Finite Group Databasebeta

← C2×D5×#462 #12966098

Subgroups — C2×D5×#462 #12966098

Order 1280.

2790 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Q16C212yesmaximal
2C2×D5×C4⋊Q8C211yesmaximal, characteristic
3C2×C4×Q8×D5C211yesmaximal, characteristic
4C2×C5×#462C211yesmaximal, characteristic, complemented
5C2×#65471C212yesmaximal, complemented
6C2×#65379C211yesmaximal, characteristic, complemented
7C2×#65320C211yesmaximal, characteristic, complemented
8D5×#462C2116yesmaximal, direct product factor
9C2×#65138C211yesmaximal, characteristic, complemented
10C2×D5×C4⋊C8C211yesmaximal, characteristic
11C2×#65082C212yesmaximal, complemented
12C2×D5×#103C212yesmaximal
13C22×Q8×D5C2212yes—
14C22×Q8×D5C2211yescharacteristic
15C22×C5×Q16C2212yes—
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×Q8×Dic5C2211yescharacteristic
19C2×#4090C2212yes—
20C22×#689C2212yes—
21C22×#689C2212yes—
22C2×D5×Q16—216no—
23C2×D5×Q16C22116yes—
24C22×Dic20C2212yes—
25C22×C8×D5C2212yes—
26D5×C4⋊Q8—24no—
27D5×C4⋊Q8C2218yes—
28C4×Q8×D5—24no—
29C4×Q8×D5C2218yes—
30C2×D5×C4⋊C4—21no—
31C2×D5×C4⋊C4—21no—
32C2×D5×C4⋊C4—21no—
33C2×D5×C4⋊C4C2211yescharacteristic
34C2×#4034—21no—
35C2×#4034—21no—
36C2×#4033—21no—
37C2×#4033C2211yescharacteristic
38C2×C42×D5—21no—
39C2×C42×D5C2211yescharacteristic
40C2×#4015C2211yescharacteristic
41C2×C4×Dic10—21no—
42C2×C4×Dic10C2211yescharacteristic
43C5×#462C2218yescomplemented
44C2×C5×C4⋊C8C2211yescharacteristic
45C2×C5×#103C2212yes—
46C2×#3967C2212yes—
47#65471C22116yescomplemented
48C2×#3948C2212yes—
49C2×#3946C2212yes—
50#65379C2218yescomplemented
51#65320C2218yescomplemented
52C2×#3942C2212yes—
53C2×C4⋊#168C2211yescharacteristic
54#65138C2218yescomplemented
55D5×C4⋊C8C2218yes—
56D5×#103C22116yes—
57#65082C22116yescomplemented
58C22×#462—51nomaximal, Sylow
59C22×C5×Q8C2312yes—
60C22×C5×Q8C2311yescharacteristic
61C2×Q8×D5—22no—
62C2×Q8×D5—24no—
63C2×Q8×D5—24no—
64C2×Q8×D5—28no—
65C2×Q8×D5—28no—
66C2×Q8×D5D418yes—
67C2×Q8×D5C2318yes—
68C2×Q8×D5C2314yes—
69C22×C4×D5—21no—
70C22×C4×D5—21no—
71C22×C4×D5—22no—
72C22×C4×D5D411yescharacteristic
73C22×C4×D5D411yescharacteristic
74C22×C4×D5C2311yescharacteristic
75C22×Dic10—21no—
76C22×Dic10—22no—
77C22×Dic10C2312yes—
78C22×Dic10C2311yescharacteristic
79C2×C5×Q16—28no—
80C2×C5×Q16C2318yes—
81C22×C5×C8C2312yes—
82C5×C4⋊Q8—22no—
83C5×C4⋊Q8C2314yes—
84C4×C5×Q8—22no—
85C4×C5×Q8C2314yes—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C42×C5—21no—
91C2×C42×C5C2311yescharacteristic
92Q8×Dic5—22no—
93Q8×Dic5C2314yes—
94#4090—24no—
95#4090C2318yes—
96C2×#689—28no—
97C2×#689—28no—
98C2×#689C2318yes—
99C2×#689C2318yes—
100C2×C4⋊Dic5—21no—
101C2×C4⋊Dic5—21no—
102C2×C4⋊Dic5—21no—
103C2×C4⋊Dic5C2311yescharacteristic
104C2×#683—21no—
105C2×#683—21no—
106C2×#683—21no—
107C2×#683—22no—
108C2×#683—22no—
109C2×C4×Dic5—21no—
110C2×C4×Dic5—21no—
111C2×C4×Dic5—21no—
112C2×C4×Dic5D411yescharacteristic
113C2×C4×Dic5D411yescharacteristic
114C2×C4×Dic5C2311yescharacteristic
115C22×#168C2312yes—
116D5×Q16—264no—
117C2×Dic20—28no—
118C2×Dic20C2318yes—
119C2×C8×D5—28no—
120C2×C8×D5C2318yes—
121D5×C4⋊C4—28no—
122D5×C4⋊C4—28no—
123D5×C4⋊C4—28no—
124D5×C4⋊C4—22no—
125D5×C4⋊C4C2314yes—
126#4034—28no—
127#4034—28no—
128#4033—28no—
129#4033—22no—
130#4033C2314yes—
131C42×D5—28no—
132C42×D5D414yes—
133C42×D5C2314yes—
134#4015—22no—
135#4015C2314yes—
136C4×Dic10—22no—
137C4×Dic10—28no—
138C4×Dic10C2314yes—
139C5×C4⋊C8C2314yes—
140C5×#103C2318yes—
141#3967C2318yes—
142#3948C2318yes—
143#3946C2318yes—
144#3942C2318yes—
145C4⋊#168C2314yes—
146C23×Q16—52no—
147C22×C4⋊Q8—51no—
148C22×C4×Q8—51no—
149C2×#462—516no—
150C2×#462—51no—
151C2×#462—52no—
152C2×#462—52no—
153C2×#462—51no—
154C2×#462—51no—
155C2×#462D511yescharacteristic, direct product factor
156C22×C4⋊C8—51no—
157C22×#103—52no—
158C23×D5C2×D411yescharacteristic
159C2×C5×Q8—21no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—24no—
163C2×C5×Q8—24no—
164C2×C5×Q8C2×D414yes—
165C2×C5×Q8C2414yes—
166C2×C5×Q8C2412yes—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—22no—
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2411yescharacteristic
173C22×Dic5—21no—
174C22×Dic5—22no—
175C22×Dic5—21no—
176C22×Dic5C2×D411yescharacteristic
177C22×Dic5C2×D411yescharacteristic
178C22×Dic5C2×D411yescharacteristic
179Q8×D5—216no—
180Q8×D5—28no—
181Q8×D5—216no—
182Q8×D5—216no—
183Q8×D5—416no—
184Q8×D5C2×D4116yes—
185C2×C4×D5—28no—
186C2×C4×D5—24no—
187C2×C4×D5—24no—
188C2×C4×D5—28no—
189C2×C4×D5—24no—
190C2×C4×D5—48no—
191C2×C4×D5—44no—
192C2×C4×D5Q1618yescomplemented
193C2×C4×D5C2×D414yes—
194C2×C4×D5C2×D412yes—
195C2×C4×D5C2×D414yes—
196C2×C4×D5C2×D414yes—
197C2×C4×D5#4114yes—
198C2×C4×D5C2412yes—
199C2×Dic10—21no—
200C2×Dic10—22no—
201C2×Dic10—28no—
202C2×Dic10—24no—
203C2×Dic10—24no—
204C2×Dic10—24no—
205C2×Dic10—22no—
206C2×Dic10—28no—
207C2×Dic10—48no—
208C2×Dic10C2×D414yes—
209C2×Dic10C2414yes—
210C2×Dic10C2412yes—
211C5×Q16—216no—
212C2×C5×C8—24no—
213C2×C5×C8C2414yes—
214C5×C4⋊C4—24no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—24no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4C2412yes—
219C42×C5—24no—
220C42×C5C2×D412yes—
221C42×C5C2412yes—
222#689—216no—
223#689—216no—
224C4⋊Dic5—21no—
225C4⋊Dic5—24no—
226C4⋊Dic5—24no—
227C4⋊Dic5—24no—
228C4⋊Dic5C2412yes—
229#683—24no—
230#683—24no—
231#683—24no—
232#683—28no—
233#683—28no—
234C4×Dic5—24no—
235C4×Dic5—24no—
236C4×Dic5—24no—
237C4×Dic5C2×D414yes—
238C4×Dic5C2×D412yes—
239C4×Dic5C2×D414yes—
240C4×Dic5C2412yes—
241C2×#168—24no—
242C2×#168C2414yes—
243Dic20—216no—
244C8×D5—216no—
245C23×Q8—51no—
246C23×Q8—52no—
247C22×Q16—52no—
248C22×Q16—52no—
249C22×Q16—516no—
250C22×Q16—52no—
251C22×Q16—1016no—
252C22×Q16C2×D512yes—
253C23×C8—52no—
254C2×C4⋊Q8—52no—
255C2×C4⋊Q8—58no—
256C2×C4⋊Q8—51no—
257C2×C4⋊Q8—101no—
258C2×C4⋊Q8—101no—
259C2×C4⋊Q8—104no—
260C2×C4⋊Q8C2×D511yescharacteristic
261C2×C4×Q8—51no—
262C2×C4×Q8—58no—
263C2×C4×Q8—51no—
264C2×C4×Q8—51no—
265C2×C4×Q8—101no—
266C2×C4×Q8—101no—
267C2×C4×Q8—104no—
268C2×C4×Q8C2×D511yescharacteristic
269C22×C4⋊C4—51no—
270C22×C4⋊C4—101no—
271C22×C4⋊C4—101no—
272C22×C4⋊C4—101no—
273C22×C42—51no—
274C22×C42—101no—
275#462—516no—
276#462—58no—
277#462—58no—
278#462—58no—
279#462—516no—
280#462C2×D518yesdirect product factor
281C2×C4⋊C8—52no—
282C2×C4⋊C8—51no—
283C2×C4⋊C8—58no—
284C2×C4⋊C8C2×D511yescharacteristic
285C2×#103—52no—
286C2×#103—52no—
287C2×#103—52no—
288C2×#103—516no—
289C2×#103C2×D512yes—
290C23×C5C22×D411yescharacteristic
291C22×D5#12114yes—
292C22×D5C2×Q1614yes—
293C22×D5#13714yes—
294C22×D5C22×D412yes—
295C5×Q8—24no—
296C5×Q8—22no—
297C5×Q8—24no—
298C5×Q8—24no—
299C5×Q8—44no—
300C5×Q8C22×D414yes—
301C2×C4×C5—24no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—24no—
306C2×C4×C5—44no—
307C2×C4×C5—42no—
308C2×C4×C5C2×Q1614yescomplemented
309C2×C4×C5C22×D412yes—
310C2×C4×C5C22×D411yescharacteristic
311C2×C4×C5C22×D412yes—
312C2×C4×C5C22×D412yes—
313C2×C4×C5C2×#4112yes—
314C2×C4×C5C2511yescharacteristic
315C2×Dic5—24no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—24no—
320C2×Dic5—44no—
321C2×Dic5—42no—
322C2×Dic5#12114yes—
323C2×Dic5C2×Q1614yescomplemented
324C2×Dic5C22×D412yes—
325C2×Dic5C22×D412yes—
326C2×Dic5C22×D412yes—
327C4×D5—216no—
328C4×D5—28no—
329C4×D5—416no—
330C4×D5—48no—
331C4×D5#12118yes—
332C4×D5C2×Q16116yescomplemented
333C4×D5C22×D414yes—
334C4×D5C2×#4114yes—
335Dic10—24no—
336Dic10—22no—
337Dic10—216no—
338Dic10—24no—
339Dic10—24no—
340Dic10—44no—
341Dic10—416no—
342Dic10C22×D414yes—
343C5×C8—24no—
344#168—24no—
345C22×Q8—58no—
346C22×Q8—54no—
347C22×Q8—58no—
348C22×Q8—51no—
349C22×Q8—52no—
350C22×Q8—101no—
351C22×Q8—102no—
352C22×Q8—102no—
353C22×Q8—104no—
354C22×Q8—104no—
355C22×Q8—108no—
356C22×Q8—108no—
357C22×Q8C22×D512yes—
358C22×Q8C22×D511yescharacteristic
359C23×C4—51no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4—101no—
363C23×C4—101no—
364C23×C4—102no—
365C2×Q16—28no—
366C2×Q16—58no—
367C2×Q16—58no—
368C2×Q16—58no—
369C2×Q16—108no—
370C2×Q16—1064no—
371C2×Q16—108no—
372C2×Q16—108no—
373C2×Q16C22×D518yes—
374C22×C8—52no—
375C22×C8—58no—
376C22×C8—108no—
377C22×C8C22×D512yes—
378C4⋊Q8—22no—
379C4⋊Q8—58no—
380C4⋊Q8—54no—
381C4⋊Q8—108no—
382C4⋊Q8—108no—
383C4⋊Q8—104no—
384C4⋊Q8—102no—
385C4⋊Q8C22×D514yes—
386C4×Q8—22no—
387C4×Q8—54no—
388C4×Q8—54no—
389C4×Q8—54no—
390C4×Q8—108no—
391C4×Q8—108no—
392C4×Q8—102no—
393C4×Q8—102no—
394C4×Q8—102no—
395C4×Q8C22×D514yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—51no—
400C2×C4⋊C4—54no—
401C2×C4⋊C4—102no—
402C2×C4⋊C4—108no—
403C2×C4⋊C4—108no—
404C2×C4⋊C4—108no—
405C2×C4⋊C4—101no—
406C2×C4⋊C4—101no—
407C2×C4⋊C4—101no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—101no—
411C2×C4⋊C4—101no—
412C2×C4⋊C4—101no—
413C2×C4⋊C4C22×D511yescharacteristic
414C2×C42—21no—
415C2×C42—51no—
416C2×C42—51no—
417C2×C42—51no—
418C2×C42—54no—
419C2×C42—54no—
420C2×C42—108no—
421C2×C42—101no—
422C2×C42—101no—
423C2×C42—101no—
424C2×C42C22×D511yescharacteristic
425C4⋊C8—58no—
426C4⋊C8—54no—
427C4⋊C8C22×D514yes—
428#103—58no—
429#103—58no—
430#103—58no—
431#103C22×D518yes—
432C22×C5C2×#12112yes—
433C22×C5C22×Q1612yes—
434C22×C5C2×#13712yes—
435C22×C5C23×D411yescharacteristic
436C2×D5#462116yesdirect product factor
437C2×D5C2×#12114yes—
438C2×D5C22×Q1614yes—
439C2×D5C2×#13714yes—
440C4×C5—24no—
441C4×C5—22no—
442C4×C5—44no—
443C4×C5—42no—
444C4×C5C2×#12112yes—
445C4×C5C22×Q1614yescomplemented
446C4×C5C23×D411yescharacteristic
447C4×C5C22×#4111yescharacteristic
448Dic5—24no—
449Dic5—22no—
450Dic5—44no—
451Dic5—42no—
452Dic5C2×#12114yes—
453Dic5C22×Q1614yescomplemented
454C24—51no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—516no—
461C2×Q8—54no—
462C2×Q8—52no—
463C2×Q8—54no—
464C2×Q8—104no—
465C2×Q8—108no—
466C2×Q8—108no—
467C2×Q8—1016no—
468C2×Q8—108no—
469C2×Q8—1016no—
470C2×Q8—1016no—
471C2×Q8—101no—
472C2×Q8—102no—
473C2×Q8—102no—
474C2×Q8—104no—
475C2×Q8—104no—
476C2×Q8—208no—
477C2×Q8—2016no—
478C2×Q8D4×D514yes—
479C2×Q8C23×D514yes—
480C2×Q8C23×D512yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—51no—
485C22×C4—51no—
486C22×C4—54no—
487C22×C4—52no—
488C22×C4—54no—
489C22×C4—54no—
490C22×C4—52no—
491C22×C4—58no—
492C22×C4—51no—
493C22×C4—54no—
494C22×C4—104no—
495C22×C4—104no—
496C22×C4—108no—
497C22×C4—104no—
498C22×C4—108no—
499C22×C4—101no—
500C22×C4—101no—
501C22×C4—102no—
502C22×C4—208no—
503C22×C4—204no—
504C22×C4D4×D511yescharacteristic
505C22×C4D4×D511yescharacteristic
506C22×C4C23×D511yescharacteristic
507Q16—216no—
508Q16—1016no—
509Q16—1016no—
510Q16—1016no—
511C2×C8—24no—
512C2×C8—54no—
513C2×C8—1016no—
514C2×C8—104no—
515C2×C8C23×D514yes—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—52no—
521C4⋊C4—104no—
522C4⋊C4—104no—
523C4⋊C4—104no—
524C4⋊C4—108no—
525C4⋊C4—108no—
526C4⋊C4—101no—
527C4⋊C4—104no—
528C4⋊C4—104no—
529C4⋊C4—104no—
530C4⋊C4C23×D512yes—
531C42—24no—
532C42—54no—
533C42—52no—
534C42—54no—
535C42—52no—
536C42—104no—
537C42—104no—
538C42—104no—
539C42D4×D512yes—
540C42C23×D512yes—
541C2×C5C2×#46214yescomplemented
542C2×C5C22×#12111yescharacteristic
543C2×C5C23×Q1611yescharacteristic
544C2×C5C22×#13711yescharacteristic
545D5C2×#46218yesdirect product factor
546C23—54no—
547C23—54no—
548C23—54no—
549C23—52no—
550C23C2×D4×D511yescharacteristic
551Q8—24no—
552Q8—22no—
553Q8—24no—
554Q8—24no—
555Q8—44no—
556Q8—54no—
557Q8—1016no—
558Q8—104no—
559Q8—102no—
560Q8—104no—
561Q8—104no—
562Q8—2016no—
563Q8—204no—
564Q8C2×D4×D514yes—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—54no—
573C2×C4—54no—
574C2×C4—52no—
575C2×C4—52no—
576C2×C4—516no—
577C2×C4—58no—
578C2×C4—54no—
579C2×C4—54no—
580C2×C4—52no—
581C2×C4—108no—
582C2×C4—1016no—
583C2×C4—102no—
584C2×C4—104no—
585C2×C4—102no—
586C2×C4—102no—
587C2×C4—104no—
588C2×C4—2016no—
589C2×C4—208no—
590C2×C4—202no—
591C2×C4—204no—
592C2×C4D5×Q1614yescomplemented
593C2×C4C2×D4×D512yes—
594C2×C4C2×D4×D512yes—
595C2×C4C2×D4×D511yescharacteristic
596C2×C4C2×D4×D512yes—
597C2×C4D5×#4112yes—
598C2×C4C24×D511yescharacteristic
599C8—24no—
600C8—104no—
601C5C22×#46211yescharacteristic, complemented, Sylow
602C22—54no—
603C22—54no—
604C22—516no—
605C22—54no—
606C22D5×#12112yes—
607C22C2×D5×Q1612yes—
608C22D5×#13712yes—
609C22C22×D4×D511yescharacteristic
610C4—22no—
611C4—24no—
612C4—42no—
613C4—44no—
614C4—54no—
615C4—54no—
616C4—102no—
617C4—104no—
618C4—202no—
619C4—204no—
620C4D5×#12112yes—
621C4C2×D5×Q1614yescomplemented
622C4C22×D4×D511yescharacteristic
623C4C2×D5×#4111yescharacteristic
624C2—58no—
625C2D5×#46214yesdirect product factor
626C2C2×D5×#12111yescharacteristic
627C2C22×D5×Q1611yescharacteristic
628C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#462C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#462D5
hypocenterC5C22×#462
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
4. C2×C5×#462C2semidirect
5. C2×#65471C2semidirect
6. C2×#65379C2semidirect
7. C2×#65320C2semidirect
8. D5×#462C2direct (N × H)
9. C2×#65138C2semidirect
11. C2×#65082C2semidirect
43. C5×#462C22semidirect
47. #65471C22semidirect
50. #65379C22semidirect
51. #65320C22semidirect
54. #65138C22semidirect
57. #65082C22semidirect
155. C2×#462D5direct (N × H)
192. C2×C4×D5Q16semidirect
280. #462C2×D5direct (N × H)
308. C2×C4×C5C2×Q16semidirect
323. C2×Dic5C2×Q16semidirect
332. C4×D5C2×Q16semidirect
436. C2×D5#462direct (N × H)
445. C4×C5C22×Q16semidirect
453. Dic5C22×Q16semidirect
541. C2×C5C2×#462semidirect
545. D5C2×#462direct (N × H)
592. C2×C4D5×Q16semidirect
601. C5C22×#462semidirect
621. C4C2×D5×Q16semidirect
625. C2D5×#462direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×Q162
C2×D5×C4⋊Q82
C2×C4×Q8×D52
C2×C5×#4622
C2×#654712
C2×#653792
C2×#653202
D5×#4622
C2×#651382
C2×D5×C4⋊C82
C2×#650822
C2×D5×#1032
C22×#4625