Finite Group Databasebeta

← #14453304

Subgroups — #14453304

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×D4×D12C211yesmaximal, characteristic, complemented
2C2×#91496C211yesmaximal, characteristic, complemented
3C2×D3×#686C211yesmaximal, characteristic, complemented
4#11752749C211yesmaximal, characteristic, complemented
5#11751115C211yesmaximal, characteristic, complemented
6C3×#65305C211yesmaximal, characteristic, complemented
7#11749058C211yesmaximal, characteristic, complemented
8#11749032C211yesmaximal, characteristic, complemented
9#11747517C211yesmaximal, characteristic, complemented
10#11747482C211yesmaximal, characteristic, complemented
11#11747352C211yesmaximal, characteristic, complemented
12#11747324C211yesmaximal, characteristic, complemented
13#11747045C211yesmaximal, characteristic, complemented
14#11747042C211yesmaximal, characteristic, complemented
15#11746999C211yesmaximal, characteristic, complemented
16#10615219—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic, complemented
19C22×C5×D12—21no—
20C2×D3×D20C2211yescharacteristic, complemented
21C2×#6769C2211yescharacteristic, complemented
22C3×C4×C5×D4C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic
24C4×D60C2211yescharacteristic, complemented
25C5×#930—21no—
26C5×#895C2211yescharacteristic
27C5×#895C2211yescharacteristic, complemented
28C5×#882—21no—
29C5×#882—21no—
30C5×#874C2211yescharacteristic, complemented
31C4×C5×D12C2211yescharacteristic
32C2×C3×#687C2211yescharacteristic, complemented
33C2×C3×#686C2211yescharacteristic
34C3×#4021C2211yescharacteristic, complemented
35#91496—24no—
36D3×#686—24no—
37#91475—21no—
38#91473—21no—
39#91461—21no—
40#91456C2211yescharacteristic, complemented
41#91369C2211yescharacteristic, complemented
42#91356—21no—
43C2×#6656C2211yescharacteristic, complemented
44C2×#6656C2211yescharacteristic, complemented
45C2×#6654C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic, complemented
47C2×#6652C2211yescharacteristic, complemented
48C2×#6652C2211yescharacteristic, complemented
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80552—51nomaximal, Hall
63C5×D42—31no—
64C2×#4078—31no—
65C22×#686—31no—
66#65884—31no—
67#65507—31no—
68#65506—31no—
69#65363—31no—
70#65361—31no—
71#65330—31no—
72#65328—31no—
73#65326—31no—
74#65325—31no—
75#65305D311yescharacteristic, complemented
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C22×D3×D5—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C22×C3×C4×C5—21no—
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C5×D3×D4—22no—
88C5×D3×D4—22no—
89C5×D3×D4—41no—
90C5×D3×D4—41no—
91C2×C5×D12—21no—
92C2×C5×D12—21no—
93C2×C5×D12—21no—
94C2×C5×D12—21no—
95C2×C5×D12—44no—
96C2×C5×D12D411yescharacteristic
97C2×C5×D12C2311yescharacteristic
98C2×C5×D12C2311yescharacteristic
99C2×C4×C5×D3C2311yescharacteristic
100C2×C4×C5×D3C2311yescharacteristic
101C2×C3×D20C2311yescharacteristic
102C2×C3×Dic10C2311yescharacteristic
103C2×#1203—21no—
104C2×#1202—21no—
105C2×#1201—21no—
106C2×#1200—21no—
107D3×D20—22no—
108D3×D20—41no—
109#6769—22no—
110#6769—41no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C42×C5C2311yescharacteristic
114#6715D414yescomplemented
115#6714—21no—
116C4⋊Dic15C2311yescharacteristic
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×(C2×D3)⋊C4—21no—
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4D411yescharacteristic
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×C4⋊Dic3D411yescharacteristic
124C3×#687—22no—
125C3×#686—22no—
126C3×#685—21no—
127C3×#685—21no—
128C2×C3×#168C2311yescharacteristic
129C2×C3×#168C2311yescharacteristic
130#6669—21no—
131(C2×D3)⋊Dic5—21no—
132#6665—21no—
133#6656—22no—
134#6656—41no—
135#6654—22no—
136#6654—22no—
137#6652—22no—
138#6652—41no—
139#6650—22no—
140D3×#168—22no—
141C2×#914—51no—
142C2×D3×D8—51no—
143#5676—51no—
144D4×D12D511yescharacteristic, complemented
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—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709—31no—
160C22×D20—31no—
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—31no—
164C5×#121—61no—
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4C2×D311yescharacteristic, complemented
169#4083—61no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#687C2×D311yescharacteristic, complemented
173#4078—64no—
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#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4040—61no—
186#4030—61no—
187D5×C22⋊C4—61no—
188#4021C2×D311yescharacteristic, complemented
189C4×D20—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168—31no—
195#3942C2×D311yescharacteristic, complemented
196#3941—31no—
197#3941C2×D311yescharacteristic, complemented
198#3940—31no—
199C4⋊#168C2×D311yescharacteristic, complemented
200#3935—31no—
201#3264—151noSylow
202C23×C3×C5—21no—
203C22×D15—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—42no—
207C22×C5×D3—42no—
208C22×C5×D3—42no—
209C22×C5×D3—42no—
210C22×C5×D3—81no—
211C22×C5×D3—81no—
212C22×C5×D3C2×D411yescharacteristic
213C22×C5×D3C2×D411yescharacteristic
214C22×C3×D5—21no—
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×D4—21no—
219C3×C5×D4C2×D412yes—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—42no—
222C2×C3×C4×C5C2×D411yescharacteristic
223C2×C3×C4×C5C2×D411yescharacteristic
224C2×C3×C4×C5C2411yescharacteristic
225C2×Dic15—21no—
226D60—21no—
227D60C2×D412yescomplemented
228C4×D15—81no—
229C5×#67—42no—
230C5×#67—42no—
231C2×C5×Dic3C2×D411yescharacteristic
232C2×C5×Dic3C2×D411yescharacteristic
233C5×D12—22no—
234C5×D12—21no—
235C5×D12—21no—
236C5×D12—21no—
237C5×D12—21no—
238C5×D12—42no—
239C5×D12—42no—
240C5×D12—42no—
241C5×D12—81no—
242C4×C5×D3—21no—
243C4×C5×D3—21no—
244C4×C5×D3—21no—
245C4×C5×D3—21no—
246C2×C3×Dic5—21no—
247C3×D20—21no—
248C3×D20—21no—
249C3×Dic10—21no—
250C3×Dic10—21no—
251#1203—42no—
252#1202—42no—
253#1201—81no—
254#1200—42no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×#239—51no—
260C2×D3×D4—51no—
261C2×D3×D4C2×D511yescharacteristic
262C2×D3×D4C2×D511yescharacteristic, complemented
263C22×D12—21no—
264C2×C3×SD16—51no—
265C2×C3×D8—51no—
266C3×#124—51no—
267C3×C4×D4C2×D511yescharacteristic, complemented
268#946—51no—
269C2×#215—51no—
270C2×#215—51no—
271#938—51no—
272C2×#213—51no—
273C2×#213—51no—
274C2×#213—51no—
275#930—21no—
276#914—104no—
277D3×D8—104no—
278C2×D24—51no—
279C2×D24—51no—
280C2×ΓL(1,𝔽25)—51no—
281C2×D3×C8—51no—
282#895C2×D511yescharacteristic
283#895C2×D511yescharacteristic, complemented
284#884—101no—
285#883—101no—
286#882—21no—
287#882—21no—
288#882—101no—
289D3×C22⋊C4—101no—
290#874C2×D511yescharacteristic, complemented
291C4×D12—51no—
292C4×D12C2×D511yescharacteristic
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—
305C24×C5—61no—
306C23×D5—61no—
307C2×C5×D4—31no—
308C2×C5×D4—31no—
309C2×C5×D4—31no—
310C2×C5×D4—61no—
311C2×C5×D4—61no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—62no—
315C2×C5×D4—62no—
316C2×C5×D4—61no—
317C2×C5×D4—61no—
318C2×C5×D4—124no—
319C2×C5×D4—121no—
320C2×C5×D4—121no—
321C2×C5×D4C22×D311yescharacteristic
322C22×C4×C5—21no—
323C22×C4×C5—31no—
324C22×C4×C5—31no—
325C2×C22⋊D5—61no—
326C2×C22⋊D5—61no—
327#709—62no—
328#709—121no—
329C2×D20—31no—
330C2×D20—62no—
331C2×D20—61no—
332C2×D20—121no—
333C2×D20C22×D311yescharacteristic
334C2×C4×D5—61no—
335C2×C4×D5—61no—
336C2×Dic10C22×D311yescharacteristic
337C5×C4⋊C4—31no—
338C5×C4⋊C4C22×D311yescharacteristic
339C5×C22⋊C4—21no—
340C5×C22⋊C4—31no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4—61no—
343C5×C22⋊C4—61no—
344C42×C5C22×D311yescharacteristic
345C22⋊Dic5—61no—
346#687—22no—
347#687—62no—
348#687—121no—
349#686—22no—
350#686—34no—
351#686—62no—
352#686—62no—
353#686—62no—
354#686—121no—
355#685—21no—
356#685—21no—
357#685—61no—
358#685—61no—
359C4⋊Dic5—31no—
360#683—61no—
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—151no—
370D42—31no—
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—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5C22×D411yescharacteristic
386C2×D15—22no—
387C2×D15—41no—
388C2×D15—41no—
389C2×C5×D3—21no—
390C2×C5×D3—21no—
391C2×C5×D3—21no—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—41no—
395C2×C5×D3—41no—
396C2×C5×D3—41no—
397C2×C5×D3—41no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C2×C5×D3—84no—
401C2×C5×D3—84no—
402C2×C5×D3AGL(1,ℤ/8)12yescomplemented
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
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
412Dic15—41no—
413C3×Dic5—41no—
414C5×Dic3—21no—
415C5×Dic3—21no—
416C23×D3—21no—
417C23×D3—21no—
418C23×D3—101no—
419C2×C3×Q8—51no—
420C2×C3×D4—51no—
421C2×C3×D4C22×D511yescharacteristic
422C22×C3×C4—21no—
423C2×#67—21no—
424C2×#67—21no—
425C2×#67—101no—
426C2×#67—101no—
427#239—102no—
428#239—201no—
429D3×D4—22no—
430D3×D4—22no—
431D3×D4—41no—
432D3×D4—41no—
433D3×D4—102no—
434D3×D4—201no—
435C2×D12—21no—
436C2×D12—21no—
437C2×D12—21no—
438C2×D12—21no—
439C2×D12—44no—
440C2×D12—51no—
441C2×D12—101no—
442C2×D12C22⋊D511yescharacteristic
443C2×D12C22×D511yescharacteristic
444C2×D12C22×D511yescharacteristic
445C2×C4×D3—101no—
446C2×C4×D3—101no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—102no—
450C3×D8—102no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4C22×D511yescharacteristic
454C3×C22⋊C4—21no—
455C3×C22⋊C4—101no—
456C3×C22⋊C4—101no—
457C3×C42C22×D511yescharacteristic
458#217—101no—
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⋊Dic3—51no—
471C4⋊Dic3C22⋊D511yescharacteristic
472Dic3⋊C4—101no—
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—61no—
484C23×C5—122no—
485C23×C5—122no—
486C23×C5—122no—
487C23×C5—122no—
488C23×C5—241no—
489C23×C5—241no—
490C22×D5—21no—
491C22×D5—61no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×D4—21no—
496C5×D4—62no—
497C5×D4—61no—
498C5×D4—61no—
499C5×D4—61no—
500C5×D4—61no—
501C5×D4—122no—
502C5×D4—122no—
503C5×D4—122no—
504C5×D4—122no—
505C5×D4—122no—
506C5×D4—241no—
507C5×D4D3×D412yes—
508C2×C4×C5—21no—
509C2×C4×C5—31no—
510C2×C4×C5—31no—
511C2×C4×C5—42no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5D3×D411yescharacteristic
518C2×C4×C5C23×D311yescharacteristic
519C22⋊D5—122no—
520C22⋊D5—241no—
521C2×Dic5—21no—
522C2×Dic5—61no—
523D20—21no—
524D20—21no—
525D20—32no—
526D20—61no—
527D20—122no—
528C4×D5—122no—
529C4×D5—241no—
530Dic10—21no—
531Dic10—21no—
532#168—21no—
533#168—21no—
534#168—32no—
535#168—61no—
536C2×#41—151no—
537C22×D4—31no—
538C22×D4—31no—
539C22×D4—61no—
540C22×D4—151no—
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—31no—
555#124—51no—
556#123—301no—
557C22⋊Q8—151no—
558#121—31no—
559#121—31no—
560#121—61no—
561#121—151no—
562#121—301no—
563#120—61no—
564#120—61no—
565#120—301no—
566C4×D4—31no—
567C4×D4—151no—
568C4×D4D3×D511yescharacteristic, complemented
569C2×C22⋊C4—301no—
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—42no—
582C2×C3×C5D4211yescharacteristic
583C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
584C2×C3×C5#57611yescharacteristic
585D15—42no—
586C3×D5—81no—
587C5×D3—22no—
588C5×D3—41no—
589C5×D3—81no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—101no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—42no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—81no—
600C22×D3—81no—
601C22×D3—101no—
602C22×D3—202no—
603C22×D3—202no—
604C22×D3—401no—
605C22×D3C2×C22⋊D511yescharacteristic
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—101no—
611C3×D4—101no—
612C3×D4D4×D512yes—
613C2×C3×C4—21no—
614C2×C3×C4—42no—
615C2×C3×C4—101no—
616C2×C3×C4C2×C22⋊D511yescharacteristic
617C2×C3×C4C2×C22⋊D511yescharacteristic
618C2×C3×C4C23×D511yescharacteristic
619#67—42no—
620#67—42no—
621#67—202no—
622#67—401no—
623C2×Dic3—101no—
624C2×Dic3C2×C22⋊D511yescharacteristic
625C2×Dic3C2×C22⋊D511yescharacteristic
626D12—22no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—42no—
632D12—42no—
633D12—42no—
634D12—52no—
635D12—81no—
636D12—101no—
637D12—202no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—202no—
643C4×D3—401no—
644C3×C8—101no—
645C3×C8—101no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—22no—
649C22×C5—32no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—61no—
653C22×C5—61no—
654C22×C5—61no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—121no—
658C22×C5—121no—
659C22×C5—121no—
660C22×C5—121no—
661C22×C5—121no—
662C22×C5—121no—
663C22×C5—244no—
664C22×C5—244no—
665C22×C5C2×D3×D411yescharacteristic
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—62no—
670C2×D5—121no—
671C2×D5—121no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—21no—
675C4×C5—41no—
676C4×C5—61no—
677C4×C5—61no—
678C4×C5C2×D3×D411yescharacteristic
679C4×C5#100911yescharacteristic
680Dic5—41no—
681Dic5—121no—
682C24—61no—
683C24—61no—
684C24—301no—
685#41—302no—
686#41—601no—
687C2×Q8—51no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—51no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—62no—
697C2×D4—62no—
698C2×D4—61no—
699C2×D4—61no—
700C2×D4—124no—
701C2×D4—121no—
702C2×D4—121no—
703C2×D4—151no—
704C2×D4—301no—
705C2×D4—302no—
706C2×D4—301no—
707C2×D4—301no—
708C2×D4—601no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—21no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—301no—
714C22×C4—301no—
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—151no—
732C4⋊C4—301no—
733C4⋊C4C2×D3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—31no—
736C22⋊C4—31no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—101no—
740C22⋊C4—101no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42C2×D3×D511yescharacteristic
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—22no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—201no—
750C22×C3—201no—
751C22×C3—201no—
752C22×C3C22×C22⋊D511yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3—84no—
766C2×D3—102no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3#407812yescomplemented
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—41no—
774C3×C4—201no—
775C3×C4C2×D4×D511yescharacteristic
776C3×C4#414411yescharacteristic
777Dic3—21no—
778Dic3—21no—
779Dic3—201no—
780C2×C5—42no—
781C2×C5—62no—
782C2×C5—121no—
783C2×C5—241no—
784C2×C5—241no—
785C2×C5#560911yescharacteristic
786C2×C5#576911yescharacteristic
787C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
788D5—81no—
789D5—122no—
790C23—21no—
791C23—31no—
792C23—31no—
793C23—61no—
794C23—61no—
795C23—101no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—122no—
800C23—241no—
801C23—241no—
802C23—301no—
803C23—602no—
804C23—602no—
805C23—1201no—
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—62no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—101no—
815D4—101no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—122no—
821D4—152no—
822D4—241no—
823D4—301no—
824D4—602no—
825D4—602no—
826D4—1201no—
827D4#677712yes—
828C2×C4—21no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—42no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—101no—
837C2×C4—301no—
838C2×C4—602no—
839C2×C4—1201no—
840C2×C4D3×C22⋊D511yescharacteristic
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—101no—
844C8—101no—
845C8—152no—
846C8—301no—
847C2×C3—42no—
848C2×C3—401no—
849C2×C3C2×#407811yescharacteristic
850C2×C3D4×C22⋊D511yescharacteristic
851C2×C3#6616911yescharacteristic
852D3—22no—
853D3—41no—
854D3—81no—
855D3—81no—
856D3—202no—
857C5#8055211yescharacteristic, complemented, Sylow
858C22—22no—
859C22—32no—
860C22—41no—
861C22—41no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—121no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—244no—
878C22—302no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—21no—
885C4—41no—
886C4—61no—
887C4—61no—
888C4—201no—
889C4—601no—
890C4C2×#677711yescharacteristic
891C4#9201811yescharacteristic
892C3#1061521911yescharacteristic, complemented, Sylow
893C2—42no—
894C2—62no—
895C2—121no—
896C2—241no—
897C2—241no—
898C2—401no—
899C2—602no—
900C2#1175465711yescharacteristic
901C2D3×#407811yescharacteristic
902C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×D4×D12C2semidirect
2. C2×#91496C2semidirect
3. C2×D3×#686C2semidirect
4. #11752749C2semidirect
5. #11751115C2semidirect
6. C3×#65305C2semidirect
7. #11749058C2semidirect
8. #11749032C2semidirect
9. #11747517C2semidirect
10. #11747482C2semidirect
11. #11747352C2semidirect
12. #11747324C2semidirect
13. #11747045C2semidirect
14. #11747042C2semidirect
15. #11746999C2semidirect
18. C2×C5×D3×D4C22semidirect
20. C2×D3×D20C22semidirect
21. C2×#6769C22semidirect
22. C3×C4×C5×D4C22semidirect
24. C4×D60C22semidirect
27. C5×#895C22semidirect
30. C5×#874C22semidirect
32. C2×C3×#687C22semidirect
34. C3×#4021C22semidirect
40. #91456C22semidirect
41. #91369C22semidirect
43. C2×#6656C22semidirect
44. C2×#6656C22semidirect
45. C2×#6654C22semidirect
46. C2×#6654C22semidirect
47. C2×#6652C22semidirect
48. C2×#6652C22semidirect
49. C2×#6650C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91093C22semidirect
53. #91092C22semidirect
54. #91087C22semidirect
55. C3×#3942C22semidirect
56. C3×#3941C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65305D3semidirect
114. #6715D4semidirect
144. D4×D12D5semidirect
168. C4×C5×D4C2×D3semidirect
172. C2×#687C2×D3semidirect
188. #4021C2×D3semidirect
195. #3942C2×D3semidirect
197. #3941C2×D3semidirect
199. C4⋊#168C2×D3semidirect
227. D60C2×D4semidirect
256. C3⋊#168C2×D4semidirect
262. C2×D3×D4C2×D5semidirect
267. C3×C4×D4C2×D5semidirect
283. #895C2×D5semidirect
290. #874C2×D5semidirect
402. C2×C5×D3AGL(1,ℤ/8)semidirect
568. C4×D4D3×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4078semidirect
857. C5#80552semidirect
892. C3#10615219semidirect

Maximal subgroups

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

subgroupindex
C5×D4×D122
C2×#914962
C2×D3×#6862
#117527492
#117511152
C3×#653052
#117490582
#117490322
#117475172
#117474822
#117473522
#117473242
#117470452
#117470422
#117469992
#106152193
#805525