C4×C5×Dic3C2311yescharacteristic
124C3×#687—22no—
125C3×#687—22no—
126C3×#687—22no—
127C3×#687D414yescomplemented
128C2×C3×#168—22no—
129C2×C3×#168C2311yescharacteristic
130C2×C3×#168C2311yescharacteristic
131#6669—21no—
132#6668—21no—
133#6667—21no—
134#6667—21no—
135(C2×D3)⋊Dic5—21no—
136Dic3×Dic5—21no—
137#6656—22no—
138#6656—41no—
139#6654—22no—
140#6650—22no—
141C22×C3×SD16—51no—
142#5817—51no—
143D4×#67D511yescharacteristic, complemented
144C2×#914—51no—
145#5227—51no—
146#5217—51no—
147#5176—51no—
148#5174—51no—
149#5172—51no—
150#5169—51no—
151#5165—51no—
152#5164—51no—
153#5163—51no—
154#5115—51no—
155#5111—51no—
156C22×C5×D4—31no—
157C22×C5×D4—61no—
158C22×C5×D4C2×D311yescharacteristic
159C2×#709—31no—
160C22×Dic10C2×D311yescharacteristic, complemented
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169#4085—61no—
170C2×#687—24no—
171C2×#687—31no—
172C2×#687—31no—
173C2×#687C2×D311yescharacteristic
174C2×#687C2×D311yescharacteristic
175C2×#687C2×D311yescharacteristic, complemented
176C2×#687C2×D311yescharacteristic, complemented
177#4078—64no—
178C2×#686—31no—
179C2×#686—31no—
180C2×#686—31no—
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168C2×D311yescharacteristic, complemented
185#4042—61no—
186#4031—61no—
187#4027—61no—
188#4021—31no—
189C4×Dic10—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942—31no—
196#3942—31no—
197#3941—31no—
198#3939—31no—
199C4⋊#168—31no—
200#3935—31no—
201#3265—151noSylow
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—42no—
205C23×C3×C5—42no—
206C23×C3×C5—81no—
207C23×C3×C5C2×D411yescharacteristic
208C22×D15—21no—
209C22×C5×D3—21no—
210C22×C5×D3—42no—
211C22×C5×D3—42no—
212C22×C5×D3—81no—
213C22×C5×D3C2×D411yescharacteristic
214C3×C5×D4—21no—
215C3×C5×D4—21no—
216C3×C5×D4—21no—
217C3×C5×D4—42no—
218C3×C5×D4C2×D412yes—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5C2×D411yescharacteristic
222C2×C3×C4×C5C2411yescharacteristic
223#1220—42no—
224C2×Dic15—21no—
225D60—21no—
226D60—21no—
227C5×#67—22no—
228C5×#67—42no—
229C5×#67—42no—
230C5×#67—42no—
231C5×#67—42no—
232C5×#67—81no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—42no—
235C2×C5×Dic3C2×D411yescharacteristic
236C2×C5×Dic3C2×D411yescharacteristic
237C2×C5×Dic3C2×D411yescharacteristic
238C5×D12—21no—
239C5×D12—21no—
240C4×C5×D3—21no—
241C4×C5×D3—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—42no—
245C3×Dic10—21no—
246C3×Dic10—21no—
247C3×Dic10—21no—
248C3×Dic10—42no—
249C3×Dic10C2×D412yescomplemented
250#1203—42no—
251#1200—42no—
252C3⋊#168—21no—
253C3⋊#168—21no—
254C3×#168—21no—
255C3×#168C2×D412yescomplemented
256C22×C3×Q8—51no—
257C22×C3×D4C2×D511yescharacteristic
258C22×#67—21no—
259C2×#239—51no—
260C2×D3×D4C2×D511yescharacteristic
261C2×C3×SD16—51no—
262C2×C3×SD16—51no—
263C2×C3×SD16—51no—
264C2×C3×SD16—51no—
265C2×C3×SD16—104no—
266C22×C3×C8—51no—
267#953—21no—
268#947—51no—
269#947—101no—
270#946—51no—
271#946—101no—
272Q8×Dic3—51no—
273C2×#215—51no—
274C2×#215—51no—
275#940C2×D511yescharacteristic
276#939—21no—
277#938C2×D511yescharacteristic
278#937—21no—
279D4×Dic3C2×D511yescharacteristic
280C2×#213—51no—
281C2×#213—51no—
282#930—51no—
283#930—101no—
284#930C2×D511yescharacteristic
285C4×#67—101no—
286C4×#67C2×D511yescharacteristic
287#914—104no—
288C2×D24—51no—
289C2×ΓL(1,𝔽25)—51no—
290#835—51no—
291#835—51no—
292#832—51no—
293#832—51no—
294#830—51no—
295#821—51no—
296#821—51no—
297(C2×D3)⋊C8—51no—
298#818—51no—
299#815—51no—
300Dic3⋊C8—51no—
301C24×C5—21no—
302C24×C5—61no—
303C2×C5×D4—22no—
304C2×C5×D4—21no—
305C2×C5×D4—31no—
306C2×C5×D4—31no—
307C2×C5×D4—41no—
308C2×C5×D4—61no—
309C2×C5×D4—61no—
310C2×C5×D4—61no—
311C2×C5×D4—62no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—121no—
315C2×C5×D4—124no—
316C2×C5×D4C22×D311yescharacteristic
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—31no—
319C22×C4×C5—61no—
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—61no—
322C2×C22⋊D5—61no—
323C22×Dic5—21no—
324#709—62no—
325#709—121no—
326C2×D20—31no—
327C2×C4×D5—61no—
328C2×Dic10—22no—
329C2×Dic10—21no—
330C2×Dic10—41no—
331C2×Dic10C22×D311yescharacteristic
332C2×Dic10C22×D311yescharacteristic
333C5×C4⋊C4—31no—
334C5×C4⋊C4—31no—
335C5×C22⋊C4—31no—
336C5×C22⋊C4—31no—
337C5×C22⋊C4—61no—
338C5×C22⋊C4—61no—
339C5×C22⋊C4—61no—
340C42×C5—31no—
341C22⋊Dic5—61no—
342#687—22no—
343#687—22no—
344#687—22no—
345#687—62no—
346#687—121no—
347#687#6714yescomplemented
348#686—62no—
349#686—62no—
350#686—121no—
351#685—61no—
352#685—61no—
353#685—61no—
354C4⋊Dic5—31no—
355#683—61no—
356#683—61no—
357C4×Dic5—61no—
358#681—62no—
359C2×#168—22no—
360C2×#168—31no—
361C2×#168—31no—
362C2×#168C22×D311yescharacteristic
363C2×#168C22×D311yescharacteristic
364C2×AGL(1,ℤ/8)—151no—
365C22×SD16—51no—
366#548—151no—
367D42—31no—
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—151no—
379C22×C3×C5—21no—
380C22×C3×C5—21no—
381C22×C3×C5—22no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—84no—
388C22×C3×C5AGL(1,ℤ/8)12yescomplemented
389C22×C3×C5C22×D411yescharacteristic
390C2×D15—41no—
391C2×D15—41no—
392C2×D15—41no—
393C2×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—21no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C2×C5×D3—84no—
400C3×C4×C5—21no—
401C3×C4×C5C22×D411yescharacteristic
402C3×C4×C5H(5,𝔽2)11yescharacteristic
403Dic15—41no—
404C3×Dic5—22no—
405C3×Dic5—41no—
406C5×Dic3—21no—
407C5×Dic3—21no—
408C5×Dic3—21no—
409C5×Dic3—41no—
410C24×C3—21no—
411C23×D3—21no—
412C2×C3×Q8—51no—
413C2×C3×Q8—51no—
414C2×C3×Q8—102no—
415C2×C3×Q8—101no—
416C2×C3×Q8—201no—
417C2×C3×D4—22no—
418C2×C3×D4—21no—
419C2×C3×D4—41no—
420C2×C3×D4C22×D511yescharacteristic
421C2×C3×D4C22×D511yescharacteristic
422C22×C3×C4—101no—
423C22×C3×C4C22×D511yescharacteristic
424C2×#67—21no—
425C2×#67—21no—
426C2×#67—21no—
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—44no—
430C2×#67—101no—
431C2×#67C22⋊D511yescharacteristic
432C22×Dic3—21no—
433#239—102no—
434#239—201no—
435D3×D4—22no—
436D3×D4—41no—
437C2×D12—51no—
438C2×D12—101no—
439C2×D12C22×D511yescharacteristic
440C2×C4×D3—101no—
441C2×C4×D3C22×D511yescharacteristic
442C3×SD16—54no—
443C3×SD16—102no—
444C3×SD16—102no—
445C3×SD16—102no—
446C2×C3×C8—51no—
447C2×C3×C8—51no—
448C2×C3×C8—102no—
449#217—21no—
450#217—21no—
451#217C22⋊D511yescharacteristic
452#215—102no—
453#215—201no—
454#213—102no—
455#213—201no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—101no—
458(C2×D3)⋊C4—101no—
459(C2×D3)⋊C4—101no—
460(C2×D3)⋊C4—101no—
461(C2×D3)⋊C4C22⋊D511yescharacteristic
462C4⋊Dic3—51no—
463C4⋊Dic3—101no—
464C4⋊Dic3C22×D511yescharacteristic
465Dic3⋊C4—101no—
466Dic3⋊C4C22⋊D511yescharacteristic
467C4×Dic3—101no—
468C4×Dic3C22×D511yescharacteristic
469C2×C3⋊C8—51no—
470C2×C3⋊C8—51no—
471D24—102no—
472ΓL(1,𝔽25)—102no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—31no—
476C23×C5—42no—
477C23×C5—42no—
478C23×C5—61no—
479C23×C5—81no—
480C23×C5—122no—
481C23×C5—122no—
482C23×C5—241no—
483C23×C5D3×D411yescharacteristic
484C22×D5—61no—
485C5×D4—21no—
486C5×D4—21no—
487C5×D4—21no—
488C5×D4—42no—
489C5×D4—62no—
490C5×D4—61no—
491C5×D4—61no—
492C5×D4—122no—
493C5×D4—122no—
494C5×D4—122no—
495C5×D4—122no—
496C5×D4—241no—
497C5×D4C2×#6712yes—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—31no—
501C2×C4×C5—31no—
502C2×C4×C5—31no—
503C2×C4×C5—61no—
504C2×C4×C5—61no—
505C2×C4×C5—61no—
506C2×C4×C5—122no—
507C2×C4×C5D3×D411yescharacteristic
508C2×C4×C5C23×D311yescharacteristic
509C22⋊D5—122no—
510C22⋊D5—122no—
511C2×Dic5—21no—
512C2×Dic5—21no—
513C2×Dic5—42no—
514C2×Dic5—61no—
515D20—61no—
516D20—61no—
517C4×D5—122no—
518Dic10—21no—
519Dic10—21no—
520Dic10—21no—
521Dic10—42no—
522Dic10C2×#6712yescomplemented
523#168—21no—
524#168—61no—
525#168—61no—
526#168C2×#6712yescomplemented
527C2×#41—151no—
528C22×Q8—51no—
529C22×D4—31no—
530C22×D4—61no—
531C22×D4D3×D511yescharacteristic
532AGL(1,ℤ/8)—304no—
533C2×SD16—51no—
534C2×SD16—51no—
535C2×SD16—51no—
536C2×SD16—51no—
537C2×SD16—104no—
538C2×SD16—151no—
539C2×SD16—151no—
540C2×D8—151no—
541C2×D8—151no—
542C2×D8—151no—
543C2×M16—151no—
544C22×C8—51no—
545#127—31no—
546#124—151no—
547#124—301no—
548C22⋊Q8—151no—
549C22⋊Q8—301no—
550#121—31no—
551#121—31no—
552#121—61no—
553#121—151no—
554#121—301no—
555#120—61no—
556#120—61no—
557C4×Q8—151no—
558C4×D4—31no—
559C4×D4—31no—
560C4×D4—301no—
561#107—151no—
562C4⋊C8—151no—
563#103—151no—
564#103—151no—
565#102—151no—
566#102—151no—
567#102—151no—
568#102—151no—
569C22⋊C8—151no—
570C22⋊C8—151no—
571#97—151no—
572C2×C3×C5—22no—
573C2×C3×C5—42no—
574C2×C3×C5—81no—
575C2×C3×C5D4211yescharacteristic
576C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
577C2×C3×C5#57711yescharacteristic
578D15—81no—
579C5×D3—41no—
580C5×D3—81no—
581C23×C3—21no—
582C23×C3—21no—
583C23×C3—42no—
584C23×C3—42no—
585C23×C3—81no—
586C23×C3C2×C22⋊D511yescharacteristic
587C22×D3—21no—
588C22×D3—42no—
589C22×D3—42no—
590C22×D3—81no—
591C22×D3—101no—
592C22×D3C2×C22⋊D511yescharacteristic
593C3×Q8—52no—
594C3×Q8—101no—
595C3×Q8—101no—
596C3×Q8—101no—
597C3×Q8—202no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—42no—
602C3×D4D4×D512yes—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—101no—
606C2×C3×C4—101no—
607C2×C3×C4—202no—
608C2×C3×C4C2×C22⋊D511yescharacteristic
609C2×C3×C4C23×D511yescharacteristic
610#67—22no—
611#67—42no—
612#67—42no—
613#67—42no—
614#67—42no—
615#67—81no—
616#67—202no—
617C2×Dic3—21no—
618C2×Dic3—42no—
619C2×Dic3—101no—
620C2×Dic3C2×C22⋊D511yescharacteristic
621C2×Dic3C2×C22⋊D511yescharacteristic
622C2×Dic3C2×C22⋊D511yescharacteristic
623D12—21no—
624D12—21no—
625D12—101no—
626D12—101no—
627D12—202no—
628C4×D3—21no—
629C4×D3—21no—
630C4×D3—202no—
631C3×C8—52no—
632C3×C8—101no—
633C3⋊C8—101no—
634C3⋊C8—101no—
635C22×C5—21no—
636C22×C5—21no—
637C22×C5—22no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5—41no—
641C22×C5—41no—
642C22×C5—41no—
643C22×C5—61no—
644C22×C5—61no—
645C22×C5—61no—
646C22×C5—84no—
647C22×C5—121no—
648C22×C5—121no—
649C22×C5—121no—
650C22×C5—244no—
651C22×C5#91412yescomplemented
652C22×C5C2×D3×D411yescharacteristic
653C2×D5—121no—
654C2×D5—121no—
655C2×D5—121no—
656C4×C5—21no—
657C4×C5—61no—
658C4×C5—61no—
659C4×C5—61no—
660C4×C5—121no—
661C4×C5#100411yescharacteristic
662C4×C5C22×#6711yescharacteristic
663Dic5—22no—
664Dic5—41no—
665Dic5—121no—
666C24—21no—
667C24—61no—
668#41—302no—
669#41—601no—
670C2×Q8—51no—
671C2×Q8—51no—
672C2×Q8—102no—
673C2×Q8—101no—
674C2×Q8—201no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—41no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—62no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—121no—
687C2×D4—124no—
688C2×D4—151no—
689C2×D4—301no—
690C2×D4—301no—
691C2×D4C2×D3×D511yescharacteristic
692C2×D4C2×D3×D511yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—101no—
696C22×C4—301no—
697C22×C4C2×D3×D511yescharacteristic
698SD16—54no—
699SD16—102no—
700SD16—102no—
701SD16—102no—
702SD16—302no—
703SD16—601no—
704D8—302no—
705D8—302no—
706D8—601no—
707M16—302no—
708C2×C8—51no—
709C2×C8—51no—
710C2×C8—102no—
711C2×C8—151no—
712C2×C8—151no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—151no—
716C4⋊C4—301no—
717C4⋊C4—301no—
718C22⋊C4—31no—
719C22⋊C4—31no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—301no—
724C22⋊C4—301no—
725C22⋊C4—301no—
726C22⋊C4—301no—
727C42—31no—
728C42—301no—
729C3×C5#326511yescharacteristic, complemented, Hall
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—84no—
739C22×C3#407812yescomplemented
740C22×C3C22×C22⋊D511yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—84no—
748C2×D3—201no—
749C2×D3—201no—
750C2×D3—201no—
751C3×C4—21no—
752C3×C4—102no—
753C3×C4—201no—
754C3×C4C2×D4×D511yescharacteristic
755C3×C4#414411yescharacteristic
756Dic3—21no—
757Dic3—21no—
758Dic3—21no—
759Dic3—41no—
760Dic3—201no—
761C2×C5—22no—
762C2×C5—42no—
763C2×C5—81no—
764C2×C5—121no—
765C2×C5—241no—
766C2×C5C2×#91411yescharacteristic
767C2×C5#576211yescharacteristic
768C2×C5D4×#6711yescharacteristic
769D5—241no—
770C23—21no—
771C23—21no—
772C23—31no—
773C23—42no—
774C23—42no—
775C23—61no—
776C23—81no—
777C23—122no—
778C23—122no—
779C23—241no—
780C23—301no—
781C23D3×C22⋊D511yescharacteristic
782Q8—52no—
783Q8—101no—
784Q8—101no—
785Q8—101no—
786Q8—202no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—42no—
791D4—62no—
792D4—61no—
793D4—61no—
794D4—122no—
795D4—122no—
796D4—122no—
797D4—122no—
798D4—241no—
799D4—301no—
800D4—301no—
801D4—602no—
802D4—602no—
803D4D5×#6712yes—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—122no—
815C2×C4—202no—
816C2×C4—301no—
817C2×C4—602no—
818C2×C4D3×C22⋊D511yescharacteristic
819C2×C4C22×D3×D511yescharacteristic
820C8—52no—
821C8—101no—
822C8—301no—
823C8—301no—
824C2×C3—22no—
825C2×C3—42no—
826C2×C3—81no—
827C2×C3C2×#407811yescharacteristic
828C2×C3D4×C22⋊D511yescharacteristic
829C2×C3#6617011yescharacteristic
830D3—41no—
831D3—81no—
832D3—401no—
833C5#8386411yescharacteristic, complemented, Sylow
834C22—21no—
835C22—21no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—84no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—244no—
850C22—601no—
851C22—601no—
852C22—601no—
853C22#9149612yescomplemented
854C22C2×D3×C22⋊D511yescharacteristic
855C4—21no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—102no—
860C4—121no—
861C4—201no—
862C4—601no—
863C4C2×D5×#6711yescharacteristic
864C4#9204911yescharacteristic
865C3#1061522211yescharacteristic, complemented, Sylow
866C2—22no—
867C2—42no—
868C2—81no—
869C2—121no—
870C2—241no—
871C2—1201no—
872C2#1175471111yescharacteristic
873C2C2×#9149611yescharacteristic
874C2#67×C22⋊D511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3265
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C5×D4×#67C2semidirect
2. C22×C3×#687C2semidirect
3. C2×#91496C2semidirect
4. #11754321C2semidirect
5. #11751318C2semidirect
6. #11749162C2semidirect
7. #11749080C2semidirect
8. #11749076C2semidirect
9. #11749058C2semidirect
10. #11749051C2semidirect
11. #11749010C2semidirect
12. #11749005C2semidirect
13. #11748529C2semidirect
14. #11748514C2semidirect
15. #11748500C2semidirect
20. C22×C3×Dic10C22semidirect
21. C2×#6769C22semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
36. C2×C3×#687C22semidirect
37. C2×C3×#687C22semidirect
38. C22×C3×#168C22semidirect
43. #91374C22semidirect
44. #91369C22semidirect
45. Dic3×Dic10C22semidirect
47. C2×#6656C22semidirect
48. C2×#6656C22semidirect
49. C2×#6654C22semidirect
50. C2×#6650C22semidirect
52. #91116C22semidirect
53. #91114C22semidirect
54. #90988C22semidirect
55. Dic3⋊#168C22semidirect
56. #90970C22semidirect
57. #90970C22semidirect
58. #90969C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
64. C22×#687D3semidirect
127. C3×#687D4semidirect
143. D4×#67D5semidirect
160. C22×Dic10C2×D3semidirect
175. C2×#687C2×D3semidirect
176. C2×#687C2×D3semidirect
184. C22×#168C2×D3semidirect
249. C3×Dic10C2×D4semidirect
255. C3×#168C2×D4semidirect
347. #687#67semidirect
388. C22×C3×C5AGL(1,ℤ/8)semidirect
522. Dic10C2×#67semidirect
526. #168C2×#67semidirect
651. C22×C5#914semidirect
729. C3×C5#3265semidirect
739. C22×C3#4078semidirect
833. C5#83864semidirect
853. C22#91496semidirect
865. C3#10615222semidirect

Maximal subgroups

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

subgroupindex
C5×D4×#672
C22×C3×#6872
C2×#914962
#117543212
#117513182
#117491622
#117490802
#117490762
#117490582
#117490512
#117490102
#117490052
#117485292
#117485142
#117485002
#106152223
#838645