Finite Group Databasebeta

← #14453814

Subgroups — #14453814

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5554C211yesmaximal, characteristic
2C2×#91486C211yesmaximal, characteristic, complemented
3C2×D3×#687C211yesmaximal, characteristic, complemented
4#11752558C211yesmaximal, characteristic, complemented
5#11751119C211yesmaximal, characteristic, complemented
6C3×#65308C211yesmaximal, characteristic, complemented
7#11749059C211yesmaximal, characteristic, complemented
8#11749058C211yesmaximal, characteristic, complemented
9#11747495C211yesmaximal, characteristic, complemented
10#11747494C211yesmaximal, characteristic, complemented
11#11747355C211yesmaximal, characteristic, complemented
12#11747353C211yesmaximal, characteristic, complemented
13#11747082C211yesmaximal, characteristic, complemented
14#11746999C211yesmaximal, characteristic, complemented
15#11746884C211yesmaximal, characteristic, complemented
16#10615237—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C2×D3×Dic10C2211yescharacteristic
20C2×D3×Dic10C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22C2×#6716C2211yescharacteristic
23C4×Dic30C2211yescharacteristic, complemented
24C5×#930—21no—
25C2×C5×(C2×D3)⋊C4—21no—
26C5×#897C2211yescharacteristic
27C5×#895C2211yescharacteristic
28C5×#886—21no—
29C5×#882—21no—
30C5×#875C2211yescharacteristic
31C4×C5×D12C2211yescharacteristic
32C2×C3×#687C2211yescharacteristic
33C2×C3×#687C2211yescharacteristic
34C3×#4015C2211yescharacteristic, complemented
35#91486—24no—
36D3×#687—24no—
37#91470—21no—
38#91436—21no—
39#91436—21no—
40#91435—21no—
41#91369C2211yescharacteristic
42#91369C2211yescharacteristic, complemented
43C2×#6663C2211yescharacteristic, complemented
44C2×#6661C2211yescharacteristic, complemented
45C2×#6661C2211yescharacteristic, complemented
46C2×#6659C2211yescharacteristic
47C2×#6656C2211yescharacteristic
48C2×#6656C2211yescharacteristic
49C2×#6650C2211yescharacteristic, complemented
50C2×D3×#168C2211yescharacteristic
51#91116C2211yescharacteristic
52#91094C2211yescharacteristic, complemented
53#91091C2211yescharacteristic, complemented
54#91087C2211yescharacteristic, complemented
55C3×#3942C2211yescharacteristic, complemented
56C3×#3942C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90973C2211yescharacteristic, complemented
59#90967C2211yescharacteristic
60(C2×D3)⋊#168C2211yescharacteristic
61(C2×D3)⋊#168C2211yescharacteristic, complemented
62#80444—51nomaximal, Hall
63C5×#546—31no—
64C2×#4097—31no—
65C22×#687—31no—
66D4×Dic10—31no—
67#65528—31no—
68#65507—31no—
69#65349—31no—
70#65343—31no—
71#65340—31no—
72#65339—31no—
73#65331—31no—
74#65329—31no—
75#65308D311yescharacteristic, complemented
76#65307—31no—
77#65300—31no—
78C23×C5×D3—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C2×C5×#67—21no—
84C22×C5×Dic3—21no—
85C5×#237—22no—
86C5×#237—41no—
87C5×D3×D4—22no—
88C5×D3×D4—41no—
89C2×C5×D12—21no—
90C2×C5×D12D411yescharacteristic
91C2×C5×D12C2311yescharacteristic
92C2×C4×C5×D3C2311yescharacteristic
93C2×C4×C5×D3C2311yescharacteristic
94C2×C5×Dic6C2311yescharacteristic
95C2×C3×Dic10C2311yescharacteristic
96C2×C3×Dic10C2311yescharacteristic
97C2×#1204—21no—
98C2×#1204—21no—
99C2×D3×Dic5—21no—
100C2×D3×Dic5—21no—
101D3×Dic10—22no—
102D3×Dic10—22no—
103D3×Dic10—41no—
104D3×Dic10—41no—
105C3×C5×C4⋊C4C2311yescharacteristic
106C3×C5×C22⋊C4—21no—
107C3×C42×C5C2311yescharacteristic
108#6716D414yescomplemented
109C4⋊Dic15C2311yescharacteristic
110#6712—21no—
111C4×Dic15—21no—
112C2×C3⋊#168C2311yescharacteristic
113C2×C3⋊#168C2311yescharacteristic
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×(C2×D3)⋊C4—21no—
118C5×(C2×D3)⋊C4D411yescharacteristic
119C5×(C2×D3)⋊C4D411yescharacteristic
120C5×C4⋊Dic3—21no—
121C5×C4⋊Dic3D411yescharacteristic
122C3×#687—22no—
123C3×#687—22no—
124C3×C4⋊Dic5—21no—
125C3×C4⋊Dic5—21no—
126C2×C3×#168C2311yescharacteristic
127C2×C3×#168C2311yescharacteristic
128#6669—21no—
129#6669—21no—
130(C2×D3)⋊Dic5—21no—
131(C2×D3)⋊Dic5—21no—
132#6663—22no—
133#6661—22no—
134#6661—41no—
135#6659—22no—
136#6656—22no—
137#6656—41no—
138#6650—22no—
139D3×#168—22no—
140C2×#915—51no—
141C2×D3×SD16—51no—
142#5727—51no—
143#5554D511yescharacteristic
144C3×#461—51no—
145#5173—51no—
146#5169—51no—
147#5086—51no—
148#5018—51no—
149#4845—51no—
150#4836—51no—
151#4813—51no—
152#4812—51no—
153#4809—51no—
154#4806—51no—
155C2×C5×#41—31no—
156C22×C5×D4—31no—
157C22×Dic10—31no—
158C22×Dic10—31no—
159C5×#124—31no—
160C5×#123—61no—
161C5×C22⋊Q8—31no—
162C5×#121—31no—
163C5×#121—61no—
164C5×#120—61no—
165C4×C5×D4—31no—
166C4×C5×D4C2×D311yescharacteristic
167C2×C5×C22⋊C4—61no—
168#4097—64no—
169C2×#689—31no—
170C2×#689—31no—
171C2×#689—31no—
172D4×Dic5—61no—
173C2×#687—31no—
174C2×#687—31no—
175C2×#687—31no—
176C2×#687—31no—
177C2×#687—64no—
178C2×#687C2×D311yescharacteristic
179C2×#687C2×D311yescharacteristic
180#4070—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4034—61no—
185#4024—61no—
186#4024—61no—
187#4015C2×D311yescharacteristic, complemented
188C4×Dic10—31no—
189#3967—31no—
190#3964—31no—
191#3964—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3942C2×D311yescharacteristic, complemented
196#3942C2×D311yescharacteristic, complemented
197#3939—31no—
198C4⋊#168C2×D311yescharacteristic, complemented
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5—21no—
202C22×C5×D3—21no—
203C22×C5×D3—42no—
204C22×C5×D3—42no—
205C22×C5×D3—81no—
206C22×C5×D3C2×D411yescharacteristic
207C22×C5×D3C2×D411yescharacteristic
208C3×C5×D4—21no—
209C3×C5×D4C2×D412yes—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—81no—
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2411yescharacteristic
215C2×Dic15—21no—
216C2×Dic15—21no—
217Dic30—21no—
218Dic30C2×D412yes—
219C5×#67—42no—
220C5×#67—42no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—42no—
223C2×C5×Dic3C2×D411yescharacteristic
224C2×C5×Dic3C2×D411yescharacteristic
225C5×D12—22no—
226C5×D12—21no—
227C5×D12—21no—
228C5×D12—81no—
229C4×C5×D3—21no—
230C4×C5×D3—21no—
231C4×C5×D3—21no—
232C4×C5×D3—21no—
233C5×Dic6—21no—
234C5×Dic6—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C3×Dic10—21no—
238C3×Dic10—21no—
239C3×Dic10—21no—
240C3×Dic10—21no—
241#1204—42no—
242#1204—42no—
243D3×Dic5—42no—
244D3×Dic5—42no—
245C3⋊#168—21no—
246C3⋊#168C2×D412yes—
247C3×#168—21no—
248C3×#168—21no—
249C2×D3×Q8—51no—
250C2×D3×Q8—51no—
251C2×#237C2×D511yescharacteristic
252C2×D3×D4C2×D511yescharacteristic
253C2×C3×SD16—51no—
254C2×C3×SD16—51no—
255C3×C4⋊Q8—51no—
256C3×C4×D4C2×D511yescharacteristic
257#946—51no—
258#946—51no—
259C2×#216—51no—
260C2×#216—51no—
261C2×#215—51no—
262C2×#215—51no—
263C2×#214—51no—
264#930—21no—
265C2×(C2×D3)⋊C4—21no—
266#915—104no—
267D3×SD16—104no—
268C2×Dic12—51no—
269C2×#204—51no—
270C2×ΓL(1,𝔽25)—51no—
271C2×D3×C8—51no—
272#897C2×D511yescharacteristic
273#896—101no—
274#896—101no—
275#895C2×D511yescharacteristic
276#893—101no—
277#888—101no—
278#886—21no—
279#882—21no—
280#875C2×D511yescharacteristic
281C4×D12C2×D511yescharacteristic
282C4×Dic6—51no—
283C3×C4⋊C8—51no—
284C3×#103—51no—
285C3×#103—51no—
286#832—51no—
287#821—51no—
288(C2×D3)⋊C8—51no—
289(C2×D3)⋊C8—51no—
290#816—51no—
291#810—51no—
292#807—51no—
293#803—51no—
294C24×C5—61no—
295C5×#41—62no—
296C5×#41—121no—
297C2×C5×Q8—31no—
298C2×C5×D4—31no—
299C2×C5×D4—31no—
300C2×C5×D4—61no—
301C2×C5×D4—61no—
302C2×C5×D4—62no—
303C2×C5×D4—61no—
304C2×C5×D4—121no—
305C2×C5×D4C22×D311yescharacteristic
306C22×C4×C5—21no—
307C22×C4×C5—31no—
308C22×C4×C5—31no—
309C22×C4×C5—61no—
310C22×Dic5—61no—
311C22×Dic5—61no—
312C2×Dic10—31no—
313C2×Dic10—62no—
314C2×Dic10—62no—
315C2×Dic10—61no—
316C2×Dic10—61no—
317C2×Dic10—121no—
318C2×Dic10—121no—
319C2×Dic10C22×D311yescharacteristic
320C2×Dic10C22×D311yescharacteristic
321C5×C4⋊C4—31no—
322C5×C4⋊C4—61no—
323C5×C4⋊C4C22×D311yescharacteristic
324C5×C22⋊C4—21no—
325C5×C22⋊C4—31no—
326C5×C22⋊C4—31no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C5×C22⋊C4—61no—
330C5×C22⋊C4—61no—
331C42×C5C22×D311yescharacteristic
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#689—62no—
335#689—62no—
336#689—121no—
337#687—22no—
338#687—22no—
339#687—34no—
340#687—62no—
341#687—62no—
342#687—121no—
343C4⋊Dic5—21no—
344C4⋊Dic5—21no—
345C4⋊Dic5—31no—
346#683—61no—
347#683—61no—
348#683—61no—
349C4×Dic5—61no—
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—62no—
354C2×#168C22×D311yescharacteristic
355C2×#168C22×D311yescharacteristic
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546—31no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—51no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—22no—
372C22×C3×C5—41no—
373C22×C3×C5—41no—
374C22×C3×C5C22×D411yescharacteristic
375C2×C5×D3—21no—
376C2×C5×D3—21no—
377C2×C5×D3—21no—
378C2×C5×D3—21no—
379C2×C5×D3—21no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—84no—
384C2×C5×D3#13712yescomplemented
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5C22×D411yescharacteristic
389C3×C4×C5H(5,𝔽2)11yescharacteristic
390Dic15—22no—
391Dic15—41no—
392C3×Dic5—41no—
393C3×Dic5—41no—
394C5×Dic3—21no—
395C5×Dic3—21no—
396C5×Dic3—41no—
397C23×D3—21no—
398C2×C3×Q8—51no—
399C2×C3×Q8—51no—
400C2×C3×D4C22×D511yescharacteristic
401C22×C3×C4—21no—
402C2×#67—21no—
403C2×#67—21no—
404C22×Dic3—21no—
405D3×Q8—102no—
406D3×Q8—102no—
407D3×Q8—201no—
408D3×Q8—201no—
409#237—22no—
410#237—41no—
411D3×D4—22no—
412D3×D4—41no—
413C2×D12—21no—
414C2×D12C22⋊D511yescharacteristic
415C2×D12C22×D511yescharacteristic
416C2×C4×D3—101no—
417C2×C4×D3—101no—
418C2×C4×D3C22×D511yescharacteristic
419C2×C4×D3C22×D511yescharacteristic
420C2×Dic6—51no—
421C2×Dic6—101no—
422C2×Dic6—101no—
423C2×Dic6C22×D511yescharacteristic
424C3×SD16—102no—
425C3×SD16—102no—
426C2×C3×C8—51no—
427C2×C3×C8—51no—
428C3×C4⋊C4—101no—
429C3×C4⋊C4—101no—
430C3×C4⋊C4C22×D511yescharacteristic
431C3×C22⋊C4—21no—
432C3×C42C22×D511yescharacteristic
433#216—102no—
434#216—201no—
435#215—102no—
436#215—201no—
437#214—54no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—21no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4C22⋊D511yescharacteristic
445(C2×D3)⋊C4C22⋊D511yescharacteristic
446C4⋊Dic3—21no—
447C4⋊Dic3—51no—
448C4⋊Dic3C22⋊D511yescharacteristic
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452C4×Dic3—101no—
453C2×C3⋊C8—51no—
454C2×C3⋊C8—51no—
455Dic12—102no—
456#204—102no—
457ΓL(1,𝔽25)—102no—
458D3×C8—102no—
459C23×C5—21no—
460C23×C5—31no—
461C23×C5—31no—
462C23×C5—61no—
463C23×C5—122no—
464C23×C5—122no—
465C23×C5—241no—
466C5×Q8—61no—
467C5×Q8—61no—
468C5×D4—21no—
469C5×D4—62no—
470C5×D4—61no—
471C5×D4—61no—
472C5×D4—122no—
473C5×D4—122no—
474C5×D4—241no—
475C5×D4D3×D412yes—
476C2×C4×C5—21no—
477C2×C4×C5—31no—
478C2×C4×C5—31no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×C4×C5—61no—
484C2×C4×C5—81no—
485C2×C4×C5—122no—
486C2×C4×C5D3×D411yescharacteristic
487C2×C4×C5D3×D411yescharacteristic
488C2×C4×C5C23×D311yescharacteristic
489C2×Dic5—21no—
490C2×Dic5—21no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—122no—
494C2×Dic5—122no—
495Dic10—21no—
496Dic10—21no—
497Dic10—21no—
498Dic10—21no—
499Dic10—32no—
500Dic10—61no—
501Dic10—122no—
502Dic10—122no—
503#168—21no—
504#168—21no—
505#168—32no—
506#168—61no—
507C2×#41—31no—
508C22×Q8—151no—
509C22×Q8—151no—
510C22×D4—31no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—51no—
516C2×SD16—51no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—51no—
525C4⋊Q8—301no—
526#124—31no—
527#123—61no—
528C22⋊Q8—31no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—31no—
534#121—61no—
535#120—61no—
536C4×Q8—151no—
537C4×D4—31no—
538C4×D4—301no—
539C4×D4D3×D511yescharacteristic
540C2×C22⋊C4—61no—
541#107—151no—
542C4⋊C8—51no—
543#103—51no—
544#103—51no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—42no—
553C2×C3×C5D4211yescharacteristic
554C2×C3×C5C2×#13711yescharacteristic
555C2×C3×C5#57711yescharacteristic
556C5×D3—22no—
557C5×D3—41no—
558C5×D3—81no—
559C23×C3—21no—
560C22×D3—21no—
561C22×D3—42no—
562C22×D3—42no—
563C22×D3—81no—
564C22×D3C2×C22⋊D511yescharacteristic
565C22×D3C2×C22⋊D511yescharacteristic
566C3×Q8—101no—
567C3×Q8—101no—
568C3×Q8—101no—
569C3×Q8—101no—
570C3×D4—21no—
571C3×D4D4×D512yes—
572C2×C3×C4—21no—
573C2×C3×C4—81no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4C2×C22⋊D511yescharacteristic
577C2×C3×C4C2×C22⋊D511yescharacteristic
578C2×C3×C4C23×D511yescharacteristic
579#67—42no—
580#67—42no—
581C2×Dic3—21no—
582C2×Dic3—42no—
583C2×Dic3—101no—
584C2×Dic3—101no—
585C2×Dic3C2×C22⋊D511yescharacteristic
586C2×Dic3C2×C22⋊D511yescharacteristic
587D12—22no—
588D12—21no—
589D12—21no—
590D12—81no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—202no—
596C4×D3—202no—
597Dic6—21no—
598Dic6—21no—
599Dic6—52no—
600Dic6—101no—
601Dic6—202no—
602Dic6—202no—
603C3×C8—101no—
604C3×C8—101no—
605C3⋊C8—52no—
606C3⋊C8—101no—
607C22×C5—22no—
608C22×C5—32no—
609C22×C5—41no—
610C22×C5—41no—
611C22×C5—61no—
612C22×C5—61no—
613C22×C5—61no—
614C22×C5—61no—
615C22×C5—61no—
616C22×C5—121no—
617C22×C5—121no—
618C22×C5—121no—
619C22×C5—244no—
620C22×C5C2×D3×D411yescharacteristic
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5—61no—
625C4×C5—61no—
626C4×C5—121no—
627C4×C5C2×D3×D411yescharacteristic
628C4×C5#100911yescharacteristic
629Dic5—41no—
630Dic5—41no—
631Dic5—62no—
632Dic5—121no—
633C24—61no—
634#41—62no—
635#41—121no—
636C2×Q8—31no—
637C2×Q8—51no—
638C2×Q8—51no—
639C2×Q8—151no—
640C2×Q8—301no—
641C2×Q8—301no—
642C2×Q8—302no—
643C2×Q8—302no—
644C2×Q8—601no—
645C2×Q8—601no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—61no—
649C2×D4—61no—
650C2×D4—62no—
651C2×D4—61no—
652C2×D4—121no—
653C2×D4C2×D3×D511yescharacteristic
654C22×C4—21no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—61no—
658C22×C4—301no—
659C22×C4—301no—
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—102no—
664SD16—102no—
665SD16—154no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—51no—
671C2×C8—51no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—31no—
676C4⋊C4—61no—
677C4⋊C4—101no—
678C4⋊C4—101no—
679C4⋊C4—151no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4C2×D3×D511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—31no—
686C22⋊C4—31no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—301no—
694C42C2×D3×D511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—22no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3C22×C22⋊D511yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—84no—
709C2×D3#409712yescomplemented
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—201no—
714C3×C4—201no—
715C3×C4C2×D4×D511yescharacteristic
716C3×C4#414411yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—102no—
721Dic3—201no—
722C2×C5—42no—
723C2×C5—62no—
724C2×C5—121no—
725C2×C5—241no—
726C2×C5#560911yescharacteristic
727C2×C5#576211yescharacteristic
728C2×C5D3×#13711yescharacteristic
729C23—21no—
730C23—31no—
731C23—31no—
732C23—61no—
733C23—122no—
734C23—122no—
735C23—241no—
736Q8—61no—
737Q8—61no—
738Q8—101no—
739Q8—101no—
740Q8—101no—
741Q8—101no—
742Q8—152no—
743Q8—301no—
744Q8—602no—
745Q8—602no—
746D4—21no—
747D4—62no—
748D4—61no—
749D4—61no—
750D4—122no—
751D4—122no—
752D4—241no—
753D4#677712yes—
754C2×C4—21no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—81no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—122no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—602no—
769C2×C4—602no—
770C2×C4D3×C22⋊D511yescharacteristic
771C2×C4D3×C22⋊D511yescharacteristic
772C2×C4C22×D3×D511yescharacteristic
773C8—101no—
774C8—101no—
775C8—152no—
776C8—301no—
777C2×C3—42no—
778C2×C3D4×C22⋊D511yescharacteristic
779C2×C3C2×#409711yescharacteristic
780C2×C3#6617011yescharacteristic
781D3—22no—
782D3—41no—
783D3—81no—
784C5#8044411yescharacteristic, complemented, Sylow
785C22—22no—
786C22—32no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—244no—
798C22C2×D3×C22⋊D511yescharacteristic
799C4—21no—
800C4—21no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—201no—
806C4—201no—
807C4—302no—
808C4—601no—
809C4C2×#677711yescharacteristic
810C4#9201811yescharacteristic
811C3#1061523711yescharacteristic, complemented, Sylow
812C2—42no—
813C2—62no—
814C2—121no—
815C2—241no—
816C2#1175465711yescharacteristic
817C2#1175471111yescharacteristic
818C2D3×#409711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5554C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3266
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
2. C2×#91486C2semidirect
3. C2×D3×#687C2semidirect
4. #11752558C2semidirect
5. #11751119C2semidirect
6. C3×#65308C2semidirect
7. #11749059C2semidirect
8. #11749058C2semidirect
9. #11747495C2semidirect
10. #11747494C2semidirect
11. #11747355C2semidirect
12. #11747353C2semidirect
13. #11747082C2semidirect
14. #11746999C2semidirect
15. #11746884C2semidirect
20. C2×D3×Dic10C22semidirect
23. C4×Dic30C22semidirect
34. C3×#4015C22semidirect
42. #91369C22semidirect
43. C2×#6663C22semidirect
44. C2×#6661C22semidirect
45. C2×#6661C22semidirect
49. C2×#6650C22semidirect
52. #91094C22semidirect
53. #91091C22semidirect
54. #91087C22semidirect
55. C3×#3942C22semidirect
56. C3×#3942C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90973C22semidirect
61. (C2×D3)⋊#168C22semidirect
75. #65308D3semidirect
108. #6716D4semidirect
187. #4015C2×D3semidirect
195. #3942C2×D3semidirect
196. #3942C2×D3semidirect
198. C4⋊#168C2×D3semidirect
384. C2×C5×D3#137semidirect
695. C3×C5#3266semidirect
709. C2×D3#4097semidirect
784. C5#80444semidirect
811. C3#10615237semidirect

Maximal subgroups

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

subgroupindex
C5×#55542
C2×#914862
C2×D3×#6872
#117525582
#117511192
C3×#653082
#117490592
#117490582
#117474952
#117474942
#117473552
#117473532
#117470822
#117469992
#117468842
#106152373
#804445