Finite Group Databasebeta

← #14424147

Subgroups — #14424147

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×D5×#235C211yesmaximal, characteristic
2C2×#91831C211yesmaximal, characteristic, complemented
3C2×C5×#942C211yesmaximal, characteristic, complemented
4C2×C3×#4092C211yesmaximal, characteristic, complemented
5#11749406C212yesmaximal, complemented
6#11749405C212yesmaximal, complemented
7#11749400C212yesmaximal, complemented
8#11749397C212yesmaximal, complemented
9#11748413C211yesmaximal, characteristic, complemented
10#11748384C211yesmaximal, characteristic, complemented
11#11748341C211yesmaximal, characteristic, complemented
12#10615712—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic, complemented
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×D5×#67—21no—
18C2×#6782—21no—
19D5×#235—24no—
20D5×#235—24no—
21C2×D5×D12C2211yescharacteristic
22C2×C4×D3×D5—21no—
23C2×#6773C2211yescharacteristic
24C2×#6772C2211yescharacteristic
25C2×#6771—21no—
26C2×D5×Dic6C2211yescharacteristic
27C2×#6718C2212yescomplemented
28#91831—24no—
29C2×#6717C2212yescomplemented
30C2×#6710C2211yescharacteristic, complemented
31C2×C5×#216C2212yescomplemented
32C5×#942—24no—
33C2×C5×#215C2212yescomplemented
34C2×C5×#208C2211yescharacteristic, complemented
35C3×#4092—21no—
36C3×#4092—21no—
37C3×#4092C2212yes—
38C3×#4092C2212yescomplemented
39C2×C3×#685—21no—
40C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
41C2×C3×#683—21no—
42#90974C2212yescomplemented
43#90972C2212yescomplemented
44#90968C2212yescomplemented
45#90966C2212yescomplemented
46#90955C2212yes—
47#90955C2212yescomplemented
48#82735—51nomaximal, Hall
49C2×D5×#41—31no—
50C2×C5×#137—31no—
51C2×#4092D311yescharacteristic, complemented
52C2×#4088—31no—
53#65521—31no—
54#65476—32no—
55#65475—32no—
56#65462—32no—
57#65458—32no—
58#65422—31no—
59#65415—31no—
60C23×C3×D5D411yescharacteristic
61C22×D3×D5—21no—
62C2×C3×C5×Q8—21no—
63C2×C3×C5×Q8—22no—
64C2×C3×C5×Q8—22no—
65C2×C3×C5×Q8C2312yes—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—21no—
69#6817—22no—
70#6817D414yes—
71C2×D60C2311yescharacteristic
72C2×C4×D15—21no—
73C2×Dic30C2311yescharacteristic
74C2×C5×#67—21no—
75C5×#235—22no—
76C5×#235D414yes—
77C2×C5×D12C2311yescharacteristic
78C2×C4×C5×D3—21no—
79C2×C5×Dic6C2311yescharacteristic
80C22×C3×Dic5—21no—
81C22×C3×Dic5D411yescharacteristic
82C2×C3×C4×D5—22no—
83C2×C3×C4×D5—22no—
84C2×C3×C4×D5D411yescharacteristic
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88D5×#67—28no—
89C2×#1204—21no—
90C2×#1203—21no—
91C2×#1202—21no—
92C2×#1201—21no—
93C2×#1200—21no—
94#6782—28no—
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97D5×D12—22no—
98D5×D12—22no—
99C4×D3×D5—28no—
100#6773—22no—
101#6773—22no—
102#6772—22no—
103#6772—22no—
104#6771—28no—
105D5×Dic6—22no—
106D5×Dic6—22no—
107#6718—24no—
108#6717—24no—
109#6710—22no—
110C2×C3⋊#168C2312yes—
111C5×#216—24no—
112C5×#215—24no—
113C5×#208—22no—
114C2×C5×C3⋊C8C2312yes—
115C3×#685—22no—
116C3×#685—22no—
117C3×C4⋊Dic5—21no—
118C3×C4⋊Dic5C2312yes—
119C3×#683—22no—
120C3×#683—22no—
121C22×#235—51no—
122C2×C3×C22⋊Q8—51no—
123C2×#942—51no—
124C2×#942D511yescharacteristic, complemented
125#5207—51no—
126#5050—52no—
127#5047—52no—
128#5047—52no—
129#5046—52no—
130#4966—51no—
131#4966—51no—
132C2×C5×#41—31no—
133C22×C5×Q8C2×D311yescharacteristic, complemented
134D5×#41—64no—
135D5×#41—64no—
136C2×#713—31no—
137C2×Q8×D5—31no—
138C2×#711—31no—
139C2×#711—61no—
140C2×D4×D5—31no—
141C2×D4×D5—61no—
142C2×#709—31no—
143C2×#709—61no—
144C22×C4×D5—61no—
145C22×C4×D5C2×D311yescharacteristic
146C5×#137—64no—
147C2×C5×Q16—32no—
148C2×C5×SD16—32no—
149C2×C5×M16—31no—
150#4092—21no—
151#4092—21no—
152#4092C2×D312yes—
153#4092C2×D312yescomplemented
154C2×#689—32no—
155#4088—64no—
156C2×#688—32no—
157C2×#685—21no—
158C2×C4⋊Dic5C2×D311yescharacteristic, complemented
159C2×#683—21no—
160C2×#681—31no—
161#3967—32no—
162#3964—32no—
163#3953—32no—
164#3952—32no—
165#3952—32no—
166#3948—32no—
167#3007—151noSylow
168C23×C3×C5C2×D411yescharacteristic
169C22×D15—21no—
170C22×C5×D3—21no—
171C22×C3×D5—22no—
172C22×C3×D5—22no—
173C22×C3×D5—41no—
174C22×C3×D5C2×D411yescharacteristic
175C22×C3×D5C2×D411yescharacteristic
176C2×D3×D5—24no—
177C2×D3×D5—42no—
178C2×D3×D5—42no—
179C3×C5×Q8—22no—
180C3×C5×Q8—22no—
181C3×C5×Q8—42no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—42no—
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D412yes—
186C2×C3×C4×C5C2×D412yes—
187C2×C3×C4×C5C2411yescharacteristic
188#1220—24no—
189C2×Dic15—21no—
190D60—21no—
191D60C2×D412yes—
192C4×D15—24no—
193Dic30—21no—
194Dic30C2×D412yes—
195C5×#67—24no—
196C2×C5×Dic3—21no—
197C5×D12—21no—
198C5×D12C2×D412yes—
199C4×C5×D3—24no—
200C5×Dic6—21no—
201C5×Dic6C2×D412yes—
202C2×C3×Dic5—22no—
203C2×C3×Dic5—22no—
204C2×C3×Dic5—42no—
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C3×C4×D5—22no—
208C3×C4×D5—22no—
209C3×C4×D5—21no—
210C3×C4×D5—21no—
211C3×C4×D5—21no—
212C3×C4×D5—21no—
213#1204—24no—
214#1203—24no—
215#1202—24no—
216#1201—24no—
217#1200—24no—
218D3×Dic5—24no—
219D5×Dic3—24no—
220C3⋊#168—22no—
221C5×C3⋊C8—22no—
222C22×C3×Q8C2×D511yescharacteristic, complemented
223C23×C3×C4—51no—
224C22×#67—101no—
225C2×#235—51no—
226C2×#235—51no—
227C2×#235—51no—
228C2×#235—101no—
229C2×#235—104no—
230C2×#235—101no—
231C2×#235—104no—
232C2×#235C2×D511yescharacteristic
233C22×D12—51no—
234C22×C4×D3—101no—
235C22×Dic6—51no—
236C3×C22⋊Q8—52no—
237C3×C22⋊Q8—52no—
238C3×C22⋊Q8—101no—
239C3×C22⋊Q8—101no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C4⋊C4—101no—
242C2×C3×C22⋊C4—101no—
243C2×#216—52no—
244C2×#216C2×D512yescomplemented
245#942—24no—
246#942—104no—
247C2×#215—52no—
248C2×#215C2×D512yescomplemented
249C2×#208—51no—
250C2×#208C2×D511yescharacteristic, complemented
251#830—52no—
252#830—52no—
253#810—52no—
254#810—52no—
255#809—52no—
256#809—52no—
257C23×D5—61no—
258C23×D5#6711yescharacteristic
259C5×#41—34no—
260C5×#41—62no—
261C2×C5×Q8—21no—
262C2×C5×Q8—22no—
263C2×C5×Q8—22no—
264C2×C5×Q8—31no—
265C2×C5×Q8C22×D312yes—
266C2×C5×D4—31no—
267C2×C5×D4—61no—
268C22×C4×C5—21no—
269C22×C4×C5—61no—
270C22×C4×C5C22×D311yescharacteristic
271C2×C22⋊D5—61no—
272C2×C22⋊D5—61no—
273C2×C22⋊D5—61no—
274C22×Dic5—21no—
275C22×Dic5—61no—
276C22×Dic5#6711yescharacteristic
277#713—62no—
278#713—62no—
279Q8×D5—62no—
280Q8×D5—62no—
281#711—62no—
282#711—62no—
283#711—68no—
284D4×D5—62no—
285D4×D5—62no—
286D4×D5—68no—
287#709—34no—
288#709—68no—
289#709—62no—
290C2×D20—31no—
291C2×D20—61no—
292C2×C4×D5—22no—
293C2×C4×D5—22no—
294C2×C4×D5—68no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5#6711yescharacteristic
299C2×C4×D5#6711yescharacteristic
300C2×C4×D5C22×D311yescharacteristic
301C2×C4×D5C22×D311yescharacteristic
302C2×Dic10—31no—
303C2×Dic10—61no—
304C5×Q16—64no—
305C5×SD16—64no—
306C5×M16—62no—
307C2×C5×C8—32no—
308#689—64no—
309#688—64no—
310#685—22no—
311#685—22no—
312C4⋊Dic5—21no—
313C4⋊Dic5C22×D312yes—
314#683—22no—
315#683—22no—
316#681—62no—
317C2×#168—32no—
318C22×#41—151no—
319C2×#137—31no—
320C2×#137—151no—
321C2×C22⋊Q8—51no—
322#452—152no—
323#452—152no—
324#451—152no—
325#450—152no—
326#417—151no—
327#417—151no—
328#407—151no—
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—22no—
337C2×C5×D3—41no—
338C2×C5×D3—41no—
339C2×C3×D5—21no—
340C2×C3×D5—21no—
341C2×C3×D5—21no—
342C2×C3×D5—21no—
343C2×C3×D5—21no—
344C2×C3×D5—44no—
345C2×C3×D5#13712yescomplemented
346D3×D5—48no—
347C3×C4×C5—42no—
348C3×C4×C5#12012yes—
349C3×C4×C5C22×D411yescharacteristic
350C3×C4×C5C22×D411yescharacteristic
351Dic15—22no—
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—42no—
355C5×Dic3—22no—
356C24×C3—51no—
357C23×D3—101no—
358C2×C3×Q8—21no—
359C2×C3×Q8—22no—
360C2×C3×Q8—22no—
361C2×C3×Q8C22×D512yes—
362C22×C3×C4—21no—
363C22×C3×C4—51no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—51no—
367C22×C3×C4—51no—
368C22×C3×C4—102no—
369C22×C3×C4—102no—
370C22×C3×C4—101no—
371C22×C3×C4C22×D511yescharacteristic
372C2×#67—21no—
373C2×#67—101no—
374C2×#67—108no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—101no—
378#235—22no—
379#235—54no—
380#235—102no—
381#235—102no—
382#235—108no—
383#235—108no—
384#235—102no—
385#235—102no—
386#235—102no—
387#235C22⋊D514yes—
388C2×D12—51no—
389C2×D12—102no—
390C2×D12—101no—
391C2×D12—102no—
392C2×D12C22×D511yescharacteristic
393C2×C4×D3—21no—
394C2×C4×D3—108no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
397C2×C4×D3—101no—
398C2×Dic6—51no—
399C2×Dic6—102no—
400C2×Dic6—101no—
401C2×Dic6—102no—
402C2×Dic6C22×D511yescharacteristic
403C3×C4⋊C4—52no—
404C3×C4⋊C4—102no—
405C3×C4⋊C4—102no—
406C3×C4⋊C4—101no—
407C3×C22⋊C4—102no—
408C3×C22⋊C4—102no—
409#216—24no—
410#216—104no—
411#215—24no—
412#215—104no—
413#208—22no—
414#208—102no—
415C2×C3⋊C8—52no—
416C2×C3⋊C8C22×D512yes—
417C23×C5—61no—
418C23×C5C2×#6711yescharacteristic
419C22×D5—22no—
420C22×D5—22no—
421C22×D5—41no—
422C22×D5—64no—
423C22×D5—61no—
424C22×D5—122no—
425C22×D5—122no—
426C22×D5C2×#6711yescharacteristic
427C22×D5C2×#6711yescharacteristic
428C5×Q8—22no—
429C5×Q8—22no—
430C5×Q8—32no—
431C5×Q8—42no—
432C5×Q8—61no—
433C5×D4—32no—
434C5×D4—64no—
435C5×D4—61no—
436C2×C4×C5—22no—
437C2×C4×C5—42no—
438C2×C4×C5—61no—
439C2×C4×C5—64no—
440C2×C4×C5D3×D412yes—
441C2×C4×C5D3×D412yes—
442C2×C4×C5C2×#6711yescharacteristic
443C2×C4×C5C23×D311yescharacteristic
444C22⋊D5—64no—
445C22⋊D5—64no—
446C22⋊D5—64no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—42no—
450C2×Dic5—64no—
451C2×Dic5—61no—
452C2×Dic5C2×#6711yescharacteristic
453C2×Dic5C2×#6711yescharacteristic
454D20—32no—
455D20—64no—
456D20—61no—
457C4×D5—22no—
458C4×D5—22no—
459C4×D5—21no—
460C4×D5—21no—
461C4×D5—21no—
462C4×D5—21no—
463C4×D5—64no—
464C4×D5—64no—
465C4×D5—64no—
466Dic10—32no—
467Dic10—64no—
468Dic10—61no—
469C5×C8—62no—
470#168—62no—
471C2×#41—31no—
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×Q8D3×D511yescharacteristic, complemented
481C22×D4—151no—
482C22×D4—301no—
483C23×C4—51no—
484C23×C4—301no—
485#137—64no—
486#137—304no—
487C2×Q16—32no—
488C2×Q16—152no—
489C2×SD16—32no—
490C2×SD16—152no—
491C2×M16—31no—
492C2×M16—151no—
493C22⋊Q8—52no—
494C22⋊Q8—52no—
495C22⋊Q8—101no—
496C22⋊Q8—101no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—101no—
499C2×C22⋊C4—101no—
500#103—152no—
501#103—152no—
502#102—152no—
503#102—152no—
504C22⋊C8—152no—
505C22⋊C8—152no—
506C2×C3×C5—22no—
507C2×C3×C5C2×#12011yescharacteristic
508C2×C3×C5C2×#13711yescharacteristic
509C2×C3×C5#57511yescharacteristic
510D15—42no—
511C3×D5—22no—
512C3×D5—41no—
513C5×D3—42no—
514C23×C3—51no—
515C23×C3—51no—
516C23×C3—102no—
517C23×C3—102no—
518C23×C3—201no—
519C23×C3D4×D511yescharacteristic
520C22×D3—21no—
521C22×D3—104no—
522C22×D3—101no—
523C22×D3—202no—
524C22×D3—202no—
525C3×Q8—22no—
526C3×Q8—22no—
527C3×Q8—42no—
528C2×C3×C4—22no—
529C2×C3×C4—42no—
530C2×C3×C4—51no—
531C2×C3×C4—51no—
532C2×C3×C4—102no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—102no—
538C2×C3×C4—102no—
539C2×C3×C4—102no—
540C2×C3×C4—202no—
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4D4×D512yes—
543C2×C3×C4C2×C22⋊D512yes—
544C2×C3×C4C23×D511yescharacteristic
545#67—24no—
546#67—104no—
547#67—104no—
548#67—104no—
549C2×Dic3—21no—
550C2×Dic3—104no—
551C2×Dic3—101no—
552D12—21no—
553D12—52no—
554D12—104no—
555D12—101no—
556D12C2×C22⋊D512yes—
557C4×D3—24no—
558C4×D3—104no—
559C4×D3—104no—
560C4×D3—104no—
561Dic6—21no—
562Dic6—52no—
563Dic6—104no—
564Dic6—101no—
565Dic6C2×C22⋊D512yes—
566C3⋊C8—22no—
567C3⋊C8—102no—
568C22×C5—21no—
569C22×C5—21no—
570C22×C5—62no—
571C22×C5—121no—
572C22×C5—121no—
573C22×C5#93712yes—
574C22×C5C22×#6711yescharacteristic
575C2×D5—21no—
576C2×D5—21no—
577C2×D5—21no—
578C2×D5—21no—
579C2×D5—21no—
580C2×D5—44no—
581C2×D5—62no—
582C2×D5—128no—
583C2×D5—121no—
584C2×D5—121no—
585C2×D5#94212yescomplemented
586C4×C5—42no—
587C4×C5—62no—
588C4×C5#93712yes—
589C4×C5C2×D3×D411yescharacteristic
590C4×C5C2×D3×D411yescharacteristic
591Dic5—21no—
592Dic5—21no—
593Dic5—42no—
594Dic5—62no—
595C24—51no—
596C24—301no—
597#41—34no—
598#41—62no—
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—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—31no—
611C2×Q8—151no—
612C2×Q8—301no—
613C2×Q8—302no—
614C2×Q8—302no—
615C2×Q8C2×D3×D512yes—
616C2×D4—31no—
617C2×D4—61no—
618C2×D4—151no—
619C2×D4—301no—
620C2×D4—301no—
621C2×D4—302no—
622C2×D4—302no—
623C2×D4—308no—
624C2×D4—301no—
625C2×D4—301no—
626C22×C4—21no—
627C22×C4—51no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—61no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—101no—
636C22×C4—301no—
637C22×C4—301no—
638C22×C4—308no—
639C22×C4—301no—
640C22×C4—301no—
641C22×C4C2×D3×D511yescharacteristic
642Q16—64no—
643Q16—304no—
644SD16—64no—
645SD16—304no—
646M16—62no—
647M16—302no—
648C2×C8—32no—
649C2×C8—152no—
650C4⋊C4—52no—
651C4⋊C4—102no—
652C4⋊C4—102no—
653C4⋊C4—101no—
654C22⋊C4—102no—
655C22⋊C4—102no—
656C3×C5#300711yescharacteristic, complemented, Hall
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—52no—
660C22×C3—101no—
661C22×C3—101no—
662C22×C3—101no—
663C22×C3—101no—
664C22×C3—101no—
665C22×C3—204no—
666C22×C3#408312yes—
667C22×C3C2×D4×D511yescharacteristic
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—102no—
672C2×D3—208no—
673C2×D3—201no—
674C2×D3—201no—
675C3×C4—42no—
676C3×C4—101no—
677C3×C4—101no—
678C3×C4—202no—
679C3×C4#408312yes—
680C3×C4C2×D4×D511yescharacteristic
681C3×C4C22×C22⋊D511yescharacteristic
682Dic3—22no—
683Dic3—102no—
684C2×C5—22no—
685C2×C5—122no—
686C2×C5C2×#93711yescharacteristic
687C2×C5C2×#94211yescharacteristic
688C2×C5#582211yescharacteristic
689D5—22no—
690D5—41no—
691D5—122no—
692C23—51no—
693C23—51no—
694C23—61no—
695C23—102no—
696C23—102no—
697C23—201no—
698C23—304no—
699C23—301no—
700C23—602no—
701C23—602no—
702C23D5×#6711yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—32no—
706Q8—42no—
707Q8—61no—
708Q8—152no—
709Q8—304no—
710Q8—301no—
711D4—32no—
712D4—64no—
713D4—61no—
714D4—152no—
715D4—304no—
716D4—304no—
717D4—304no—
718D4—304no—
719D4—301no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—51no—
723C2×C4—51no—
724C2×C4—61no—
725C2×C4—64no—
726C2×C4—102no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—202no—
735C2×C4—304no—
736C2×C4—304no—
737C2×C4—304no—
738C2×C4—301no—
739C2×C4—304no—
740C2×C4D5×#6711yescharacteristic
741C2×C4D3×C22⋊D512yes—
742C2×C4#679012yes—
743C2×C4C22×D3×D511yescharacteristic
744C8—62no—
745C8—302no—
746C2×C3—22no—
747C2×C3—102no—
748C2×C3—201no—
749C2×C3D5×#13711yescharacteristic
750C2×C3#6611111yescharacteristic
751C2×C3C2×#408311yescharacteristic
752D3—42no—
753D3—202no—
754C5#8273511yescharacteristic, complemented, Sylow
755C22—21no—
756C22—21no—
757C22—52no—
758C22—62no—
759C22—101no—
760C22—101no—
761C22—101no—
762C22—101no—
763C22—101no—
764C22—121no—
765C22—121no—
766C22—204no—
767C22—302no—
768C22—608no—
769C22—601no—
770C22—601no—
771C22#9157712yes—
772C22C2×D5×#6711yescharacteristic
773C4—42no—
774C4—62no—
775C4—101no—
776C4—101no—
777C4—202no—
778C4—302no—
779C4#9157712yes—
780C4C2×D3×C22⋊D511yescharacteristic
781C4C2×#679011yescharacteristic
782C3#1061571211yescharacteristic, complemented, Sylow
783C2—22no—
784C2—102no—
785C2—122no—
786C2—201no—
787C2—602no—
788C2D5×#94211yescharacteristic
789C2#1175508411yescharacteristic
790C2C2×#9157711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×#235C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91831C2semidirect
3. C2×C5×#942C2semidirect
4. C2×C3×#4092C2semidirect
5. #11749406C2semidirect
6. #11749405C2semidirect
7. #11749400C2semidirect
8. #11749397C2semidirect
9. #11748413C2semidirect
10. #11748384C2semidirect
11. #11748341C2semidirect
13. C22×C3×C5×Q8C22semidirect
27. C2×#6718C22semidirect
29. C2×#6717C22semidirect
30. C2×#6710C22semidirect
31. C2×C5×#216C22semidirect
33. C2×C5×#215C22semidirect
34. C2×C5×#208C22semidirect
38. C3×#4092C22semidirect
40. C2×C3×C4⋊Dic5C22semidirect
42. #90974C22semidirect
43. #90972C22semidirect
44. #90968C22semidirect
45. #90966C22semidirect
47. #90955C22semidirect
51. C2×#4092D3semidirect
124. C2×#942D5semidirect
133. C22×C5×Q8C2×D3semidirect
153. #4092C2×D3semidirect
158. C2×C4⋊Dic5C2×D3semidirect
222. C22×C3×Q8C2×D5semidirect
244. C2×#216C2×D5semidirect
248. C2×#215C2×D5semidirect
250. C2×#208C2×D5semidirect
345. C2×C3×D5#137semidirect
480. C22×Q8D3×D5semidirect
585. C2×D5#942semidirect
656. C3×C5#3007semidirect
754. C5#82735semidirect
782. C3#10615712semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C2×#918312
C2×C5×#9422
C2×C3×#40922
#117494062
#117494052
#117494002
#117493972
#117484132
#117483842
#117483412
#106157123
#827355