Finite Group Databasebeta

← #14453337

Subgroups — #14453337

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
1C5×#5676C211yesmaximal, characteristic, complemented
2C2×#91504C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4D12×D20C211yesmaximal, characteristic, complemented
5#11751159C211yesmaximal, characteristic, complemented
6C3×#65346C211yesmaximal, characteristic, complemented
7#11749398C211yesmaximal, characteristic, complemented
8#11749282C211yesmaximal, characteristic, complemented
9#11749280C211yesmaximal, characteristic, complemented
10#11749152C211yesmaximal, characteristic, complemented
11#11749037C211yesmaximal, characteristic, complemented
12#11749033C211yesmaximal, characteristic, complemented
13#11747037C211yesmaximal, characteristic, complemented
14#11747021C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic, complemented
18C2×C5×D3×D4C2211yescharacteristic, complemented
19C2×D3×D20C2211yescharacteristic
20C2×D3×D20C2211yescharacteristic, complemented
21C2×D5×D12—21no—
22C3×C5×#124C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic, complemented
24C2×#6717C2211yescharacteristic, complemented
25C2×#6715C2211yescharacteristic, complemented
26C2×#6715C2211yescharacteristic, complemented
27#91763C2211yescharacteristic, complemented
28C5×#946C2211yescharacteristic, complemented
29C5×#938C2211yescharacteristic, complemented
30C5×#884—21no—
31C5×#883—21no—
32C5×#882—21no—
33C5×D3×C22⋊C4—21no—
34C4×C5×D12C2211yescharacteristic
35C4×C5×D12C2211yescharacteristic, complemented
36C2×C3×#688C2211yescharacteristic, complemented
37C2×C3×#686C2211yescharacteristic
38C3×C4×D20C2211yescharacteristic, complemented
39#91504—24no—
40D3×#686—24no—
41#91476—21no—
42#91476—21no—
43#91460C2211yescharacteristic
44#91460C2211yescharacteristic, complemented
45#91450—21no—
46C2×#6654C2211yescharacteristic, complemented
47C2×#6654C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91087C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3964C2211yescharacteristic, complemented
54C3×C4⋊#168C2211yescharacteristic, complemented
55#90986C2211yescharacteristic, complemented
56#90969C2211yescharacteristic, complemented
57#90969C2211yescharacteristic, complemented
58#90966C2211yescharacteristic, complemented
59#90964C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80552—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20—31no—
67#65527—31no—
68#65506—31no—
69#65347—31no—
70#65346D311yescharacteristic, complemented
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325—31no—
75#65304—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C22×D3×D5—21no—
80C22×D3×D5—21no—
81C2×C3×C5×Q8C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C2×D60—21no—
84C2×D60—21no—
85C2×D60C2311yescharacteristic
86C2×D60C2311yescharacteristic
87C2×C5×#67—21no—
88C2×C5×#67—21no—
89C5×#239—22no—
90C5×#239—41no—
91C5×D3×D4—22no—
92C5×D3×D4—41no—
93C2×C5×D12—21no—
94C2×C5×D12D411yescharacteristic
95C2×C5×D12C2311yescharacteristic
96C2×C4×C5×D3—21no—
97C2×C4×C5×D3—21no—
98C2×C4×C5×D3C2311yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C2×C3×D20C2311yescharacteristic
101C2×C3×C4×D5—21no—
102C2×#1203—21no—
103C2×#1203—21no—
104C2×#1202—21no—
105C2×#1202—21no—
106D3×D20—22no—
107D3×D20—22no—
108D3×D20—41no—
109D3×D20—41no—
110D5×D12—44no—
111C3×C5×C22⋊C4—21no—
112C3×C5×C22⋊C4—21no—
113C3×C42×C5C2311yescharacteristic
114#6717—22no—
115#6717—41no—
116#6715—22no—
117#6715—41no—
118C2×C3⋊#168C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C5×#217—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4D411yescharacteristic
124C5×(C2×D3)⋊C4D411yescharacteristic
125C5×C4⋊Dic3D411yescharacteristic
126C5×C4⋊Dic3C2311yescharacteristic
127C5×Dic3⋊C4—21no—
128C3×#688—22no—
129C3×#686—22no—
130C3×#685—21no—
131C3×C4⋊Dic5C2311yescharacteristic
132C2×C3×#168C2311yescharacteristic
133C2×C3×#168C2311yescharacteristic
134#6667—21no—
135#6667—21no—
136#6654—22no—
137#6654—22no—
138#6652D414yescomplemented
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×D8—51no—
143#5676D511yescharacteristic, complemented
144D4×D12—51no—
145C3×#463—51no—
146#5169—51no—
147#5156—51no—
148#5058—51no—
149#5014—51no—
150#4843—51no—
151#4836—51no—
152#4810—51no—
153#4807—51no—
154#4782—51no—
155#4773—51no—
156C2×C5×#41—31no—
157C22×C5×D4—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20—31no—
161C5×#124C2×D311yescharacteristic, complemented
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—31no—
165C5×#121—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
169C2×C5×C22⋊C4—61no—
170#4095—64no—
171C2×#688—31no—
172C2×#688—31no—
173C2×#688C2×D311yescharacteristic, complemented
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—31no—
179C2×#686—64no—
180C2×#686C2×D311yescharacteristic
181#4076—31no—
182#4076—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4041—61no—
186#4028—61no—
187#4028—61no—
188#4020—31no—
189C4×D20C2×D311yescharacteristic, complemented
190#3967C2×D311yescharacteristic, complemented
191#3964—31no—
192#3964C2×D311yescharacteristic, complemented
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3941—31no—
196#3941—31no—
197#3941—31no—
198#3940—31no—
199C4⋊#168C2×D311yescharacteristic, complemented
200#3935—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C22×D15—21no—
204C22×D15—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—81no—
209C22×C5×D3C2×D411yescharacteristic
210C22×C5×D3C2×D411yescharacteristic
211C22×C3×D5—21no—
212C2×D3×D5—42no—
213C2×D3×D5—42no—
214C2×D3×D5—42no—
215C2×D3×D5—42no—
216C2×D3×D5—81no—
217C2×D3×D5—81no—
218C3×C5×Q8—21no—
219C3×C5×Q8—21no—
220C3×C5×D4—21no—
221C3×C5×D4—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226D60—21no—
227D60—21no—
228D60—21no—
229D60—21no—
230D60—42no—
231D60—81no—
232C5×#67—42no—
233C5×#67—81no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3C2×D411yescharacteristic
236C2×C5×Dic3C2×D411yescharacteristic
237C5×D12—22no—
238C5×D12—21no—
239C5×D12—42no—
240C5×D12C2×D412yescomplemented
241C4×C5×D3—21no—
242C4×C5×D3—21no—
243C4×C5×D3—21no—
244C4×C5×D3—21no—
245C4×C5×D3—42no—
246C4×C5×D3—81no—
247C2×C3×Dic5—21no—
248C3×D20—21no—
249C3×D20C2×D412yes—
250C3×C4×D5—42no—
251#1203—42no—
252#1203—42no—
253#1202—42no—
254#1202—42no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×#239C2×D511yescharacteristic, complemented
260C2×D3×D4—51no—
261C2×D3×D4—51no—
262C2×D3×D4C2×D511yescharacteristic, complemented
263C22×D12—101no—
264C2×C3×SD16—51no—
265C2×C3×D8—51no—
266C3×#124C2×D511yescharacteristic, complemented
267C3×C4×D4—51no—
268#946C2×D511yescharacteristic, complemented
269C2×#215—51no—
270C2×#215—51no—
271#938C2×D511yescharacteristic, complemented
272C2×#213—51no—
273C2×#213—51no—
274C2×#213—51no—
275#930—101no—
276#914—104no—
277D3×D8—104no—
278C2×D24—51no—
279C2×D24—51no—
280C2×ΓL(1,𝔽25)—51no—
281C2×D3×C8—51no—
282#895—51no—
283#895—51no—
284#884—21no—
285#883—21no—
286#882—21no—
287#882—101no—
288#882—101no—
289D3×C22⋊C4—21no—
290#874—51no—
291C4×D12C2×D511yescharacteristic
292C4×D12C2×D511yescharacteristic, complemented
293C3×C4⋊C8—51no—
294C3×#103—51no—
295C3×#102—51no—
296#832—51no—
297#821—51no—
298#821—51no—
299(C2×D3)⋊C8—51no—
300(C2×D3)⋊C8—51no—
301#809—51no—
302#808—51no—
303#803—51no—
304C24×C5—61no—
305C23×D5—61no—
306C23×D5—61no—
307C5×#41—62no—
308C5×#41—121no—
309C2×C5×Q8C22×D311yescharacteristic
310C2×C5×D4—31no—
311C2×C5×D4—31no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—62no—
315C2×C5×D4—61no—
316C2×C5×D4—121no—
317C2×C5×D4C22×D311yescharacteristic
318C22×C4×C5—31no—
319C22×C4×C5—31no—
320C22×C4×C5—61no—
321C22×C4×C5—61no—
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324D4×D5—124no—
325C2×D20—31no—
326C2×D20—31no—
327C2×D20—62no—
328C2×D20—62no—
329C2×D20—61no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—121no—
334C2×D20—121no—
335C2×D20C22×D311yescharacteristic
336C2×C4×D5—21no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4—31no—
339C5×C4⋊C4—61no—
340C5×C22⋊C4—21no—
341C5×C22⋊C4—21no—
342C5×C22⋊C4—31no—
343C5×C22⋊C4—31no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4—61no—
346C5×C22⋊C4—61no—
347C42×C5C22×D311yescharacteristic
348#688—22no—
349#688—62no—
350#688—121no—
351#686—22no—
352#686—34no—
353#686—62no—
354#686—62no—
355#686—62no—
356#686—121no—
357#685—21no—
358#685—61no—
359#685—61no—
360C4⋊Dic5C22×D311yescharacteristic
361#681—62no—
362C2×#168—31no—
363C2×#168—31no—
364C2×#168—62no—
365C2×#168C22×D311yescharacteristic
366C2×#168C22×D311yescharacteristic
367C2×AGL(1,ℤ/8)—151no—
368C22×D8—151no—
369#546—31no—
370D42—151no—
371#496—151no—
372#469—151no—
373#465—151no—
374#463—51no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—41no—
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—21no—
395C2×C5×D3—22no—
396C2×C5×D3—21no—
397C2×C5×D3—21no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C2×C5×D3—84no—
401C2×C5×D3AGL(1,ℤ/8)12yescomplemented
402C2×C3×D5—22no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405D3×D5—84no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—21no—
409C3×C4×C5—41no—
410C3×C4×C5C22×D411yescharacteristic
411C3×C4×C5H(5,𝔽2)11yescharacteristic
412C3×Dic5—41no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C23×D3—21no—
417C23×D3—101no—
418C23×D3—101no—
419C2×C3×Q8C22×D511yescharacteristic
420C2×C3×D4—51no—
421C2×C3×D4C22×D511yescharacteristic
422C22×C3×C4—101no—
423C2×#67—21no—
424C2×#67—21no—
425C2×#67—101no—
426C2×#67—101no—
427#239—22no—
428#239—41no—
429D3×D4—22no—
430D3×D4—41no—
431D3×D4—102no—
432D3×D4—102no—
433D3×D4—201no—
434D3×D4—201no—
435C2×D12—21no—
436C2×D12—51no—
437C2×D12—51no—
438C2×D12—101no—
439C2×D12—101no—
440C2×D12—101no—
441C2×D12—101no—
442C2×D12—204no—
443C2×D12C22⋊D511yescharacteristic
444C2×D12C22×D511yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×D8—102no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4—51no—
454C3×C22⋊C4—21no—
455C3×C22⋊C4—21no—
456C3×C22⋊C4—101no—
457C3×C42C22×D511yescharacteristic
458#217—21no—
459#215—102no—
460#215—201no—
461#213—54no—
462#213—102no—
463#213—201no—
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—101no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4C22⋊D511yescharacteristic
469(C2×D3)⋊C4C22⋊D511yescharacteristic
470C4⋊Dic3C22⋊D511yescharacteristic
471C4⋊Dic3C22×D511yescharacteristic
472Dic3⋊C4—21no—
473C2×C3⋊C8—51no—
474C2×C3⋊C8—51no—
475D24—102no—
476D24—102no—
477ΓL(1,𝔽25)—102no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—31no—
481C23×C5—31no—
482C23×C5—61no—
483C23×C5—122no—
484C23×C5—122no—
485C23×C5—241no—
486C22×D5—21no—
487C22×D5—61no—
488C22×D5—61no—
489C22×D5—122no—
490C22×D5—122no—
491C22×D5—122no—
492C22×D5—122no—
493C22×D5—241no—
494C22×D5—241no—
495C5×Q8—21no—
496C5×Q8—21no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—32no—
500C5×D4—62no—
501C5×D4—61no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—241no—
505C2×C4×C5—21no—
506C2×C4×C5—31no—
507C2×C4×C5—31no—
508C2×C4×C5—61no—
509C2×C4×C5—61no—
510C2×C4×C5—61no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—122no—
514C2×C4×C5—241no—
515C2×C4×C5D3×D411yescharacteristic
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—122no—
519C22⋊D5—122no—
520C2×Dic5—21no—
521D20—21no—
522D20—61no—
523D20—61no—
524D20—61no—
525D20—61no—
526D20—122no—
527D20—122no—
528D20—122no—
529D20—241no—
530D20D3×D412yes—
531C4×D5—42no—
532#168—21no—
533#168—21no—
534#168—32no—
535#168—61no—
536C2×#41—31no—
537C22×D4—31no—
538C22×D4—151no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—51no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—151no—
547C2×D8—151no—
548C2×D8—151no—
549C2×D8—151no—
550C2×D8—151no—
551C2×D8—304no—
552C2×M16—151no—
553C22×C8—151no—
554#127—151no—
555#124D3×D511yescharacteristic, complemented
556#123—61no—
557C22⋊Q8—31no—
558#121—31no—
559#121—61no—
560#121—151no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—301no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—51no—
569C2×C22⋊C4—61no—
570#106—151no—
571C4⋊C8—51no—
572#103—51no—
573#102—51no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—151no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—81no—
582C2×C3×C5D4211yescharacteristic
583C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
584C2×C3×C5#57611yescharacteristic
585D15—81no—
586D15—81no—
587C3×D5—42no—
588C5×D3—22no—
589C5×D3—41no—
590C5×D3—42no—
591C23×C3—21no—
592C23×C3—101no—
593C22×D3—21no—
594C22×D3—42no—
595C22×D3—42no—
596C22×D3—81no—
597C22×D3—101no—
598C22×D3—101no—
599C22×D3—202no—
600C22×D3—202no—
601C22×D3—202no—
602C22×D3—202no—
603C22×D3—401no—
604C22×D3—401no—
605C22×D3C2×C22⋊D511yescharacteristic
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—52no—
612C3×D4—101no—
613C2×C3×C4—21no—
614C2×C3×C4—101no—
615C2×C3×C4—202no—
616C2×C3×C4C2×C22⋊D511yescharacteristic
617C2×C3×C4C2×C22⋊D511yescharacteristic
618C2×C3×C4C23×D511yescharacteristic
619#67—42no—
620#67—81no—
621#67—202no—
622#67—202no—
623C2×Dic3—21no—
624C2×Dic3C2×C22⋊D511yescharacteristic
625C2×Dic3C2×C22⋊D511yescharacteristic
626D12—22no—
627D12—21no—
628D12—42no—
629D12—101no—
630D12—101no—
631D12—101no—
632D12—101no—
633D12—202no—
634D12—202no—
635D12—202no—
636D12—401no—
637D12D4×D512yescomplemented
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—42no—
643C4×D3—81no—
644C3×C8—101no—
645C3×C8—101no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—32no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—61no—
653C22×C5—61no—
654C22×C5—61no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—62no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—244no—
661C22×C5C2×D3×D411yescharacteristic
662C2×D5—22no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—121no—
666C2×D5—121no—
667C2×D5—121no—
668C2×D5—121no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—244no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5—61no—
677C4×C5—61no—
678C4×C5—121no—
679C4×C5C2×D3×D411yescharacteristic
680C4×C5#100911yescharacteristic
681Dic5—41no—
682C24—61no—
683C24—301no—
684C24—301no—
685#41—62no—
686#41—121no—
687C2×Q8C2×D3×D511yescharacteristic
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—51no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—121no—
696C2×D4—151no—
697C2×D4—151no—
698C2×D4—301no—
699C2×D4—301no—
700C2×D4—302no—
701C2×D4—302no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—301no—
705C2×D4—301no—
706C2×D4—601no—
707C2×D4—601no—
708C2×D4—604no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—61no—
713C22×C4—61no—
714C22×C4—101no—
715SD16—102no—
716SD16—302no—
717SD16—601no—
718D8—102no—
719D8—154no—
720D8—302no—
721D8—302no—
722D8—302no—
723D8—601no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—51no—
733C4⋊C4—61no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—31no—
737C22⋊C4—31no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
741C22⋊C4—101no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42C2×D3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—102no—
750C22×C3—201no—
751C22×C3—201no—
752C22×C3C22×C22⋊D511yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—22no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—84no—
762C2×D3—201no—
763C2×D3—201no—
764C2×D3—201no—
765C2×D3—201no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—404no—
769C2×D3—404no—
770C2×D3#409512yescomplemented
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—201no—
775C3×C4C2×D4×D511yescharacteristic
776C3×C4#414411yescharacteristic
777Dic3—21no—
778Dic3—21no—
779Dic3—41no—
780C2×C5—62no—
781C2×C5—81no—
782C2×C5—121no—
783C2×C5—122no—
784C2×C5#560911yescharacteristic
785C2×C5#576911yescharacteristic
786C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
787D5—42no—
788D5—241no—
789D5—241no—
790C23—21no—
791C23—31no—
792C23—31no—
793C23—61no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—241no—
798C23—301no—
799C23—301no—
800C23—602no—
801C23—602no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23—1201no—
806Q8—21no—
807Q8—21no—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—52no—
812D4—62no—
813D4—61no—
814D4—101no—
815D4—122no—
816D4—122no—
817D4—241no—
818D4—301no—
819D4—301no—
820D4—301no—
821D4—301no—
822D4—602no—
823D4—602no—
824D4—602no—
825D4—602no—
826D4—602no—
827D4—1201no—
828C2×C4—21no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—101no—
837C2×C4—122no—
838C2×C4—202no—
839C2×C4—241no—
840C2×C4D3×C22⋊D511yescharacteristic
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—101no—
844C8—101no—
845C8—152no—
846C8—301no—
847C2×C3—81no—
848C2×C3—202no—
849C2×C3D4×C22⋊D511yescharacteristic
850C2×C3C2×#409511yescharacteristic
851C2×C3#6616911yescharacteristic
852D3—22no—
853D3—41no—
854D3—42no—
855D3—401no—
856D3—401no—
857C5#8055211yescharacteristic, complemented, Sylow
858C22—32no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—62no—
866C22—61no—
867C22—61no—
868C22—102no—
869C22—121no—
870C22—121no—
871C22—201no—
872C22—201no—
873C22—244no—
874C22—601no—
875C22—601no—
876C22—601no—
877C22—601no—
878C22—601no—
879C22—601no—
880C22—1204no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—61no—
887C4—61no—
888C4—121no—
889C4—201no—
890C4D3×D4×D511yescharacteristic
891C4#9202711yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—62no—
894C2—81no—
895C2—121no—
896C2—122no—
897C2—202no—
898C2—1201no—
899C2—1201no—
900C2#1175503611yescharacteristic
901C2D3×#409511yescharacteristic
902C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5676C2semidirect
2. C2×#91504C2semidirect
3. C2×D3×#686C2semidirect
4. D12×D20C2semidirect
5. #11751159C2semidirect
6. C3×#65346C2semidirect
7. #11749398C2semidirect
8. #11749282C2semidirect
9. #11749280C2semidirect
10. #11749152C2semidirect
11. #11749037C2semidirect
12. #11749033C2semidirect
13. #11747037C2semidirect
14. #11747021C2semidirect
15. #11746999C2semidirect
17. C2×C5×#239C22semidirect
18. C2×C5×D3×D4C22semidirect
20. C2×D3×D20C22semidirect
22. C3×C5×#124C22semidirect
23. C2×#6717C22semidirect
24. C2×#6717C22semidirect
25. C2×#6715C22semidirect
26. C2×#6715C22semidirect
27. #91763C22semidirect
28. C5×#946C22semidirect
29. C5×#938C22semidirect
35. C4×C5×D12C22semidirect
36. C2×C3×#688C22semidirect
38. C3×C4×D20C22semidirect
44. #91460C22semidirect
46. C2×#6654C22semidirect
47. C2×#6654C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91087C22semidirect
52. C3×#3967C22semidirect
53. C3×#3964C22semidirect
54. C3×C4⋊#168C22semidirect
55. #90986C22semidirect
56. #90969C22semidirect
57. #90969C22semidirect
58. #90966C22semidirect
59. #90964C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
70. #65346D3semidirect
138. #6652D4semidirect
143. #5676D5semidirect
161. C5×#124C2×D3semidirect
173. C2×#688C2×D3semidirect
189. C4×D20C2×D3semidirect
190. #3967C2×D3semidirect
192. #3964C2×D3semidirect
199. C4⋊#168C2×D3semidirect
240. C5×D12C2×D4semidirect
256. C3⋊#168C2×D4semidirect
259. C2×#239C2×D5semidirect
262. C2×D3×D4C2×D5semidirect
266. C3×#124C2×D5semidirect
268. #946C2×D5semidirect
271. #938C2×D5semidirect
292. C4×D12C2×D5semidirect
401. C2×C5×D3AGL(1,ℤ/8)semidirect
555. #124D3×D5semidirect
637. D12D4×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4095semidirect
857. C5#80552semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#56762
C2×#915042
C2×D3×#6862
D12×D202
#117511592
C3×#653462
#117493982
#117492822
#117492802
#117491522
#117490372
#117490332
#117470372
#117470212
#117469992
#106152333
#805525