Finite Group Databasebeta

← #14453331

Subgroups — #14453331

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×#5612C211yesmaximal, characteristic, complemented
2C2×D3×#686C211yesmaximal, characteristic, complemented
3#67×D20C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751140C211yesmaximal, characteristic, complemented
6C3×#65325C211yesmaximal, characteristic, complemented
7#11749098C211yesmaximal, characteristic, complemented
8#11749032C211yesmaximal, characteristic, complemented
9#11748982C211yesmaximal, characteristic, complemented
10#11748521C211yesmaximal, characteristic, complemented
11#11748496C211yesmaximal, characteristic, complemented
12#11747483C211yesmaximal, characteristic, complemented
13#11747402C211yesmaximal, characteristic, complemented
14#11747321C211yesmaximal, characteristic, complemented
15#11747220C211yesmaximal, characteristic, complemented
16#10615233—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic, complemented
18C2×C5×#235C2211yescharacteristic, complemented
19C22×C3×D20C2211yescharacteristic, complemented
20C2×D5×#67—21no—
21C2×D3×D20C2211yescharacteristic
22C3×C5×#121C2211yescharacteristic, complemented
23C2×#6715C2211yescharacteristic, complemented
24#91819C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C5×#938—21no—
27C5×#937—21no—
28C5×#936C2211yescharacteristic, complemented
29C4×C5×#67C2211yescharacteristic
30C5×#897C2211yescharacteristic, complemented
31C5×#893C2211yescharacteristic, complemented
32C5×#883—21no—
33C5×D3×C22⋊C4—21no—
34C2×C3×#686C2211yescharacteristic
35C2×C3×#686C2211yescharacteristic, complemented
36#91564—21no—
37D3×#686—24no—
38#91474—21no—
39#91458C2211yescharacteristic, complemented
40#91456C2211yescharacteristic
41Dic3×D20C2211yescharacteristic, complemented
42#91409—21no—
43C2×#6660C2211yescharacteristic, complemented
44C2×#6655C2211yescharacteristic, complemented
45C2×#6655C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic, complemented
47#91298—24no—
48C2×#6652C2211yescharacteristic
49C2×#6652C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91093C2211yescharacteristic, complemented
53#91092C2211yescharacteristic, complemented
54C3×C22⋊#168C2211yescharacteristic, complemented
55C3×#3941C2211yescharacteristic, complemented
56C3×#3941C2211yescharacteristic, complemented
57Dic3⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90967C2211yescharacteristic, complemented
60(C2×D3)⋊#168C2211yescharacteristic, complemented
61#90953C2211yescharacteristic, complemented
62#80012—51nomaximal, Hall
63C5×#546—31no—
64C2×#4095—31no—
65C22×#686—31no—
66D4×D20—31no—
67#65527—31no—
68#65506—31no—
69#65347—31no—
70#65346—31no—
71#65337—31no—
72#65335—31no—
73#65328—31no—
74#65325D311yescharacteristic, complemented
75#65304—31no—
76#65303—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C23×C3×D5—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×#67D411yescharacteristic
89C5×D3×D4—22no—
90C5×D3×D4—41no—
91C5×#235—22no—
92C5×#235—41no—
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3—21no—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C5×Dic6C2311yescharacteristic
98C2×C3×D20—22no—
99C2×C3×D20—21no—
100C2×C3×D20—41no—
101C2×C3×D20C2311yescharacteristic
102C2×C3×D20C2311yescharacteristic
103D5×#67—44no—
104C2×#1202—21no—
105C2×#1202—21no—
106C2×#1202—21no—
107C2×#1201—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×#217—21no—
120C5×#217—21no—
121C5×#217D411yescharacteristic
122C5×(C2×D3)⋊C4—21no—
123C5×(C2×D3)⋊C4—21no—
124C5×(C2×D3)⋊C4D411yescharacteristic
125C5×C4⋊Dic3—21no—
126C5×Dic3⋊C4D411yescharacteristic
127C4×C5×Dic3C2311yescharacteristic
128C3×#686—22no—
129C3×#686—41no—
130C2×C3×#168C2311yescharacteristic
131C2×C3×#168C2311yescharacteristic
132#6665—21no—
133#6665—21no—
134#6660—41no—
135#6655—22no—
136#6655—22no—
137#6654—22no—
138#6652—22no—
139#6652D414yescomplemented
140D3×#168—22no—
141D4×#67—51no—
142C2×#932—51no—
143C2×D3×D8—51no—
144#5612D511yescharacteristic, complemented
145C3×#447—51no—
146#5156—51no—
147#5154—51no—
148#5153—51no—
149#5039—51no—
150#4786—51no—
151#4785—51no—
152#4778—51no—
153#4776—51no—
154#4734—51no—
155#4728—51no—
156C2×C5×#41—31no—
157C22×C5×D4—31no—
158C2×D4×D5—61no—
159C22×D20—31no—
160C22×D20C2×D311yescharacteristic, complemented
161C5×#124—31no—
162C5×#123—61no—
163C5×C22⋊Q8—31no—
164C5×#121—61no—
165C5×#121C2×D311yescharacteristic, complemented
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×#688—31no—
174C2×#686—31no—
175C2×#686—31no—
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—64no—
179C2×#686C2×D311yescharacteristic
180C2×#686C2×D311yescharacteristic, complemented
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×D20—31no—
190#3967—31no—
191#3964—31no—
192#3964—31no—
193C22⋊#168—31no—
194C22⋊#168C2×D311yescharacteristic, complemented
195#3941—31no—
196#3941C2×D311yescharacteristic, complemented
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—42no—
207C22×C5×D3—42no—
208C22×C5×D3—81no—
209C22×C5×D3C2×D411yescharacteristic
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—42no—
213C22×C3×D5—42no—
214C22×C3×D5—81no—
215C2×D3×D5—42no—
216C2×D3×D5—42no—
217C2×D3×D5—81no—
218C3×C5×D4—21no—
219C3×C5×D4—21no—
220C3×C5×D4—81no—
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—42no—
227C2×Dic15—21no—
228D60—21no—
229D60—21no—
230C5×#67—22no—
231C5×#67—42no—
232C5×#67—42no—
233C2×C5×Dic3—21no—
234C2×C5×Dic3C2×D411yescharacteristic
235C2×C5×Dic3C2×D411yescharacteristic
236C2×C5×Dic3C2×D411yescharacteristic
237C5×D12—21no—
238C5×D12C2×D412yescomplemented
239C4×C5×D3—21no—
240C4×C5×D3—21no—
241C4×C5×D3—42no—
242C4×C5×D3—81no—
243C5×Dic6—21no—
244C5×Dic6—21no—
245C3×D20—21no—
246C3×D20—21no—
247C3×D20—21no—
248C3×D20—42no—
249C3×D20C2×D412yes—
250#1202—42no—
251#1202—42no—
252#1202—81no—
253#1201—42no—
254D5×Dic3—42no—
255C3⋊#168—21no—
256C3⋊#168C2×D412yescomplemented
257C3×#168—21no—
258C3×#168—21no—
259C22×C3×D4—51no—
260C22×#67—101no—
261C2×D3×D4—51no—
262C2×D3×D4C2×D511yescharacteristic, complemented
263C2×#235C2×D511yescharacteristic, complemented
264C2×C3×D8—51no—
265C2×C3×D8—51no—
266C3×#121C2×D511yescharacteristic, complemented
267#953—101no—
268#940—51no—
269#939—101no—
270#938—21no—
271#938—51no—
272#937—21no—
273#937—101no—
274#936C2×D511yescharacteristic, complemented
275D4×Dic3—51no—
276C2×#214—51no—
277C2×#214—51no—
278#932—104no—
279C2×#213—51no—
280C2×#213—51no—
281C2×#213—51no—
282#930—51no—
283C4×#67C2×D511yescharacteristic
284C2×#208—51no—
285D3×D8—104no—
286C2×D24—51no—
287C2×#204—51no—
288C2×D3×C8—51no—
289#897C2×D511yescharacteristic, complemented
290#893C2×D511yescharacteristic, complemented
291#883—21no—
292D3×C22⋊C4—21no—
293C3×#102—51no—
294C3×#102—51no—
295C3×C22⋊C8—51no—
296#832—51no—
297#821—51no—
298(C2×D3)⋊C8—51no—
299#816—51no—
300#815—51no—
301Dic3⋊C8—51no—
302#809—51no—
303#808—51no—
304C24×C5—61no—
305C23×D5—21no—
306C23×D5—61no—
307C5×#41—62no—
308C5×#41—121no—
309C2×C5×Q8—31no—
310C2×C5×D4—21no—
311C2×C5×D4—31no—
312C2×C5×D4—31no—
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—61no—
320C22×C4×C5—61no—
321C22×C4×C5C22×D311yescharacteristic
322C2×C22⋊D5—61no—
323C2×C22⋊D5—61no—
324D4×D5—124no—
325C2×D20—22no—
326C2×D20—21no—
327C2×D20—31no—
328C2×D20—41no—
329C2×D20—62no—
330C2×D20—61no—
331C2×D20—61no—
332C2×D20—61no—
333C2×D20—121no—
334C2×D20C22×D311yescharacteristic
335C2×D20C22×D311yescharacteristic
336C2×C4×D5—61no—
337C5×C4⋊C4—31no—
338C5×C4⋊C4—61no—
339C5×C4⋊C4C22×D311yescharacteristic
340C5×C22⋊C4—21no—
341C5×C22⋊C4—31no—
342C5×C22⋊C4—31no—
343C5×C22⋊C4—61no—
344C5×C22⋊C4—61no—
345C5×C22⋊C4—61no—
346C5×C22⋊C4—61no—
347C42×C5—31no—
348#688—62no—
349#688—62no—
350#688—121no—
351#686—22no—
352#686—34no—
353#686—41no—
354#686—62no—
355#686—62no—
356#686—62no—
357#685—61no—
358#685—61no—
359#685—61no—
360C4⋊Dic5—31no—
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—151no—
375#459—151no—
376#450—151no—
377#449—151no—
378#447—51no—
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—84no—
398C2×C5×D3AGL(1,ℤ/8)12yescomplemented
399C2×C3×D5—22no—
400C2×C3×D5—41no—
401C2×C3×D5—41no—
402C2×C3×D5—41no—
403C2×C3×D5—41no—
404C2×C3×D5—41no—
405C2×C3×D5—84no—
406D3×D5—84no—
407C3×C4×C5—21no—
408C3×C4×C5—41no—
409C3×C4×C5C22×D411yescharacteristic
410C3×C4×C5H(5,𝔽2)11yescharacteristic
411Dic15—41no—
412C5×Dic3—21no—
413C5×Dic3—21no—
414C5×Dic3—21no—
415C5×Dic3—41no—
416C24×C3—101no—
417C23×D3—21no—
418C23×D3—101no—
419C2×C3×D4—21no—
420C2×C3×D4—51no—
421C2×C3×D4—51no—
422C2×C3×D4—102no—
423C2×C3×D4—101no—
424C2×C3×D4—201no—
425C2×C3×D4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—101no—
430C2×#67—101no—
431C2×#67—101no—
432C2×#67—101no—
433C2×#67—101no—
434C2×#67—204no—
435C2×#67C22⋊D511yescharacteristic
436C22×Dic3—101no—
437D3×D4—22no—
438D3×D4—41no—
439D3×D4—102no—
440D3×D4—201no—
441#235—22no—
442#235—41no—
443C2×D12—51no—
444C2×D12C22×D511yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3C22×D511yescharacteristic
448C2×Dic6C22×D511yescharacteristic
449C3×D8—102no—
450C3×D8—201no—
451C2×C3×C8—51no—
452C2×C3×C8—51no—
453C3×C4⋊C4C22×D511yescharacteristic
454C3×C22⋊C4—21no—
455#217—21no—
456#217—21no—
457#217—101no—
458#217—101no—
459#217C22⋊D511yescharacteristic
460#214—102no—
461#214—102no—
462#213—54no—
463#213—102no—
464#213—102no—
465(C2×D3)⋊C4—21no—
466(C2×D3)⋊C4—21no—
467(C2×D3)⋊C4—101no—
468(C2×D3)⋊C4C22⋊D511yescharacteristic
469C4⋊Dic3—21no—
470C4⋊Dic3—51no—
471Dic3⋊C4C22⋊D511yescharacteristic
472C4×Dic3C22×D511yescharacteristic
473#208—102no—
474C2×C3⋊C8—51no—
475C2×C3⋊C8—51no—
476D24—102no—
477#204—201no—
478D3×C8—102no—
479C23×C5—21no—
480C23×C5—31no—
481C23×C5—61no—
482C23×C5—122no—
483C23×C5—122no—
484C23×C5—241no—
485C23×C5D3×D411yescharacteristic
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—42no—
489C22×D5—42no—
490C22×D5—61no—
491C22×D5—81no—
492C22×D5—122no—
493C22×D5—122no—
494C22×D5—241no—
495C5×Q8—61no—
496C5×Q8—61no—
497C5×D4—21no—
498C5×D4—21no—
499C5×D4—32no—
500C5×D4—62no—
501C5×D4—61no—
502C5×D4—81no—
503C5×D4—122no—
504C5×D4—122no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—31no—
509C2×C4×C5—31no—
510C2×C4×C5—31no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—122no—
515C2×C4×C5—241no—
516C2×C4×C5D3×D411yescharacteristic
517C2×C4×C5C23×D311yescharacteristic
518C22⋊D5—122no—
519C22⋊D5—122no—
520C2×Dic5—61no—
521D20—21no—
522D20—21no—
523D20—21no—
524D20—42no—
525D20—61no—
526D20—61no—
527D20—122no—
528D20—122no—
529D20—241no—
530D20D3×D412yes—
531C4×D5—122no—
532#168—21no—
533#168—21no—
534#168—32no—
535#168—61no—
536C2×#41—31no—
537C22×D4—31no—
538C22×D4—51no—
539C22×D4—151no—
540C22×D4—301no—
541AGL(1,ℤ/8)—304no—
542C2×SD16—151no—
543C2×SD16—151no—
544C2×SD16—151no—
545C2×D8—51no—
546C2×D8—51no—
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#124—31no—
556#123—61no—
557C22⋊Q8—31no—
558#121—61no—
559#121—151no—
560#121—151no—
561#121—301no—
562#121D3×D511yescharacteristic, complemented
563#120—61no—
564#120—301no—
565#120—301no—
566C4×D4—31no—
567C4×D4—31no—
568C4×D4—151no—
569C2×C22⋊C4—61no—
570#106—151no—
571C4⋊C8—151no—
572#103—151no—
573#102—51no—
574#102—51no—
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—
588C3×D5—81no—
589C5×D3—22no—
590C5×D3—42no—
591C23×C3—21no—
592C23×C3—101no—
593C23×C3—101no—
594C23×C3—202no—
595C23×C3—202no—
596C23×C3—401no—
597C23×C3C2×C22⋊D511yescharacteristic
598C22×D3—21no—
599C22×D3—42no—
600C22×D3—42no—
601C22×D3—81no—
602C22×D3—101no—
603C22×D3—202no—
604C22×D3—202no—
605C22×D3—401no—
606C22×D3C2×C22⋊D511yescharacteristic
607C3×D4—21no—
608C3×D4—21no—
609C3×D4—52no—
610C3×D4—81no—
611C3×D4—101no—
612C3×D4—101no—
613C3×D4—101no—
614C3×D4—202no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4C2×C22⋊D511yescharacteristic
619C2×C3×C4C23×D511yescharacteristic
620#67—22no—
621#67—42no—
622#67—42no—
623#67—202no—
624#67—202no—
625#67—202no—
626#67—202no—
627#67—401no—
628C2×Dic3—21no—
629C2×Dic3—101no—
630C2×Dic3—202no—
631C2×Dic3C2×C22⋊D511yescharacteristic
632C2×Dic3C2×C22⋊D511yescharacteristic
633C2×Dic3C2×C22⋊D511yescharacteristic
634D12—21no—
635D12—101no—
636D12—101no—
637D12D4×D512yescomplemented
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—81no—
642Dic6—21no—
643Dic6—21no—
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—244no—
661C22×C5C2×D3×D411yescharacteristic
662C2×D5—22no—
663C2×D5—41no—
664C2×D5—41no—
665C2×D5—41no—
666C2×D5—41no—
667C2×D5—41no—
668C2×D5—84no—
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×C5—121no—
679C4×C5C2×D3×D411yescharacteristic
680C4×C5#100411yescharacteristic
681Dic5—121no—
682C24—61no—
683C24—101no—
684C24—301no—
685#41—62no—
686#41—121no—
687C2×Q8—31no—
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—51no—
692C2×D4—51no—
693C2×D4—61no—
694C2×D4—62no—
695C2×D4—61no—
696C2×D4—102no—
697C2×D4—101no—
698C2×D4—121no—
699C2×D4—151no—
700C2×D4—201no—
701C2×D4—301no—
702C2×D4—301no—
703C2×D4—301no—
704C2×D4—302no—
705C2×D4—301no—
706C2×D4—301no—
707C2×D4—601no—
708C2×D4—604no—
709C2×D4C2×D3×D511yescharacteristic
710C22×C4—31no—
711C22×C4—61no—
712C22×C4—61no—
713C22×C4—301no—
714C22×C4C2×D3×D511yescharacteristic
715SD16—302no—
716SD16—302no—
717SD16—601no—
718D8—102no—
719D8—154no—
720D8—201no—
721D8—302no—
722D8—302no—
723D8—302no—
724M16—302no—
725C2×C8—51no—
726C2×C8—51no—
727C2×C8—151no—
728C2×C8—151no—
729C2×C8—302no—
730C4⋊C4—31no—
731C4⋊C4—61no—
732C4⋊C4—151no—
733C4⋊C4C2×D3×D511yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—31no—
736C22⋊C4—31no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
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×C3—201no—
756C22×C3—201no—
757C22×C3—201no—
758C22×C3—404no—
759C22×C3C22×C22⋊D511yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—22no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—84no—
766C2×D3—201no—
767C2×D3—201no—
768C2×D3—201no—
769C2×D3—404no—
770C2×D3#409512yescomplemented
771C3×C4—21no—
772C3×C4—41no—
773C3×C4C2×D4×D511yescharacteristic
774C3×C4#414411yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—21no—
778Dic3—41no—
779Dic3—201no—
780C2×C5—41no—
781C2×C5—62no—
782C2×C5—81no—
783C2×C5—122no—
784C2×C5#559011yescharacteristic
785C2×C5#575711yescharacteristic
786C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
787D5—42no—
788D5—81no—
789D5—241no—
790C23—21no—
791C23—31no—
792C23—61no—
793C23—101no—
794C23—101no—
795C23—122no—
796C23—122no—
797C23—202no—
798C23—202no—
799C23—241no—
800C23—301no—
801C23—401no—
802C23—602no—
803C23—602no—
804C23—1201no—
805C23D3×C22⋊D511yescharacteristic
806Q8—61no—
807Q8—61no—
808D4—21no—
809D4—21no—
810D4—32no—
811D4—52no—
812D4—62no—
813D4—61no—
814D4—81no—
815D4—101no—
816D4—101no—
817D4—101no—
818D4—122no—
819D4—122no—
820D4—202no—
821D4—301no—
822D4—301no—
823D4—602no—
824D4—602no—
825D4—602no—
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—61no—
837C2×C4—122no—
838C2×C4—241no—
839C2×C4—301no—
840C2×C4—602no—
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×C3—401no—
851C2×C3D4×C22⋊D511yescharacteristic
852C2×C3C2×#409511yescharacteristic
853C2×C3#6616911yescharacteristic
854D3—22no—
855D3—42no—
856D3—401no—
857C5#8001211yescharacteristic, 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—201no—
872C22—201no—
873C22—201no—
874C22—201no—
875C22—201no—
876C22—244no—
877C22—404no—
878C22—601no—
879C22—601no—
880C22—601no—
881C22—1204no—
882C22C2×D3×C22⋊D511yescharacteristic
883C4—21no—
884C4—41no—
885C4—61no—
886C4—61no—
887C4—61no—
888C4—121no—
889C4—601no—
890C4D3×D4×D511yescharacteristic
891C4#9202511yescharacteristic
892C3#1061523311yescharacteristic, complemented, Sylow
893C2—41no—
894C2—62no—
895C2—81no—
896C2—122no—
897C2—202no—
898C2—401no—
899C2—1201no—
900C2#1175469711yescharacteristic
901C2#1175503211yescharacteristic
902C2D3×#409511yescharacteristic
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×#5612C2semidirect
2. C2×D3×#686C2semidirect
3. #67×D20C2semidirect
4. C2×#91298C2semidirect
5. #11751140C2semidirect
6. C3×#65325C2semidirect
7. #11749098C2semidirect
8. #11749032C2semidirect
9. #11748982C2semidirect
10. #11748521C2semidirect
11. #11748496C2semidirect
12. #11747483C2semidirect
13. #11747402C2semidirect
14. #11747321C2semidirect
15. #11747220C2semidirect
17. C2×C5×D3×D4C22semidirect
18. C2×C5×#235C22semidirect
19. C22×C3×D20C22semidirect
22. C3×C5×#121C22semidirect
23. C2×#6715C22semidirect
24. #91819C22semidirect
25. C2×#6710C22semidirect
28. C5×#936C22semidirect
30. C5×#897C22semidirect
31. C5×#893C22semidirect
35. C2×C3×#686C22semidirect
39. #91458C22semidirect
41. Dic3×D20C22semidirect
43. C2×#6660C22semidirect
44. C2×#6655C22semidirect
45. C2×#6655C22semidirect
46. C2×#6654C22semidirect
49. C2×#6652C22semidirect
50. C2×D3×#168C22semidirect
51. #91116C22semidirect
52. #91093C22semidirect
53. #91092C22semidirect
54. C3×C22⋊#168C22semidirect
55. C3×#3941C22semidirect
56. C3×#3941C22semidirect
57. Dic3⋊#168C22semidirect
58. #90973C22semidirect
59. #90967C22semidirect
60. (C2×D3)⋊#168C22semidirect
61. #90953C22semidirect
74. #65325D3semidirect
139. #6652D4semidirect
144. #5612D5semidirect
160. C22×D20C2×D3semidirect
165. C5×#121C2×D3semidirect
180. C2×#686C2×D3semidirect
194. C22⋊#168C2×D3semidirect
196. #3941C2×D3semidirect
197. #3941C2×D3semidirect
238. C5×D12C2×D4semidirect
256. C3⋊#168C2×D4semidirect
262. C2×D3×D4C2×D5semidirect
263. C2×#235C2×D5semidirect
266. C3×#121C2×D5semidirect
274. #936C2×D5semidirect
289. #897C2×D5semidirect
290. #893C2×D5semidirect
398. C2×C5×D3AGL(1,ℤ/8)semidirect
562. #121D3×D5semidirect
637. D12D4×D5semidirect
745. C3×C5#3264semidirect
770. C2×D3#4095semidirect
857. C5#80012semidirect
892. C3#10615233semidirect

Maximal subgroups

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

subgroupindex
C5×#56122
C2×D3×#6862
#67×D202
C2×#912982
#117511402
C3×#653252
#117490982
#117490322
#117489822
#117485212
#117484962
#117474832
#117474022
#117473212
#117472202
#106152333
#800125