Finite Group Databasebeta

← #14453387

Subgroups — #14453387

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×#5609C211yesmaximal, characteristic, complemented
2C2×D3×#686C211yesmaximal, characteristic, complemented
3#11754638C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic, complemented
5#11751140C211yesmaximal, characteristic, complemented
6C3×#65326C211yesmaximal, characteristic, complemented
7#11749076C211yesmaximal, characteristic, complemented
8#11749058C211yesmaximal, characteristic, complemented
9#11748981C211yesmaximal, characteristic, complemented
10#11748520C211yesmaximal, characteristic, complemented
11#11748496C211yesmaximal, characteristic, complemented
12#11747482C211yesmaximal, characteristic, complemented
13#11747377C211yesmaximal, characteristic, complemented
14#11747352C211yesmaximal, characteristic, complemented
15#11747220C211yesmaximal, characteristic, complemented
16#10615219—31nomaximal, Hall
17C2×C5×D3×D4—21no—
18C2×C5×D3×D4C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic, complemented
20C2×C3×#709C2211yescharacteristic, complemented
21C2×D3×D20C2211yescharacteristic, complemented
22C3×C5×#121C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C5×#940C2211yescharacteristic, complemented
27C5×#937—21no—
28C4×C5×#67C2211yescharacteristic
29C5×#895C2211yescharacteristic
30C5×#893C2211yescharacteristic, complemented
31C5×#884—21no—
32C5×#882—21no—
33C2×C3×#687C2211yescharacteristic, complemented
34C2×C3×#686C2211yescharacteristic, complemented
35#91577—21no—
36#91550—21no—
37D3×#686—24no—
38D5×(C2×D3)⋊C4—21no—
39Dic3×D20C2211yescharacteristic, complemented
40#91374C2211yescharacteristic, complemented
41#91369C2211yescharacteristic, complemented
42#91348—21no—
43C2×#6656C2211yescharacteristic, complemented
44C2×#6656C2211yescharacteristic, complemented
45C2×#6654C2211yescharacteristic
46C2×#6654C2211yescharacteristic, complemented
47#91299—24no—
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57Dic3⋊#168C2211yescharacteristic, complemented
58#90967C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80120—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#65326D311yescharacteristic, complemented
74#65325—31no—
75#65305—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C5×D3—21no—
80C22×D3×D5—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×#1220—21no—
85C2×D60C2311yescharacteristic
86C2×C5×#67—21no—
87C2×C5×#67—21no—
88C2×C5×#67—21no—
89C2×C5×#67D411yescharacteristic
90C5×D3×D4—22no—
91C5×D3×D4—41no—
92C5×D3×D4—44no—
93C2×C5×D12—22no—
94C2×C5×D12—21no—
95C2×C5×D12—21no—
96C2×C5×D12—41no—
97C2×C5×D12C2311yescharacteristic
98C2×C5×D12C2311yescharacteristic
99C2×C4×C5×D3—21no—
100C2×C4×C5×D3C2311yescharacteristic
101C2×C3×C22⋊D5—21no—
102C3×#709—22no—
103C3×#709—41no—
104C2×C3×D20C2311yescharacteristic
105C2×C3×C4×D5—21no—
106C2×C3×Dic10C2311yescharacteristic
107C2×#1202—21no—
108C2×D5×Dic3—21no—
109D3×D20—22no—
110D3×D20—41no—
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113#6715—22no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116#6710—22no—
117C2×C3⋊#168C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C5×#217D411yescharacteristic
120C5×(C2×D3)⋊C4—21no—
121C5×(C2×D3)⋊C4—21no—
122C5×(C2×D3)⋊C4D411yescharacteristic
123C5×Dic3⋊C4D411yescharacteristic
124C4×C5×Dic3C2311yescharacteristic
125C3×#687—41no—
126C3×#686—22no—
127C2×C3×#168C2311yescharacteristic
128C2×C3×#168C2311yescharacteristic
129#6669—21no—
130#6667—21no—
131#6667—21no—
132(C2×D3)⋊Dic5—21no—
133#6665—21no—
134#6656—22no—
135#6656—22no—
136#6654—22no—
137#6654—41no—
138#6652—22no—
139#6652D414yescomplemented
140D3×#168—22no—
141#5829—51no—
142C2×#949—51no—
143C2×D3×D8—51no—
144#5609D511yescharacteristic, complemented
145C3×#449—51no—
146#5176—51no—
147#5169—51no—
148#5150—51no—
149#5039—51no—
150#4819—51no—
151#4807—51no—
152#4785—51no—
153#4773—51no—
154#4732—51no—
155#4728—51no—
156C22×C5×D4—31no—
157C22×C5×D4—31no—
158C22×C5×D4—61no—
159C2×#709C2×D311yescharacteristic, complemented
160C22×D20—31no—
161C5×#127—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#121C2×D311yescharacteristic, complemented
165C5×#120—61no—
166C5×#120—61no—
167C4×C5×D4—31no—
168C4×C5×D4—31no—
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, complemented
181#4076—31no—
182#4070—31no—
183C2×#681—31no—
184C22×#168—31no—
185#4040—61no—
186#4030—61no—
187D5×C22⋊C4—61no—
188#4021—31no—
189C4×D20—31no—
190#3964—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3942C2×D311yescharacteristic, complemented
196#3941—31no—
197#3941C2×D311yescharacteristic, complemented
198#3940—31no—
199C4⋊#168—31no—
200#3935—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—42no—
210C22×C5×D3—42no—
211C22×C5×D3—81no—
212C22×C5×D3—81no—
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×D4—21no—
220C3×C5×D4—42no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5C2×D411yescharacteristic
225C2×C3×C4×C5C2411yescharacteristic
226#1220—81no—
227C2×Dic15—21no—
228D60—21no—
229D60—21no—
230C5×#67—22no—
231C5×#67—42no—
232C5×#67—42no—
233C5×#67—81no—
234C2×C5×Dic3C2×D411yescharacteristic
235C2×C5×Dic3C2×D411yescharacteristic
236C2×C5×Dic3C2×D411yescharacteristic
237C5×D12—21no—
238C5×D12—21no—
239C5×D12—21no—
240C5×D12—42no—
241C5×D12—42no—
242C5×D12C2×D412yes—
243C4×C5×D3—21no—
244C4×C5×D3—21no—
245C4×C5×D3—42no—
246C3×C22⋊D5—42no—
247C2×C3×Dic5—21no—
248C3×D20—21no—
249C3×D20C2×D412yescomplemented
250C3×C4×D5—42no—
251C3×Dic10—21no—
252C3×Dic10—21no—
253#1202—42no—
254D5×Dic3—81no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C2×C3×#41—51no—
260C2×D3×D4—21no—
261C2×D3×D4—51no—
262C2×D3×D4C2×D511yescharacteristic
263C22×D12C2×D511yescharacteristic, complemented
264C2×C3×SD16—51no—
265C2×C3×D8—51no—
266C3×#121C2×D511yescharacteristic, complemented
267#949—104no—
268#947—51no—
269#946—51no—
270C2×#215—51no—
271C2×#215—51no—
272#940C2×D511yescharacteristic, complemented
273#939—101no—
274#937—21no—
275#937—101no—
276D4×Dic3—51no—
277C2×#213—51no—
278C2×#213—51no—
279C2×#213—51no—
280#930—51no—
281#929—101no—
282C4×#67C2×D511yescharacteristic
283C2×(C2×D3)⋊C4—101no—
284C2×#208—51no—
285D3×D8—104no—
286C2×D24—51no—
287C2×D24—51no—
288C2×D3×C8—51no—
289#895C2×D511yescharacteristic
290#893C2×D511yescharacteristic, complemented
291#884—21no—
292#882—21no—
293C3×#103—51no—
294C3×#102—51no—
295C3×C22⋊C8—51no—
296#832—51no—
297#821—51no—
298#821—51no—
299(C2×D3)⋊C8—51no—
300#815—51no—
301Dic3⋊C8—51no—
302#809—51no—
303#808—51no—
304C24×C5—61no—
305C24×C5—61no—
306C23×D5—61no—
307C2×C5×D4—21no—
308C2×C5×D4—31no—
309C2×C5×D4—31no—
310C2×C5×D4—31no—
311C2×C5×D4—62no—
312C2×C5×D4—61no—
313C2×C5×D4—61no—
314C2×C5×D4—61no—
315C2×C5×D4—61no—
316C2×C5×D4—62no—
317C2×C5×D4—61no—
318C2×C5×D4—121no—
319C2×C5×D4—121no—
320C2×C5×D4—124no—
321C2×C5×D4C22×D311yescharacteristic
322C22×C4×C5—31no—
323C22×C4×C5—61no—
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—21no—
326C2×C22⋊D5—61no—
327#709—22no—
328#709—41no—
329C2×D20—31no—
330C2×D20—62no—
331C2×D20—61no—
332C2×D20—121no—
333C2×D20C22×D311yescharacteristic
334C2×C4×D5—21no—
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×C5—31no—
345C22⋊Dic5—61no—
346#687—41no—
347#687—62no—
348#687—62no—
349#686—22no—
350#686—34no—
351#686—62no—
352#686—62no—
353#686—62no—
354#686—121no—
355#685—61no—
356#685—61no—
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—151no—
375#459—151no—
376#450—151no—
377#449—51no—
378#447—151no—
379#447—151no—
380#442—151no—
381#435—151no—
382C22×C3×C5—21no—
383C22×C3×C5—21no—
384C22×C3×C5—21no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C22×D411yescharacteristic
389C2×D15—41no—
390C2×D15—41no—
391C2×D15—41no—
392C2×C5×D3—21no—
393C2×C5×D3—21no—
394C2×C5×D3—22no—
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—22no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
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—41no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—21no—
416C23×D3—21no—
417C23×D3—21no—
418C23×D3—101no—
419C3×#41—102no—
420C3×#41—201no—
421C2×C3×Q8—51no—
422C2×C3×D4—21no—
423C2×C3×D4—51no—
424C2×C3×D4—101no—
425C2×C3×D4C22×D511yescharacteristic
426C22×C3×C4—101no—
427C22×C3×C4C22×D511yescharacteristic
428C2×#67—21no—
429C2×#67—21no—
430C2×#67—21no—
431C2×#67—101no—
432C2×#67—101no—
433C2×#67C22⋊D511yescharacteristic
434C22×Dic3—101no—
435D3×D4—22no—
436D3×D4—41no—
437D3×D4—44no—
438D3×D4—102no—
439D3×D4—201no—
440C2×D12—22no—
441C2×D12—21no—
442C2×D12—21no—
443C2×D12—41no—
444C2×D12—51no—
445C2×D12C22×D511yescharacteristic
446C2×D12C22×D511yescharacteristic
447C2×C4×D3—21no—
448C2×C4×D3C22×D511yescharacteristic
449C3×SD16—201no—
450C3×D8—102no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4C22×D511yescharacteristic
454C3×C22⋊C4—21no—
455#217—101no—
456#217C22⋊D511yescharacteristic
457#215—102no—
458#215—102no—
459#213—54no—
460#213—102no—
461#213—102no—
462(C2×D3)⋊C4—21no—
463(C2×D3)⋊C4—21no—
464(C2×D3)⋊C4—101no—
465(C2×D3)⋊C4—101no—
466(C2×D3)⋊C4—101no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4C22⋊D511yescharacteristic
469C4⋊Dic3—51no—
470Dic3⋊C4—101no—
471Dic3⋊C4C22⋊D511yescharacteristic
472C4×Dic3C22×D511yescharacteristic
473#208—102no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476D24—102no—
477D24—201no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—31no—
481C23×C5—61no—
482C23×C5—61no—
483C23×C5—122no—
484C23×C5—122no—
485C23×C5—122no—
486C23×C5—122no—
487C23×C5—241no—
488C23×C5—241no—
489C23×C5D3×D411yescharacteristic
490C22×D5—21no—
491C22×D5—61no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×D4—21no—
496C5×D4—21no—
497C5×D4—32no—
498C5×D4—42no—
499C5×D4—62no—
500C5×D4—61no—
501C5×D4—61no—
502C5×D4—61no—
503C5×D4—122no—
504C5×D4—122no—
505C5×D4—122no—
506C5×D4—122no—
507C5×D4—241no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—31no—
512C2×C4×C5—31no—
513C2×C4×C5—31no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—122no—
517C2×C4×C5D3×D411yescharacteristic
518C2×C4×C5C23×D311yescharacteristic
519C22⋊D5—42no—
520C22⋊D5—241no—
521C2×Dic5—21no—
522C2×Dic5—61no—
523D20—21no—
524D20—61no—
525D20—61no—
526D20—122no—
527D20D3×D412yescomplemented
528C4×D5—42no—
529C4×D5—241no—
530Dic10—21no—
531Dic10—21no—
532#168—21no—
533#168—21no—
534#168—32no—
535#168—61no—
536C2×#41—51no—
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—151no—
556#123—301no—
557C22⋊Q8—151no—
558#121—31no—
559#121—61no—
560#121—151no—
561#121—301no—
562#121D3×D511yescharacteristic, complemented
563#120—61no—
564#120—61no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—301no—
570#106—151no—
571C4⋊C8—151no—
572#103—51no—
573#102—51no—
574#102—151no—
575#102—151no—
576#102—151no—
577#102—151no—
578C22⋊C8—51no—
579C22⋊C8—151no—
580#97—151no—
581C2×C3×C5—41no—
582C2×C3×C5—81no—
583C2×C3×C5D4211yescharacteristic
584C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
585C2×C3×C5#57611yescharacteristic
586D15—81no—
587C3×D5—42no—
588C5×D3—22no—
589C5×D3—42no—
590C5×D3—81no—
591C23×C3—21no—
592C23×C3—101no—
593C23×C3C2×C22⋊D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—42no—
597C22×D3—42no—
598C22×D3—42no—
599C22×D3—42no—
600C22×D3—81no—
601C22×D3—81no—
602C22×D3—101no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3C2×C22⋊D511yescharacteristic
607C3×Q8—101no—
608C3×Q8—101no—
609C3×D4—21no—
610C3×D4—21no—
611C3×D4—42no—
612C3×D4—52no—
613C3×D4—101no—
614C3×D4—202no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—101no—
619C2×C3×C4—202no—
620C2×C3×C4C2×C22⋊D511yescharacteristic
621C2×C3×C4C23×D511yescharacteristic
622#67—22no—
623#67—42no—
624#67—42no—
625#67—81no—
626#67—202no—
627#67—401no—
628C2×Dic3—101no—
629C2×Dic3—401no—
630C2×Dic3C2×C22⋊D511yescharacteristic
631C2×Dic3C2×C22⋊D511yescharacteristic
632C2×Dic3C2×C22⋊D511yescharacteristic
633D12—21no—
634D12—21no—
635D12—21no—
636D12—42no—
637D12—42no—
638D12—101no—
639D12—101no—
640D12D4×D512yes—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—42no—
644C3×C8—101no—
645C3×C8—101no—
646C3⋊C8—52no—
647C3⋊C8—101no—
648C22×C5—21no—
649C22×C5—21no—
650C22×C5—21no—
651C22×C5—32no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—61no—
656C22×C5—61no—
657C22×C5—62no—
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—22no—
667C2×D5—41no—
668C2×D5—41no—
669C2×D5—121no—
670C2×D5—121no—
671C2×D5—121no—
672C2×D5—244no—
673C4×C5—21no—
674C4×C5—41no—
675C4×C5—61no—
676C4×C5—61no—
677C4×C5—61no—
678C4×C5C2×D3×D411yescharacteristic
679C4×C5#100411yescharacteristic
680Dic5—41no—
681Dic5—121no—
682C24—61no—
683C24—61no—
684C24—301no—
685#41—102no—
686#41—201no—
687C2×Q8—51no—
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—51no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—61no—
697C2×D4—61no—
698C2×D4—62no—
699C2×D4—61no—
700C2×D4—101no—
701C2×D4—121no—
702C2×D4—121no—
703C2×D4—124no—
704C2×D4—151no—
705C2×D4—301no—
706C2×D4—302no—
707C2×D4—301no—
708C2×D4—601no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—61no—
712C22×C4—101no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—201no—
716SD16—302no—
717SD16—302no—
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—301no—
740C22⋊C4—301no—
741C22⋊C4—301no—
742C22⋊C4—301no—
743C22⋊C4—301no—
744C42—31no—
745C3×C5#326411yescharacteristic, complemented, Hall
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—102no—
753C22×C3—201no—
754C22×C3—201no—
755C22×C3C22×C22⋊D511yescharacteristic
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3—84no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3#407812yescomplemented
771C3×C4—21no—
772C3×C4—41no—
773C3×C4—201no—
774C3×C4C2×D4×D511yescharacteristic
775C3×C4#414411yescharacteristic
776Dic3—21no—
777Dic3—21no—
778Dic3—21no—
779Dic3—201no—
780C2×C5—41no—
781C2×C5—62no—
782C2×C5—81no—
783C2×C5—122no—
784C2×C5—241no—
785C2×C5#559011yescharacteristic
786C2×C5#576911yescharacteristic
787C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
788D5—42no—
789D5—241no—
790C23—21no—
791C23—31no—
792C23—61no—
793C23—61no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—122no—
798C23—122no—
799C23—241no—
800C23—241no—
801C23—301no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23D3×C22⋊D511yescharacteristic
806Q8—101no—
807Q8—101no—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—42no—
812D4—52no—
813D4—62no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—101no—
818D4—122no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—202no—
823D4—241no—
824D4—301no—
825D4—301no—
826D4—602no—
827D4—1201no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—31no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—101no—
837C2×C4—122no—
838C2×C4—202no—
839C2×C4—301no—
840C2×C4—1201no—
841C2×C4D3×C22⋊D511yescharacteristic
842C2×C4C22×D3×D511yescharacteristic
843C8—101no—
844C8—101no—
845C8—152no—
846C8—301no—
847C2×C3—41no—
848C2×C3—81no—
849C2×C3—202no—
850C2×C3C2×#407811yescharacteristic
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3#6616911yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—401no—
857C5#8012011yescharacteristic, complemented, Sylow
858C22—21no—
859C22—21no—
860C22—21no—
861C22—32no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—61no—
866C22—61no—
867C22—62no—
868C22—102no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—244no—
878C22—601no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—41no—
885C4—61no—
886C4—61no—
887C4—61no—
888C4—201no—
889C4—601no—
890C4D3×D4×D511yescharacteristic
891C4#9202511yescharacteristic
892C3#1061521911yescharacteristic, complemented, Sylow
893C2—41no—
894C2—62no—
895C2—81no—
896C2—122no—
897C2—202no—
898C2—241no—
899C2—1201no—
900C2D3×#407811yescharacteristic
901C2#1175503211yescharacteristic
902C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3264
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C5×#5609C2semidirect
2. C2×D3×#686C2semidirect
3. #11754638C2semidirect
4. C2×#91299C2semidirect
5. #11751140C2semidirect
6. C3×#65326C2semidirect
7. #11749076C2semidirect
8. #11749058C2semidirect
9. #11748981C2semidirect
10. #11748520C2semidirect
11. #11748496C2semidirect
12. #11747482C2semidirect
13. #11747377C2semidirect
14. #11747352C2semidirect
15. #11747220C2semidirect
19. C22×C5×D12C22semidirect
20. C2×C3×#709C22semidirect
21. C2×D3×D20C22semidirect
22. C3×C5×#121C22semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
25. C2×#6710C22semidirect
26. C5×#940C22semidirect
30. C5×#893C22semidirect
33. C2×C3×#687C22semidirect
34. C2×C3×#686C22semidirect
39. Dic3×D20C22semidirect
40. #91374C22semidirect
41. #91369C22semidirect
43. C2×#6656C22semidirect
44. C2×#6656C22semidirect
46. C2×#6654C22semidirect
49. C2×#6652C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91093C22semidirect
53. #91092C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×#3942C22semidirect
56. C3×#3941C22semidirect
57. Dic3⋊#168C22semidirect
58. #90967C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
73. #65326D3semidirect
139. #6652D4semidirect
144. #5609D5semidirect
159. C2×#709C2×D3semidirect
164. C5×#121C2×D3semidirect
172. C2×#687C2×D3semidirect
180. C2×#686C2×D3semidirect
194. C22⋊#168C2×D3semidirect
195. #3942C2×D3semidirect
197. #3941C2×D3semidirect
249. C3×D20C2×D4semidirect
256. C3⋊#168C2×D4semidirect
263. C22×D12C2×D5semidirect
266. C3×#121C2×D5semidirect
272. #940C2×D5semidirect
290. #893C2×D5semidirect
402. C2×C5×D3AGL(1,ℤ/8)semidirect
527. D20D3×D4semidirect
562. #121D3×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4078semidirect
857. C5#80120semidirect
892. C3#10615219semidirect

Maximal subgroups

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

subgroupindex
C5×#56092
C2×D3×#6862
#117546382
C2×#912992
#117511402
C3×#653262
#117490762
#117490582
#117489812
#117485202
#117484962
#117474822
#117473772
#117473522
#117472202
#106152193
#801205