Finite Group Databasebeta

← #14424165

Subgroups — #14424165

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×#91798C211yesmaximal, characteristic, complemented
3C2×#91365C211yesmaximal, characteristic, complemented
4C2×#91313C211yesmaximal, characteristic, complemented
5C5×#5126C211yesmaximal, characteristic, complemented
6C3×#65422C211yesmaximal, characteristic, complemented
7#11748413C211yesmaximal, characteristic, complemented
8#11748166C212yesmaximal, complemented
9#11748162C212yesmaximal, complemented
10#11748133C212yesmaximal, complemented
11#11748120C212yesmaximal, complemented
12#10610371—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic, complemented
15C22×C4×C5×D3C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
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
28#91798—24no—
29C2×Dic60C2212yescomplemented
30C2×#6706C2212yescomplemented
31C2×C5×#208C2211yescharacteristic, complemented
32C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
33C2×#6668—21no—
34C2×(C2×D3)⋊Dic5—21no—
35#91365—21no—
36#91365—21no—
37#91365C2212yes—
38#91365C2212yescomplemented
39C2×#6662C2212yescomplemented
40#91313—24no—
41C2×#6657C2212yescomplemented
42C5×(C2×D3)⋊C8C2212yes—
43C5×(C2×D3)⋊C8C2212yescomplemented
44C3×#3953C2212yescomplemented
45C3×#3948C2212yescomplemented
46#90974C2212yescomplemented
47#90968C2212yescomplemented
48#78885—51nomaximal, Hall
49C22×#709—31no—
50C2×#4070—31no—
51C2×#4055—31no—
52C2×#4055—31no—
53C5×#407—31no—
54#65422—31no—
55#65422D311yescharacteristic, complemented
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×Dic30—22no—
70C2×Dic30—22no—
71C2×Dic30—21no—
72C2×Dic30C2312yes—
73C2×Dic30C2311yescharacteristic
74C22×C5×Dic3D411yescharacteristic
75C2×C4×C5×D3—22no—
76C2×C4×C5×D3—22no—
77C2×C4×C5×D3D411yescharacteristic
78C2×C4×C5×D3D411yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C4×C5×D3C2311yescharacteristic
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C3×#709—22no—
84C3×#709D414yes—
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5—21no—
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—
109Dic60—24no—
110#6706—24no—
111C5×#208—22no—
112C2×C5×C3⋊C8C2312yes—
113C3×C4⋊Dic5—21no—
114C3×C4⋊Dic5C2312yes—
115#6668—22no—
116#6668—22no—
117(C2×D3)⋊Dic5—22no—
118(C2×D3)⋊Dic5—22no—
119#6662—24no—
120#6657—24no—
121C2×D3×#41—51no—
122C2×#951—51no—
123C2×#909—51no—
124C2×#897—51no—
125C3×#417—51no—
126#5126D511yescharacteristic, complemented
127#4966—51no—
128#4809—52no—
129#4808—52no—
130#4783—52no—
131#4776—52no—
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×Dic10—31no—
146C2×C5×M16—31no—
147C2×C5×M16C2×D311yescharacteristic, complemented
148C2×C22⋊Dic5—61no—
149C2×C4⋊Dic5C2×D311yescharacteristic, complemented
150#4070—32no—
151#4070—32no—
152#4070—61no—
153#4070—61no—
154C2×#683—61no—
155#4055—64no—
156#4055—64no—
157C2×Dic20—32no—
158C2×Dic20—32no—
159C2×#677—32no—
160C2×#677—32no—
161C5×C22⋊C8—32no—
162C5×C22⋊C8—32no—
163#3953—32no—
164#3953C2×D312yescomplemented
165#3948—32no—
166#3948C2×D312yescomplemented
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—
191Dic30—22no—
192Dic30—22no—
193Dic30—42no—
194Dic30C2×D412yes—
195C2×C5×Dic3—22no—
196C2×C5×Dic3C2×D411yescharacteristic
197C2×C5×Dic3C2×D411yescharacteristic
198C4×C5×D3—22no—
199C4×C5×D3—22no—
200C4×C5×D3—21no—
201C4×C5×D3—21no—
202C4×C5×D3—21no—
203C4×C5×D3—21no—
204C3×C22⋊D5—24no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—22no—
207C2×C3×Dic5—42no—
208C3×D20—21no—
209C3×D20C2×D412yes—
210C3×C4×D5—24no—
211C3×Dic10—21no—
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—
223D3×#41—104no—
224D3×#41—104no—
225C2×#239—51no—
226C2×D3×Q8—51no—
227C2×#237—51no—
228C2×#237—101no—
229C2×D3×D4—51no—
230C2×D3×D4—101no—
231C2×#235—51no—
232C2×#235—101no—
233C22×C4×D3—101no—
234C22×C4×D3C2×D511yescharacteristic
235C22×Dic6—51no—
236C2×C3×M16C2×D511yescharacteristic, complemented
237C2×C3×C4⋊C4—51no—
238#951—104no—
239C2×#216—52no—
240C2×#214—52no—
241C2×(C2×D3)⋊C4—101no—
242C2×C4⋊Dic3—101no—
243C2×#208C2×D511yescharacteristic, complemented
244#909—104no—
245C2×Dic12—52no—
246C2×#204—52no—
247#897—52no—
248#897—52no—
249#897—101no—
250#897—101no—
251C3×#103—52no—
252C3×#102—52no—
253(C2×D3)⋊C8C2×D512yes—
254(C2×D3)⋊C8C2×D512yescomplemented
255#810—52no—
256#809—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#709D1214yes—
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—31no—
296C2×Dic10—32no—
297C2×Dic10—62no—
298C2×Dic10—61no—
299C2×Dic10—62no—
300C2×Dic10—62no—
301C2×Dic10—62no—
302C2×Dic10—61no—
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—21no—
311C4⋊Dic5C22×D312yes—
312#683—62no—
313#683—62no—
314Dic20—64no—
315Dic20—64no—
316#677—64no—
317#677—64no—
318C22×#41—151no—
319C2×#137—151no—
320C2×#137—151no—
321C2×C22⋊Q8—151no—
322#452—152no—
323#452—152no—
324#451—152no—
325#450—152no—
326#417—51no—
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×D4—51no—
362C2×C3×D4—101no—
363C22×C3×C4—101no—
364C22×C3×C4—101no—
365C22×C3×C4C22×D511yescharacteristic
366C2×#67—101no—
367C2×#67—101no—
368C2×#67—101no—
369C22×Dic3—101no—
370C22×Dic3—101no—
371C22×Dic3D2011yescharacteristic
372#239—102no—
373#239—102no—
374D3×Q8—102no—
375D3×Q8—102no—
376#237—102no—
377#237—102no—
378#237—108no—
379D3×D4—102no—
380D3×D4—102no—
381D3×D4—108no—
382#235—54no—
383#235—108no—
384#235—102no—
385C2×D12—51no—
386C2×D12—101no—
387C2×C4×D3—22no—
388C2×C4×D3—22no—
389C2×C4×D3—108no—
390C2×C4×D3—101no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3D2011yescharacteristic
394C2×C4×D3D2011yescharacteristic
395C2×C4×D3C22×D511yescharacteristic
396C2×C4×D3C22×D511yescharacteristic
397C2×Dic6—51no—
398C2×Dic6—52no—
399C2×Dic6—101no—
400C2×Dic6—102no—
401C2×Dic6—102no—
402C2×Dic6—101no—
403C3×M16—22no—
404C2×C3×C8C22×D512yes—
405C3×C4⋊C4—52no—
406C3×C4⋊C4—101no—
407#216—104no—
408#214—104no—
409(C2×D3)⋊C4—102no—
410(C2×D3)⋊C4—102no—
411C4⋊Dic3—102no—
412C4⋊Dic3—102no—
413#208—22no—
414C2×C3⋊C8C22×D512yes—
415Dic12—104no—
416#204—104no—
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×C5C2×D1212yes—
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5D3×D412yes—
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×D1212yes—
457C4×D5—24no—
458C4×D5—64no—
459C4×D5—64no—
460C4×D5—64no—
461Dic10—21no—
462Dic10—32no—
463Dic10—64no—
464Dic10—61no—
465Dic10—62no—
466Dic10—62no—
467Dic10—122no—
468Dic10C2×D1212yes—
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—151no—
480C22×Q8—151no—
481C22×D4—151no—
482C22×D4—301no—
483C23×C4—31no—
484C23×C4—301no—
485#137—304no—
486#137—304no—
487C2×Q16—152no—
488C2×Q16—152no—
489C2×SD16—152no—
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—51no—
498C2×C4⋊C4—301no—
499C2×C22⋊C4—301no—
500#103—52no—
501#103—152no—
502#102—52no—
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×D4—52no—
528C3×D4—104no—
529C3×D4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—104no—
532C2×C3×C4—102no—
533C2×C3×C4—202no—
534C2×C3×C4C2×D2011yescharacteristic
535C2×C3×C4D4×D512yes—
536C2×C3×C4D4×D512yes—
537C2×C3×C4C23×D511yescharacteristic
538#67—104no—
539#67—104no—
540#67—104no—
541C2×Dic3—22no—
542C2×Dic3—104no—
543C2×Dic3—101no—
544C2×Dic3—102no—
545C2×Dic3—202no—
546C2×Dic3C2×D2011yescharacteristic
547C2×Dic3C2×D2011yescharacteristic
548D12—52no—
549D12—104no—
550D12—101no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—104no—
558C4×D3—104no—
559C4×D3—104no—
560Dic6—52no—
561Dic6—104no—
562Dic6—101no—
563Dic6—102no—
564Dic6—102no—
565Dic6—202no—
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#88212yes—
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#88212yes—
589C4×C5C22×D1211yescharacteristic
590C4×C5C2×D3×D411yescharacteristic
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—151no—
609C2×Q8—152no—
610C2×Q8—301no—
611C2×Q8—302no—
612C2×Q8—302no—
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—304no—
643Q16—304no—
644SD16—304no—
645SD16—304no—
646M16—22no—
647M16—62no—
648C2×C8—32no—
649C2×C8C2×D3×D512yes—
650C4⋊C4—52no—
651C4⋊C4—101no—
652C4⋊C4—302no—
653C4⋊C4—302no—
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×C5C2×#88211yescharacteristic
688C2×C5#577311yescharacteristic
689C2×C5D3×#13711yescharacteristic
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—152no—
706Q8—304no—
707Q8—301no—
708Q8—302no—
709Q8—302no—
710Q8—602no—
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×C4D5×D1212yes—
741C2×C4D3×D2011yescharacteristic
742C2×C4#679012yes—
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#7888511yescharacteristic, 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#9147612yes—
772C22C2×D3×D2011yescharacteristic
773C4—61no—
774C4—61no—
775C4—102no—
776C4—202no—
777C4—302no—
778C4—602no—
779C4#9147612yes—
780C4C2×D5×D1211yescharacteristic
781C4C2×#679011yescharacteristic
782C3#1061037111yescharacteristic, complemented, Sylow
783C2—22no—
784C2—62no—
785C2—121no—
786C2—202no—
787C2—602no—
788C2D3×#405511yescharacteristic
789C2#1175402911yescharacteristic
790C2C2×#9147611yescharacteristic
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×#91798C2semidirect
3. C2×#91365C2semidirect
4. C2×#91313C2semidirect
5. C5×#5126C2semidirect
6. C3×#65422C2semidirect
7. #11748413C2semidirect
8. #11748166C2semidirect
9. #11748162C2semidirect
10. #11748133C2semidirect
11. #11748120C2semidirect
14. C22×Dic30C22semidirect
27. C2×C3×C5×M16C22semidirect
29. C2×Dic60C22semidirect
30. C2×#6706C22semidirect
31. C2×C5×#208C22semidirect
32. C2×C3×C4⋊Dic5C22semidirect
38. #91365C22semidirect
39. C2×#6662C22semidirect
41. C2×#6657C22semidirect
43. C5×(C2×D3)⋊C8C22semidirect
44. C3×#3953C22semidirect
45. C3×#3948C22semidirect
46. #90974C22semidirect
47. #90968C22semidirect
55. #65422D3semidirect
126. #5126D5semidirect
147. C2×C5×M16C2×D3semidirect
149. C2×C4⋊Dic5C2×D3semidirect
164. #3953C2×D3semidirect
166. #3948C2×D3semidirect
236. C2×C3×M16C2×D5semidirect
243. C2×#208C2×D5semidirect
254. (C2×D3)⋊C8C2×D5semidirect
342. C2×C5×D3#137semidirect
492. C2×M16D3×D5semidirect
656. C3×C5#3007semidirect
674. C2×D3#4055semidirect
754. C5#78885semidirect
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×#917982
C2×#913652
C2×#913132
C5×#51262
C3×#654222
#117484132
#117481662
#117481622
#117481332
#117481202
#106103713
#788855