Finite Group Databasebeta

← #14424164

Subgroups — #14424164

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#709C211yesmaximal, characteristic
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3C2×#91369C211yesmaximal, characteristic, complemented
4C2×#91315C211yesmaximal, characteristic, complemented
5#11751234C211yesmaximal, characteristic, complemented
6C5×#5126C211yesmaximal, characteristic, complemented
7#11748369C211yesmaximal, characteristic, complemented
8#11748152C212yesmaximal, complemented
9#11748147C212yesmaximal, complemented
10#11748125C212yesmaximal, complemented
11#11748110C212yesmaximal, complemented
12#10610371—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic, complemented
17C2×D3×C22⋊D5—21no—
18C2×#6779—21no—
19D3×#709—24no—
20D3×#709—24no—
21C2×D3×D20C2211yescharacteristic
22C2×C4×D3×D5—21no—
23C2×#6771—21no—
24C2×#6769C2211yescharacteristic
25C2×D3×Dic10C2211yescharacteristic
26C2×#6765C2211yescharacteristic
27C2×C3×C5×M16C2211yescharacteristic, complemented
28C2×C4⋊Dic15C2211yescharacteristic, complemented
29C2×C5×#208C2211yescharacteristic, complemented
30C3×#4055—24no—
31C2×C3×Dic20C2212yescomplemented
32C2×C3×#677C2212yescomplemented
33C2×#6669—21no—
34C2×(C2×D3)⋊Dic5—21no—
35#91369—21no—
36#91369—21no—
37#91369C2212yes—
38#91369C2212yescomplemented
39C2×#6662C2212yescomplemented
40#91315—24no—
41C2×#6658C2212yescomplemented
42#91105C2212yescomplemented
43#91100C2212yescomplemented
44C5×(C2×D3)⋊C8C2212yes—
45C5×(C2×D3)⋊C8C2212yescomplemented
46#90971C2212yescomplemented
47#90965C2212yescomplemented
48#83981—51nomaximal, Hall
49C22×#709—31no—
50C2×#4070—31no—
51C2×#4055—31no—
52C2×#4055D311yescharacteristic, complemented
53C5×#407—31no—
54#65422—31no—
55#65422—31no—
56#65028—32no—
57#65022—32no—
58#65022—32no—
59#65020—32no—
60C23×C5×D3D411yescharacteristic
61C22×D3×D5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C22×Dic15—21no—
65#6817—22no—
66#6817D414yes—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C22×C5×Dic3D411yescharacteristic
71C2×C4×C5×D3—22no—
72C2×C4×C5×D3—22no—
73C2×C4×C5×D3D411yescharacteristic
74C2×C4×C5×D3D411yescharacteristic
75C2×C4×C5×D3C2311yescharacteristic
76C2×C4×C5×D3C2311yescharacteristic
77C2×C3×C22⋊D5—21no—
78C22×C3×Dic5—21no—
79C3×#709—22no—
80C3×#709D414yes—
81C2×C3×D20C2311yescharacteristic
82C2×C3×C4×D5—21no—
83C2×C3×Dic10—22no—
84C2×C3×Dic10—22no—
85C2×C3×Dic10—21no—
86C2×C3×Dic10C2312yes—
87C2×C3×Dic10C2311yescharacteristic
88D3×C22⋊D5—28no—
89C2×#1204—21no—
90C2×#1203—21no—
91C2×#1202—21no—
92C2×#1201—21no—
93C2×#1200—21no—
94C2×D3×Dic5—21no—
95#6779—28no—
96C2×D5×Dic3—21no—
97D3×D20—22no—
98D3×D20—22no—
99C4×D3×D5—28no—
100#6771—28no—
101#6769—22no—
102#6769—22no—
103D3×Dic10—22no—
104D3×Dic10—22no—
105#6765—22no—
106#6765—22no—
107C3×C5×M16—22no—
108C2×C3×C5×C8C2312yes—
109C4⋊Dic15—21no—
110C4⋊Dic15C2312yes—
111C5×#208—22no—
112C2×C5×C3⋊C8C2312yes—
113C3×Dic20—24no—
114C3×#677—24no—
115#6669—22no—
116#6669—22no—
117(C2×D3)⋊Dic5—22no—
118(C2×D3)⋊Dic5—22no—
119#6662—24no—
120#6658—24no—
121C2×D3×#41—51no—
122C2×C3×#137—51no—
123C2×#946—51no—
124C2×#942—51no—
125#5232—51no—
126#5187—52no—
127#5186—52no—
128#5173—52no—
129#5169—52no—
130#5133—51no—
131#5126D511yescharacteristic, complemented
132C23×C4×C5—31no—
133C22×C22⋊D5—61no—
134C2×#709—31no—
135C2×#709—31no—
136C2×#709—31no—
137C2×#709—61no—
138C2×#709—64no—
139C2×#709—61no—
140C2×#709—64no—
141C2×#709C2×D311yescharacteristic
142C22×D20—31no—
143C22×C4×D5—61no—
144C22×Dic10—31no—
145C22×Dic10C2×D311yescharacteristic, complemented
146C2×C5×M16—31no—
147C2×C5×M16C2×D311yescharacteristic, complemented
148C2×C22⋊Dic5—61no—
149C2×C4⋊Dic5—31no—
150#4070—32no—
151#4070—32no—
152#4070—61no—
153#4070—61no—
154C2×#683—61no—
155#4055—24no—
156#4055—64no—
157C2×Dic20—32no—
158C2×Dic20C2×D312yescomplemented
159C2×#677—32no—
160C2×#677C2×D312yescomplemented
161C5×C22⋊C8—32no—
162C5×C22⋊C8—32no—
163#3953—32no—
164#3953—32no—
165#3948—32no—
166#3948—32no—
167#3007—151noSylow
168C23×C3×C5C2×D411yescharacteristic
169C22×D15—21no—
170C22×C5×D3—22no—
171C22×C5×D3—22no—
172C22×C5×D3—41no—
173C22×C5×D3C2×D411yescharacteristic
174C22×C5×D3C2×D411yescharacteristic
175C22×C3×D5—21no—
176C2×D3×D5—24no—
177C2×D3×D5—42no—
178C2×D3×D5—42no—
179C2×C3×C4×C5C2×D411yescharacteristic
180C2×C3×C4×C5C2×D412yes—
181C2×C3×C4×C5C2×D412yes—
182C2×C3×C4×C5C2411yescharacteristic
183#1220—24no—
184C2×Dic15—21no—
185C2×Dic15—22no—
186C2×Dic15—42no—
187D60—21no—
188D60C2×D412yes—
189C4×D15—24no—
190Dic30—21no—
191Dic30C2×D412yes—
192C2×C5×Dic3—22no—
193C2×C5×Dic3C2×D411yescharacteristic
194C2×C5×Dic3C2×D411yescharacteristic
195C4×C5×D3—22no—
196C4×C5×D3—22no—
197C4×C5×D3—21no—
198C4×C5×D3—21no—
199C4×C5×D3—21no—
200C4×C5×D3—21no—
201C3×C22⋊D5—24no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—22no—
204C2×C3×Dic5—42no—
205C3×D20—21no—
206C3×D20C2×D412yes—
207C3×C4×D5—24no—
208C3×Dic10—21no—
209C3×Dic10—22no—
210C3×Dic10—22no—
211C3×Dic10—42no—
212C3×Dic10C2×D412yes—
213#1204—24no—
214#1203—24no—
215#1202—24no—
216#1201—24no—
217#1200—24no—
218D3×Dic5—24no—
219D5×Dic3—24no—
220C3×C5×C8—22no—
221C5×C3⋊C8—22no—
222C2×C3×#41—51no—
223C22×C3×Q8—51no—
224D3×#41—104no—
225D3×#41—104no—
226C2×#239—51no—
227C2×D3×Q8—51no—
228C2×#237—51no—
229C2×#237—101no—
230C2×D3×D4—51no—
231C2×D3×D4—101no—
232C2×#235—51no—
233C2×#235—101no—
234C22×C4×D3—101no—
235C22×C4×D3C2×D511yescharacteristic
236C3×#137—104no—
237C2×C3×Q16—52no—
238C2×C3×SD16—52no—
239C2×C3×M16C2×D511yescharacteristic, complemented
240#946—52no—
241#946—52no—
242#946—101no—
243#946—101no—
244C2×#216—52no—
245#942—104no—
246C2×#215—52no—
247C2×(C2×D3)⋊C4—101no—
248C2×C4⋊Dic3—51no—
249C2×Dic3⋊C4—101no—
250C2×#208C2×D511yescharacteristic, complemented
251#835—52no—
252#832—52no—
253#821—52no—
254(C2×D3)⋊C8C2×D512yes—
255(C2×D3)⋊C8C2×D512yescomplemented
256#816—52no—
257C24×C5—31no—
258C23×D5—61no—
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—62no—
265C22×C4×C5—62no—
266C22×C4×C5C22×D311yescharacteristic
267C2×C22⋊D5—21no—
268C2×C22⋊D5—61no—
269C2×C22⋊D5—68no—
270C2×C22⋊D5—61no—
271C2×C22⋊D5—61no—
272C22×Dic5—21no—
273C22×Dic5—61no—
274C22×Dic5—61no—
275#709—22no—
276#709—34no—
277#709—62no—
278#709—62no—
279#709—68no—
280#709—68no—
281#709—62no—
282#709—62no—
283#709—62no—
284#709#6714yes—
285C2×D20—31no—
286C2×D20—62no—
287C2×D20—61no—
288C2×D20—62no—
289C2×D20C22×D311yescharacteristic
290C2×C4×D5—21no—
291C2×C4×D5—68no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×Dic10—22no—
296C2×Dic10—22no—
297C2×Dic10—21no—
298C2×Dic10—31no—
299C2×Dic10—62no—
300C2×Dic10—61no—
301C2×Dic10—62no—
302C2×Dic10C22×D312yes—
303C2×Dic10C22×D311yescharacteristic
304C5×M16—22no—
305C5×M16—62no—
306C2×C5×C8—32no—
307C2×C5×C8C22×D312yes—
308C22⋊Dic5—62no—
309C22⋊Dic5—62no—
310C4⋊Dic5—32no—
311C4⋊Dic5—61no—
312#683—62no—
313#683—62no—
314Dic20—24no—
315Dic20—64no—
316#677—24no—
317#677—64no—
318C22×#41—151no—
319C2×#137—51no—
320C2×#137—151no—
321C2×C22⋊Q8—151no—
322#452—152no—
323#452—152no—
324#451—152no—
325#450—152no—
326#417—151no—
327#417—151no—
328#407—31no—
329C22×C3×C5—21no—
330C22×C3×C5—21no—
331C22×C3×C5#12012yes—
332C22×C3×C5C22×D411yescharacteristic
333C2×D15—22no—
334C2×D15—41no—
335C2×D15—41no—
336C2×C5×D3—21no—
337C2×C5×D3—21no—
338C2×C5×D3—21no—
339C2×C5×D3—21no—
340C2×C5×D3—21no—
341C2×C5×D3—44no—
342C2×C5×D3#13712yescomplemented
343C2×C3×D5—22no—
344C2×C3×D5—41no—
345C2×C3×D5—41no—
346D3×D5—48no—
347C3×C4×C5#12012yes—
348C3×C4×C5C22×D411yescharacteristic
349C3×C4×C5C22×D411yescharacteristic
350Dic15—22no—
351Dic15—42no—
352C3×Dic5—22no—
353C3×Dic5—42no—
354C5×Dic3—21no—
355C5×Dic3—21no—
356C23×D3—101no—
357C23×D3D2011yescharacteristic
358C3×#41—54no—
359C3×#41—102no—
360C2×C3×Q8—51no—
361C2×C3×Q8—52no—
362C2×C3×Q8—101no—
363C2×C3×Q8—102no—
364C2×C3×Q8—102no—
365C2×C3×D4—51no—
366C2×C3×D4—101no—
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4C22×D511yescharacteristic
370C2×#67—101no—
371C2×#67—101no—
372C2×#67—101no—
373C22×Dic3—101no—
374C22×Dic3—101no—
375C22×Dic3D2011yescharacteristic
376#239—102no—
377#239—102no—
378D3×Q8—102no—
379D3×Q8—102no—
380#237—102no—
381#237—102no—
382#237—108no—
383D3×D4—102no—
384D3×D4—102no—
385D3×D4—108no—
386#235—54no—
387#235—108no—
388#235—102no—
389C2×D12—51no—
390C2×D12—101no—
391C2×C4×D3—22no—
392C2×C4×D3—22no—
393C2×C4×D3—108no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
397C2×C4×D3D2011yescharacteristic
398C2×C4×D3D2011yescharacteristic
399C2×C4×D3C22×D511yescharacteristic
400C2×C4×D3C22×D511yescharacteristic
401C2×Dic6—51no—
402C2×Dic6—101no—
403C3×Q16—104no—
404C3×SD16—104no—
405C3×M16—22no—
406C2×C3×C8C22×D512yes—
407#216—104no—
408#215—104no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4—102no—
411C4⋊Dic3—52no—
412C4⋊Dic3—101no—
413Dic3⋊C4—102no—
414Dic3⋊C4—102no—
415#208—22no—
416C2×C3⋊C8C22×D512yes—
417C23×C5—31no—
418C23×C5—31no—
419C23×C5—62no—
420C23×C5—62no—
421C23×C5—121no—
422C23×C5D3×D411yescharacteristic
423C22×D5—21no—
424C22×D5—64no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C2×C4×C5—31no—
429C2×C4×C5—31no—
430C2×C4×C5—62no—
431C2×C4×C5—62no—
432C2×C4×C5—62no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5D3×D411yescharacteristic
438C2×C4×C5D3×D412yes—
439C2×C4×C5C2×#6712yes—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—24no—
442C22⋊D5—64no—
443C22⋊D5—64no—
444C22⋊D5—64no—
445C2×Dic5—21no—
446C2×Dic5—22no—
447C2×Dic5—42no—
448C2×Dic5—64no—
449C2×Dic5—61no—
450C2×Dic5—62no—
451C2×Dic5—122no—
452D20—21no—
453D20—32no—
454D20—64no—
455D20—61no—
456D20C2×#6712yes—
457C4×D5—24no—
458C4×D5—64no—
459C4×D5—64no—
460C4×D5—64no—
461Dic10—21no—
462Dic10—22no—
463Dic10—22no—
464Dic10—32no—
465Dic10—42no—
466Dic10—64no—
467Dic10—61no—
468Dic10C2×#6712yes—
469C5×C8—22no—
470C5×C8—62no—
471C2×#41—51no—
472C2×#41—151no—
473C2×#41—151no—
474C2×#41—151no—
475C2×#41—301no—
476C2×#41—301no—
477C2×#41—304no—
478C2×#41—304no—
479C22×Q8—51no—
480C22×Q8—151no—
481C22×D4—151no—
482C22×D4—301no—
483C23×C4—31no—
484C23×C4—301no—
485#137—104no—
486#137—304no—
487C2×Q16—52no—
488C2×Q16—152no—
489C2×SD16—52no—
490C2×SD16—152no—
491C2×M16—31no—
492C2×M16D3×D511yescharacteristic, complemented
493C22⋊Q8—152no—
494C22⋊Q8—152no—
495C22⋊Q8—301no—
496C22⋊Q8—301no—
497C2×C4⋊C4—151no—
498C2×C4⋊C4—301no—
499C2×C22⋊C4—301no—
500#103—152no—
501#103—152no—
502#102—152no—
503#102—152no—
504C22⋊C8—32no—
505C22⋊C8—32no—
506C2×C3×C5—22no—
507C2×C3×C5C2×#12011yescharacteristic
508C2×C3×C5C2×#13711yescharacteristic
509C2×C3×C5#57511yescharacteristic
510D15—42no—
511C3×D5—42no—
512C5×D3—22no—
513C5×D3—41no—
514C23×C3—101no—
515C23×C3C2×D2011yescharacteristic
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—41no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3C2×D2011yescharacteristic
524C22×D3C2×D2011yescharacteristic
525C3×Q8—52no—
526C3×Q8—101no—
527C3×Q8—102no—
528C3×Q8—102no—
529C3×Q8—202no—
530C3×D4—52no—
531C3×D4—104no—
532C3×D4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—104no—
535C2×C3×C4—102no—
536C2×C3×C4—202no—
537C2×C3×C4C2×D2011yescharacteristic
538C2×C3×C4D4×D512yes—
539C2×C3×C4D4×D512yes—
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543#67—104no—
544C2×Dic3—22no—
545C2×Dic3—104no—
546C2×Dic3—101no—
547C2×Dic3—102no—
548C2×Dic3—202no—
549C2×Dic3C2×D2011yescharacteristic
550C2×Dic3C2×D2011yescharacteristic
551D12—52no—
552D12—104no—
553D12—101no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—22no—
559C4×D3—22no—
560C4×D3—104no—
561C4×D3—104no—
562C4×D3—104no—
563Dic6—52no—
564Dic6—104no—
565Dic6—101no—
566C3×C8—22no—
567C3⋊C8—22no—
568C22×C5—21no—
569C22×C5—21no—
570C22×C5—32no—
571C22×C5—61no—
572C22×C5—61no—
573C22×C5—61no—
574C22×C5—61no—
575C22×C5—61no—
576C22×C5—124no—
577C22×C5#93712yes—
578C22×C5C2×D3×D411yescharacteristic
579C2×D5—22no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—62no—
583C2×D5—128no—
584C2×D5—121no—
585C2×D5—121no—
586C4×C5—61no—
587C4×C5—61no—
588C4×C5#93712yes—
589C4×C5C2×D3×D411yescharacteristic
590C4×C5C22×#6711yescharacteristic
591Dic5—22no—
592Dic5—42no—
593Dic5—62no—
594Dic5—122no—
595C24—31no—
596C24—301no—
597#41—54no—
598#41—102no—
599#41—154no—
600#41—308no—
601#41—302no—
602#41—302no—
603#41—308no—
604#41—302no—
605#41—302no—
606#41—302no—
607C2×Q8—51no—
608C2×Q8—52no—
609C2×Q8—101no—
610C2×Q8—102no—
611C2×Q8—102no—
612C2×Q8—151no—
613C2×Q8—301no—
614C2×Q8—302no—
615C2×Q8—302no—
616C2×D4—51no—
617C2×D4—101no—
618C2×D4—151no—
619C2×D4—301no—
620C2×D4—302no—
621C2×D4—302no—
622C2×D4—301no—
623C2×D4—308no—
624C2×D4—301no—
625C2×D4—301no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—62no—
632C22×C4—62no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4—308no—
638C22×C4—301no—
639C22×C4—301no—
640C22×C4—301no—
641C22×C4C2×D3×D511yescharacteristic
642Q16—104no—
643Q16—304no—
644SD16—104no—
645SD16—304no—
646M16—22no—
647M16—62no—
648C2×C8—32no—
649C2×C8C2×D3×D512yes—
650C4⋊C4—152no—
651C4⋊C4—302no—
652C4⋊C4—302no—
653C4⋊C4—301no—
654C22⋊C4—302no—
655C22⋊C4—302no—
656C3×C5#300711yescharacteristic, complemented, Hall
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—102no—
660C22×C3—201no—
661C22×C3—201no—
662C22×C3#402812yes—
663C22×C3C22×D2011yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—44no—
670C2×D3—102no—
671C2×D3—208no—
672C2×D3—201no—
673C2×D3—201no—
674C2×D3#405512yescomplemented
675C3×C4—102no—
676C3×C4—202no—
677C3×C4#402812yes—
678C3×C4C2×D4×D511yescharacteristic
679C3×C4C2×D4×D511yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—102no—
683Dic3—202no—
684C2×C5—22no—
685C2×C5—62no—
686C2×C5—121no—
687C2×C5D3×#13711yescharacteristic
688C2×C5#577711yescharacteristic
689C2×C5C2×#93711yescharacteristic
690D5—42no—
691D5—122no—
692C23—31no—
693C23—31no—
694C23—62no—
695C23—62no—
696C23—101no—
697C23—121no—
698C23—304no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23D3×D2011yescharacteristic
703Q8—52no—
704Q8—101no—
705Q8—102no—
706Q8—102no—
707Q8—152no—
708Q8—202no—
709Q8—304no—
710Q8—301no—
711D4—52no—
712D4—104no—
713D4—101no—
714D4—152no—
715D4—304no—
716D4—304no—
717D4—304no—
718D4—304no—
719D4—301no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—101no—
730C2×C4—104no—
731C2×C4—102no—
732C2×C4—202no—
733C2×C4—304no—
734C2×C4—304no—
735C2×C4—304no—
736C2×C4—301no—
737C2×C4—304no—
738C2×C4—302no—
739C2×C4—602no—
740C2×C4D3×D2011yescharacteristic
741C2×C4#677712yes—
742C2×C4D5×#6712yes—
743C2×C4C22×D3×D511yescharacteristic
744C8—22no—
745C8—62no—
746C2×C3—22no—
747C2×C3—202no—
748C2×C3C2×#402811yescharacteristic
749C2×C3C2×#405511yescharacteristic
750C2×C3#6608211yescharacteristic
751D3—22no—
752D3—41no—
753D3—202no—
754C5#8398111yescharacteristic, complemented, Sylow
755C22—21no—
756C22—21no—
757C22—32no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—102no—
764C22—124no—
765C22—201no—
766C22—201no—
767C22—302no—
768C22—608no—
769C22—601no—
770C22—601no—
771C22#9147412yes—
772C22C2×D3×D2011yescharacteristic
773C4—61no—
774C4—61no—
775C4—102no—
776C4—202no—
777C4—302no—
778C4—602no—
779C4#9147412yes—
780C4C2×#677711yescharacteristic
781C4C2×D5×#6711yescharacteristic
782C3#1061037111yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—121no—
786C2—202no—
787C2—602no—
788C2D3×#405511yescharacteristic
789C2#1175402811yescharacteristic
790C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×#709C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4055C2semidirect
3. C2×#91369C2semidirect
4. C2×#91315C2semidirect
5. #11751234C2semidirect
6. C5×#5126C2semidirect
7. #11748369C2semidirect
8. #11748152C2semidirect
9. #11748147C2semidirect
10. #11748125C2semidirect
11. #11748110C2semidirect
16. C22×C3×Dic10C22semidirect
27. C2×C3×C5×M16C22semidirect
28. C2×C4⋊Dic15C22semidirect
29. C2×C5×#208C22semidirect
31. C2×C3×Dic20C22semidirect
32. C2×C3×#677C22semidirect
38. #91369C22semidirect
39. C2×#6662C22semidirect
41. C2×#6658C22semidirect
42. #91105C22semidirect
43. #91100C22semidirect
45. C5×(C2×D3)⋊C8C22semidirect
46. #90971C22semidirect
47. #90965C22semidirect
52. C2×#4055D3semidirect
131. #5126D5semidirect
145. C22×Dic10C2×D3semidirect
147. C2×C5×M16C2×D3semidirect
158. C2×Dic20C2×D3semidirect
160. C2×#677C2×D3semidirect
239. C2×C3×M16C2×D5semidirect
250. C2×#208C2×D5semidirect
255. (C2×D3)⋊C8C2×D5semidirect
342. C2×C5×D3#137semidirect
492. C2×M16D3×D5semidirect
656. C3×C5#3007semidirect
674. C2×D3#4055semidirect
754. C5#83981semidirect
782. C3#10610371semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7092
C2×C3×#40552
C2×#913692
C2×#913152
#117512342
C5×#51262
#117483692
#117481522
#117481472
#117481252
#117481102
#106103713
#839815