Finite Group Databasebeta

← C2×#10612795 #12971340

Subgroups — C2×#10612795 #12971340

Order 1280.

2286 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#65882C211yesmaximal, characteristic
3C2×C5×#476C211yesmaximal, characteristic, complemented
4C2×#65373C211yesmaximal, characteristic, complemented
5C2×#65297C211yesmaximal, characteristic, complemented
6#10612795C2116yesmaximal, direct product factor
7C2×#65152C212yesmaximal, complemented
8C2×#65144C212yesmaximal, complemented
9C2×#65131C211yesmaximal, characteristic, complemented
10C2×#65122C211yesmaximal, characteristic, complemented
11C2×#65066C212yesmaximal, complemented
12C2×#65049C212yesmaximal, complemented
13C22×Q8×D5—21no—
14C22×#709—21no—
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C4×C5×D4C2211yescharacteristic
17C2×#4090—21no—
18C2×#4086C2211yescharacteristic
19C2×#4084C2211yescharacteristic
20C2×C4×C22⋊D5—21no—
21D5×C4⋊Q8—24no—
22D5×C4⋊Q8C2218yescomplemented
23#65882—24no—
24#65882C2218yes—
25C2×#4041C2211yescharacteristic
26C2×D5×C4⋊C4—21no—
27C2×D5×C4⋊C4C2212yes—
28C2×#4034—21no—
29C2×#4034C2212yes—
30C2×#4034C2211yescharacteristic
31C2×#4031—21no—
32C2×#4030—21no—
33C2×C4×D20C2211yescharacteristic
34C2×C42×D5C2211yescharacteristic
35C2×#4015C2211yescharacteristic
36C5×#476C2218yescomplemented
37C2×C5×#106C2212yes—
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×#102C2212yes—
40C2×#3964C2212yes—
41C2×#3953C2212yes—
42C2×#3952C2212yes—
43C2×#3949C2212yes—
44C2×C8×Dic5C2212yes—
45#65373C2218yescomplemented
46#65297C2218yescomplemented
47C2×#3941C2212yes—
48C2×#3940C2212yes—
49C2×#3940C2212yes—
50C2×C4⋊#168C2211yescharacteristic
51#65152C22116yescomplemented
52#65144C22116yescomplemented
53#65131C2218yescomplemented
54#65122C2218yescomplemented
55#65066C22116yescomplemented
56#65049C22116yescomplemented
57C2×#3227—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C5×D4C2311yescharacteristic
60C23×C4×C5—21no—
61C22×C22⋊D5—21no—
62C22×C22⋊D5—21no—
63C22×C22⋊D5—21no—
64C2×Q8×D5—28no—
65C2×Q8×D5—48no—
66C2×#709—28no—
67C2×#709—48no—
68C22×D20—21no—
69C22×D20C2311yescharacteristic
70C22×C4×D5—22no—
71C22×C4×D5—21no—
72C22×C4×D5D411yescharacteristic
73C22×C4×D5D411yescharacteristic
74C22×C4×D5C2311yescharacteristic
75C22×Dic10—21no—
76C22×Dic10—21no—
77C22×Dic10—22no—
78C22×C5×C8C2312yes—
79C5×C4⋊Q8—22no—
80C5×C4⋊Q8C2314yes—
81C4×C5×D4—22no—
82C4×C5×D4C2314yes—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4C2312yes—
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C22⋊C4—21no—
87C2×C42×C5C2311yescharacteristic
88C2×C22⋊Dic5—21no—
89#4090—28no—
90#4086—22no—
91#4086C2314yes—
92#4084—22no—
93#4084C2314yes—
94C4×C22⋊D5—28no—
95C2×#685—21no—
96C2×#685—21no—
97C2×C4⋊Dic5—21no—
98C2×C4⋊Dic5C2312yes—
99C2×C4⋊Dic5C2311yescharacteristic
100C2×#683—21no—
101C2×#683—22no—
102C2×#683—22no—
103C2×C4×Dic5D411yescharacteristic
104C2×C4×Dic5D411yescharacteristic
105C2×C4×Dic5C2311yescharacteristic
106C22×#168C2312yes—
107#4041—22no—
108#4041C2314yes—
109D5×C4⋊C4—24no—
110D5×C4⋊C4—28no—
111D5×C4⋊C4C2318yes—
112#4034—24no—
113#4034—28no—
114#4034—22no—
115#4034C2318yes—
116#4034C2314yes—
117#4031—28no—
118#4030—28no—
119C4×D20—22no—
120C4×D20C2314yes—
121C42×D5D414yes—
122C42×D5C2314yes—
123#4015—22no—
124#4015C2314yes—
125C5×#106C2318yes—
126C5×C4⋊C8C2314yes—
127C5×#102C2318yes—
128#3964C2318yes—
129#3953C2318yes—
130#3952C2318yes—
131#3949C2318yes—
132C8×Dic5C2318yes—
133#3941C2318yes—
134#3940C2318yes—
135#3940C2318yes—
136C4⋊#168C2314yes—
137C2×#532—51no—
138C22×C4⋊Q8—51no—
139#3227—516no—
140C2×#498—52no—
141C2×#486—52no—
142C2×#481—52no—
143C2×#481—52no—
144C2×#476—51no—
145C2×#476—51no—
146C2×#476—51no—
147C2×#476D511yescharacteristic, complemented
148C2×#431—51no—
149C24×C5—21no—
150C23×D5—21no—
151C23×D5C2×D411yescharacteristic
152C2×C5×Q8—24no—
153C2×C5×Q8—44no—
154C2×C5×D4—21no—
155C2×C5×D4—22no—
156C2×C5×D4—22no—
157C2×C5×D4C2412yes—
158C22×C4×C5—21no—
159C22×C4×C5—22no—
160C22×C4×C5—24no—
161C22×C4×C5—44no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2411yescharacteristic
165C2×C22⋊D5—24no—
166C2×C22⋊D5—24no—
167C2×C22⋊D5—24no—
168C2×C22⋊D5—44no—
169C2×C22⋊D5—44no—
170C2×C22⋊D5—44no—
171C22×Dic5—21no—
172C22×Dic5—22no—
173C22×Dic5C2×D411yescharacteristic
174C22×Dic5C2×D411yescharacteristic
175C22×Dic5C2×D411yescharacteristic
176Q8×D5—432no—
177#709—432no—
178C2×D20—22no—
179C2×D20—22no—
180C2×D20—24no—
181C2×D20—21no—
182C2×D20—44no—
183C2×D20C2412yes—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5—24no—
187C2×C4×D5—28no—
188C2×C4×D5—24no—
189C2×C4×D5—48no—
190C2×C4×D5—44no—
191C2×C4×D5SD1618yes—
192C2×C4×D5C2×D414yes—
193C2×C4×D5C2×D412yes—
194C2×C4×D5C2×D414yes—
195C2×C4×D5C2412yes—
196C2×Dic10—24no—
197C2×Dic10—24no—
198C2×Dic10—28no—
199C2×Dic10—44no—
200C2×Dic10—44no—
201C2×Dic10—48no—
202C2×C5×C8—24no—
203C2×C5×C8C2414yes—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4C2412yes—
208C5×C4⋊C4C2414yes—
209C5×C22⋊C4—24no—
210C42×C5C2×D412yes—
211C42×C5C2412yes—
212C22⋊Dic5—24no—
213#685—24no—
214#685—24no—
215C4⋊Dic5—22no—
216C4⋊Dic5—24no—
217C4⋊Dic5—21no—
218C4⋊Dic5C2412yes—
219C4⋊Dic5C2414yes—
220#683—24no—
221#683—28no—
222#683—28no—
223C4×Dic5C2×D412yes—
224C4×Dic5C2×D414yes—
225C4×Dic5C2×D414yes—
226C4×Dic5C2412yes—
227C2×#168—24no—
228C2×#168C2414yes—
229C22×#41—101no—
230C23×Q8—101no—
231#532—58no—
232#532—104no—
233C2×C4⋊Q8—58no—
234C2×C4⋊Q8—52no—
235C2×C4⋊Q8—51no—
236C2×C4⋊Q8—51no—
237C2×C4⋊Q8—101no—
238C2×C4⋊Q8—104no—
239C2×C4⋊Q8—101no—
240C2×C4⋊Q8C2×D511yescharacteristic
241C2×#127—51no—
242C2×#124—101no—
243C2×#121—51no—
244C2×#121—51no—
245C2×#121—101no—
246C2×C4×D4—51no—
247C2×C4×D4—101no—
248C2×C4×D4C2×D511yescharacteristic
249C22×C4⋊C4—52no—
250C22×C4⋊C4—101no—
251C22×C42—51no—
252#498—516no—
253#486—516no—
254#481—516no—
255#481—516no—
256#476—58no—
257#476—58no—
258#476—58no—
259#476C2×D518yescomplemented
260#431—58no—
261C2×#106—52no—
262C2×#106—52no—
263C2×#106—52no—
264C2×#106C2×D512yes—
265C2×C4⋊C8—51no—
266C2×C4⋊C8C2×D511yescharacteristic
267C2×#102—52no—
268C2×#102—52no—
269C2×#102—52no—
270C2×#102C2×D512yes—
271C2×C22⋊C8—52no—
272C2×C4×C8—52no—
273C23×C5—22no—
274C23×C5—42no—
275C23×C5—42no—
276C23×C5—42no—
277C23×C5C22×D411yescharacteristic
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—42no—
282C22×D5—42no—
283C22×D5—42no—
284C22×D5C2×SD1614yes—
285C22×D5C22×D412yes—
286C5×Q8—48no—
287C5×D4—22no—
288C5×D4—22no—
289C5×D4—42no—
290C2×C4×C5—22no—
291C2×C4×C5—24no—
292C2×C4×C5—22no—
293C2×C4×C5—42no—
294C2×C4×C5—44no—
295C2×C4×C5—48no—
296C2×C4×C5C2×SD1614yes—
297C2×C4×C5C22×D412yes—
298C2×C4×C5C22×D411yescharacteristic
299C2×C4×C5C22×D412yes—
300C2×C4×C52−1+412yes—
301C2×C4×C52−1+412yes—
302C2×C4×C5C2511yescharacteristic
303C22⋊D5—48no—
304C22⋊D5—48no—
305C22⋊D5—48no—
306C2×Dic5—22no—
307C2×Dic5—24no—
308C2×Dic5—22no—
309C2×Dic5—42no—
310C2×Dic5—44no—
311C2×Dic5C2×SD1614yes—
312C2×Dic5AGL(1,ℤ/8)14yes—
313C2×Dic5C22×D412yes—
314C2×Dic5C22×D412yes—
315C2×Dic5C22×D412yes—
316D20—22no—
317D20—22no—
318D20—48no—
319D20—42no—
320C4×D5—24no—
321C4×D5—22no—
322C4×D5—22no—
323C4×D5—28no—
324C4×D5—416no—
325C4×D5—48no—
326C4×D5C2×SD16116yes—
327Dic10—48no—
328Dic10—48no—
329Dic10—416no—
330C5×C8—24no—
331#168—24no—
332C2×#41—108no—
333C2×#41—208no—
334C22×Q8—21no—
335C22×Q8—101no—
336C22×Q8—102no—
337C22×Q8—108no—
338C22×Q8—101no—
339C22×Q8—208no—
340C22×D4—51no—
341C22×D4—101no—
342C22×D4—101no—
343C22×D4—101no—
344C22×D4—101no—
345C22×D4C22×D511yescharacteristic
346C23×C4—21no—
347C23×C4—51no—
348C23×C4—51no—
349C23×C4—51no—
350C23×C4—102no—
351C23×C4—101no—
352C22×C8—52no—
353C22×C8C22×D512yes—
354C4⋊Q8—22no—
355C4⋊Q8—58no—
356C4⋊Q8—54no—
357C4⋊Q8—54no—
358C4⋊Q8—108no—
359C4⋊Q8—104no—
360C4⋊Q8—102no—
361C4⋊Q8—108no—
362C4⋊Q8—102no—
363C4⋊Q8C22×D514yes—
364#127—54no—
365#127—102no—
366#124—108no—
367#121—54no—
368#121—54no—
369#121—108no—
370#121—102no—
371#121—102no—
372C4×D4—22no—
373C4×D4—54no—
374C4×D4—108no—
375C4×D4—102no—
376C4×D4C22×D514yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—52no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4—58no—
381C2×C4⋊C4—104no—
382C2×C4⋊C4—108no—
383C2×C4⋊C4—102no—
384C2×C4⋊C4—102no—
385C2×C4⋊C4—101no—
386C2×C4⋊C4—101no—
387C2×C4⋊C4C22×D512yes—
388C2×C4⋊C4C22×D511yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—101no—
391C2×C22⋊C4—101no—
392C2×C22⋊C4—101no—
393C2×C42—51no—
394C2×C42—51no—
395C2×C42—51no—
396C2×C42—54no—
397C2×C42—54no—
398C2×C42C22×D511yescharacteristic
399#106—58no—
400#106—58no—
401#106—58no—
402#106C22×D518yes—
403C4⋊C8—54no—
404C4⋊C8C22×D514yes—
405#102—58no—
406#102—58no—
407#102—58no—
408#102C22×D518yes—
409C22⋊C8—58no—
410C4×C8—58no—
411C22×C5—42no—
412C22×C5—42no—
413C22×C5—42no—
414C22×C5—84no—
415C22×C5#53612yes—
416C22×C5C22×SD1612yes—
417C22×C5C2×AGL(1,ℤ/8)12yes—
418C22×C5C23×D411yescharacteristic
419C2×D5—22no—
420C2×D5—28no—
421C2×D5—22no—
422C2×D5—42no—
423C2×D5—42no—
424C2×D5—42no—
425C2×D5—84no—
426C2×D5C22×SD1614yes—
427C4×C5—22no—
428C4×C5—42no—
429C4×C5—44no—
430C4×C5#53612yes—
431C4×C5C22×SD1614yes—
432C4×C5C2×2−1+411yescharacteristic
433C4×C5C2×2−1+411yescharacteristic
434Dic5—22no—
435Dic5—42no—
436Dic5—44no—
437Dic5C22×SD1614yes—
438Dic5C2×AGL(1,ℤ/8)14yes—
439C24—21no—
440C24—51no—
441C24—101no—
442#41—2032no—
443C2×Q8—24no—
444C2×Q8—44no—
445C2×Q8—104no—
446C2×Q8—108no—
447C2×Q8—104no—
448C2×Q8—204no—
449C2×Q8—208no—
450C2×Q8—204no—
451C2×Q8—2032no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—52no—
456C2×D4—104no—
457C2×D4—104no—
458C2×D4—104no—
459C2×D4—104no—
460C2×D4—101no—
461C2×D4—102no—
462C2×D4—102no—
463C2×D4—204no—
464C2×D4—204no—
465C2×D4—204no—
466C2×D4—204no—
467C2×D4C23×D512yes—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—44no—
472C22×C4—51no—
473C22×C4—51no—
474C22×C4—54no—
475C22×C4—58no—
476C22×C4—51no—
477C22×C4—52no—
478C22×C4—54no—
479C22×C4—52no—
480C22×C4—104no—
481C22×C4—108no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—101no—
485C22×C4—102no—
486C22×C4—104no—
487C22×C4—208no—
488C22×C4—204no—
489C22×C4D4×D511yescharacteristic
490C22×C4D4×D511yescharacteristic
491C22×C4C23×D511yescharacteristic
492C2×C8—24no—
493C2×C8—54no—
494C2×C8—104no—
495C2×C8C23×D514yes—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—54no—
500C4⋊C4—52no—
501C4⋊C4—108no—
502C4⋊C4—108no—
503C4⋊C4—104no—
504C4⋊C4—102no—
505C4⋊C4—101no—
506C4⋊C4—104no—
507C4⋊C4C23×D514yes—
508C4⋊C4C23×D512yes—
509C22⋊C4—24no—
510C22⋊C4—104no—
511C22⋊C4—104no—
512C22⋊C4—104no—
513C42—54no—
514C42—54no—
515C42—52no—
516C42—52no—
517C42D4×D512yes—
518C42C23×D512yes—
519C2×C5—82no—
520C2×C5#322714yescomplemented
521C2×C5C2×#53611yescharacteristic
522C2×C5C23×SD1611yescharacteristic
523C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
524D5—24no—
525D5—82no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—54no—
531C23—52no—
532C23—102no—
533C23—102no—
534C23—102no—
535C23—202no—
536C23—202no—
537C23—202no—
538C23C2×D4×D511yescharacteristic
539Q8—48no—
540Q8—208no—
541Q8—2016no—
542Q8—208no—
543D4—22no—
544D4—22no—
545D4—42no—
546D4—102no—
547D4—102no—
548D4—208no—
549D4—208no—
550D4—208no—
551D4—208no—
552D4—202no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—54no—
560C2×C4—54no—
561C2×C4—52no—
562C2×C4—52no—
563C2×C4—516no—
564C2×C4—52no—
565C2×C4—108no—
566C2×C4—102no—
567C2×C4—104no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—104no—
572C2×C4—2016no—
573C2×C4—202no—
574C2×C4—204no—
575C2×C4—208no—
576C2×C4D5×SD1614yes—
577C2×C4C2×D4×D512yes—
578C2×C4C2×D4×D512yes—
579C2×C4C2×D4×D511yescharacteristic
580C2×C4#414712yes—
581C2×C4#415012yes—
582C2×C4C24×D511yescharacteristic
583C8—24no—
584C8—104no—
585C5C2×#322711yescharacteristic, complemented, Sylow
586C22—42no—
587C22—42no—
588C22—42no—
589C22—54no—
590C22—84no—
591C22—102no—
592C22—108no—
593C22—102no—
594C22—202no—
595C22—202no—
596C22—202no—
597C22—404no—
598C22#6596212yes—
599C22C2×D5×SD1612yes—
600C22D5×AGL(1,ℤ/8)12yes—
601C22C22×D4×D511yescharacteristic
602C4—22no—
603C4—42no—
604C4—44no—
605C4—54no—
606C4—54no—
607C4—102no—
608C4—202no—
609C4—204no—
610C4#6596212yes—
611C4C2×D5×SD1614yes—
612C4C2×#414711yescharacteristic
613C4C2×#415011yescharacteristic
614C2—82no—
615C2—104no—
616C2—402no—
617C2#1061279514yesdirect product factor
618C2C2×#6596211yescharacteristic
619C2C22×D5×SD1611yescharacteristic
620C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#476C2
socleC23×C5C22×D4
prime radicalC2×#65882C2
hypercenterC2×#476D5
hypocenterC5C2×#3227
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×D5×C4⋊Q8C2semidirect
3. C2×C5×#476C2semidirect
4. C2×#65373C2semidirect
5. C2×#65297C2semidirect
6. #10612795C2direct (N × H)
7. C2×#65152C2semidirect
8. C2×#65144C2semidirect
9. C2×#65131C2semidirect
10. C2×#65122C2semidirect
11. C2×#65066C2semidirect
12. C2×#65049C2semidirect
22. D5×C4⋊Q8C22semidirect
36. C5×#476C22semidirect
45. #65373C22semidirect
46. #65297C22semidirect
51. #65152C22semidirect
52. #65144C22semidirect
53. #65131C22semidirect
54. #65122C22semidirect
55. #65066C22semidirect
56. #65049C22semidirect
147. C2×#476D5semidirect
259. #476C2×D5semidirect
520. C2×C5#3227semidirect
585. C5C2×#3227semidirect
617. C2#10612795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#658822
C2×C5×#4762
C2×#653732
C2×#652972
#106127952
C2×#651522
C2×#651442
C2×#651312
C2×#651222
C2×#650662
C2×#650492
C2×#32275