Finite Group Databasebeta

← C2×#10599615 #12126751

Subgroups — C2×#10599615 #12126751

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4041C211yesmaximal, characteristic
2C22×#3953C211yesmaximal, characteristic, complemented
3C22×#3952C211yesmaximal, characteristic, complemented
4C2×#65276C211yesmaximal, characteristic, complemented
5C22×#3941C211yesmaximal, characteristic, complemented
6C22×#3939C211yesmaximal, characteristic, complemented
7C2×C5×#340C211yesmaximal, characteristic, complemented
8#10599615C218yesmaximal, direct product factor
9C23×D20—21no—
10C23×D20C2211yescharacteristic
11C23×C4×D5C2211yescharacteristic
12C23×C5×C8C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×#685—21no—
16C22×#685—21no—
17C22×C4⋊Dic5C2211yescharacteristic
18C23×#168C2211yescharacteristic
19C2×#4041—24no—
20C2×#4041—22no—
21C2×#4041—24no—
22C2×#4041C2214yes—
23C2×#3963—21no—
24C2×#3953—24no—
25C2×#3953C2214yescomplemented
26C2×#3952—24no—
27C2×#3952C2214yescomplemented
28#65276—22no—
29#65276C2214yescomplemented
30C2×#3941—24no—
31C2×#3941C2214yescomplemented
32C2×#3939—24no—
33C2×#3939C2214yescomplemented
34C5×#340C2214yescomplemented
35C2×#2033—51nomaximal, Sylow
36C24×D5—21no—
37C24×D5D411yescharacteristic
38C23×C4×C5—21no—
39C23×C4×C5—21no—
40C23×C4×C5C2311yescharacteristic
41C23×Dic5—21no—
42C23×Dic5D411yescharacteristic
43C22×D20—22no—
44C22×D20—22no—
45C22×D20—22no—
46C22×D20—22no—
47C22×D20—28no—
48C22×D20—24no—
49C22×D20—22no—
50C22×D20—21no—
51C22×D20—44no—
52C22×D20—44no—
53C22×D20D414yes—
54C22×D20C2312yes—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—22no—
60C22×C4×D5—22no—
61C22×C4×D5D412yes—
62C22×C4×D5C2312yes—
63C22×C5×C8—22no—
64C22×C5×C8—22no—
65C22×C5×C8—22no—
66C22×C5×C8C2312yes—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4D414yes—
73C2×C5×C4⋊C4C2312yes—
74C2×C5×C4⋊C4C2312yes—
75C2×#685—28no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—44no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5C2312yes—
83C22×#168—22no—
84C22×#168—22no—
85C22×#168D414yescomplemented
86C22×#168C2312yes—
87#4041—216no—
88#4041—28no—
89#4041—28no—
90#3963—24no—
91#3953—28no—
92#3952—28no—
93#3941—28no—
94#3939—28no—
95C22×#121—51no—
96C22×#107—51no—
97C22×#102—51no—
98C22×#102—51no—
99C22×C22⋊C8—51no—
100C2×#380—51no—
101#2033—58no—
102C2×#340D511yescharacteristic, complemented
103C24×C5C2×D411yescharacteristic
104C23×D5—22no—
105C23×D5—22no—
106C23×D5—22no—
107C23×D5—22no—
108C23×D5—22no—
109C23×D5—22no—
110C23×D5—24no—
111C23×D5—22no—
112C23×D5—42no—
113C23×D5—42no—
114C23×D5—42no—
115C23×D5—42no—
116C23×D5—42no—
117C23×D5—42no—
118C23×D5D814yes—
119C23×D5C2×D412yes—
120C22×C4×C5—24no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—42no—
124C22×C4×C5—42no—
125C22×C4×C5—42no—
126C22×C4×C5—42no—
127C22×C4×C5—42no—
128C22×C4×C5C2×D412yes—
129C22×C4×C5C2×D411yescharacteristic
130C22×C4×C5C2×D412yes—
131C22×C4×C5C2×D412yes—
132C22×C4×C5#4112yes—
133C22×C4×C5#4112yes—
134C22×C4×C5#4112yes—
135C22×C4×C5C2411yescharacteristic
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—42no—
141C22×Dic5—42no—
142C22×Dic5—42no—
143C22×Dic5C2×D412yes—
144C2×D20—28no—
145C2×D20—28no—
146C2×D20—22no—
147C2×D20—22no—
148C2×D20—22no—
149C2×D20—22no—
150C2×D20—216no—
151C2×D20—24no—
152C2×D20—22no—
153C2×D20—48no—
154C2×D20—432no—
155C2×D20—48no—
156C2×D20—42no—
157C2×D20—44no—
158C2×D20—42no—
159C2×D20—44no—
160C2×D20C2×D414yes—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—24no—
164C2×C4×D5—22no—
165C2×C4×D5—22no—
166C2×C4×D5—22no—
167C2×C4×D5—22no—
168C2×C4×D5—22no—
169C2×C4×D5—22no—
170C2×C4×D5—44no—
171C2×C4×D5—44no—
172C2×C4×D5—44no—
173C2×C4×D5—44no—
174C2×C5×C8—22no—
175C2×C5×C8—22no—
176C2×C5×C8—22no—
177C2×C5×C8—44no—
178C5×C4⋊C4—24no—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—42no—
183C5×C4⋊C4C2×D414yes—
184#685—216no—
185#685—48no—
186C4⋊Dic5—22no—
187C4⋊Dic5—22no—
188C4⋊Dic5—42no—
189C2×#168—28no—
190C2×#168—22no—
191C2×#168—22no—
192C2×#168C2×D414yescomplemented
193C23×D4—51no—
194C23×D4—101no—
195C24×C4—51no—
196C23×C8—51no—
197C23×C8C2×D511yescharacteristic
198C2×#121—54no—
199C2×#121—102no—
200C2×#121—104no—
201C2×#121—104no—
202C22×C4⋊C4—51no—
203C22×C4⋊C4C2×D511yescharacteristic
204C22×C4⋊C4C2×D511yescharacteristic
205C22×C22⋊C4—101no—
206C22×C22⋊C4—101no—
207C2×#107—54no—
208C2×#107—104no—
209C2×#102—54no—
210C2×#102—54no—
211C2×#102—104no—
212C2×#102—104no—
213C2×C22⋊C8—54no—
214C2×C22⋊C8—104no—
215#380—54no—
216#380—102no—
217C2×#95—101no—
218#340C2×D514yescomplemented
219C23×C5#12012yes—
220C23×C5#12112yes—
221C23×C5#12312yes—
222C23×C5C2×D812yes—
223C23×C5#13512yes—
224C23×C5AGL(1,ℤ/8)12yes—
225C23×C5#13712yes—
226C23×C5C22×D411yescharacteristic
227C22×D5—22no—
228C22×D5—22no—
229C22×D5—22no—
230C22×D5—22no—
231C22×D5—22no—
232C22×D5—22no—
233C22×D5—28no—
234C22×D5—28no—
235C22×D5—28no—
236C22×D5—24no—
237C22×D5—44no—
238C22×D5—44no—
239C22×D5—44no—
240C22×D5—44no—
241C22×D5—42no—
242C22×D5—42no—
243C22×D5—42no—
244C22×D5—42no—
245C22×D5—42no—
246C22×D5—42no—
247C22×D5—48no—
248C22×D5—48no—
249C22×D5—48no—
250C22×D5—84no—
251C22×D5—84no—
252C22×D5—84no—
253C22×D5—84no—
254C22×D5C2×D814yes—
255C2×C4×C5—24no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—48no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—84no—
263C2×C4×C5#12012yes—
264C2×C4×C5#12114yes—
265C2×C4×C5#12112yes—
266C2×C4×C5#12114yes—
267C2×C4×C5#12314yes—
268C2×C4×C5#12312yes—
269C2×C4×C5#12414yes—
270C2×C4×C5C22×D411yescharacteristic
271C2×C4×C5C22×D411yescharacteristic
272C2×C4×C5C22×D411yescharacteristic
273C2×C4×C5C2×#4111yescharacteristic
274C2×C4×C5C2×#4111yescharacteristic
275C2×C4×C5C2×#4111yescharacteristic
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—44no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—84no—
284D20—24no—
285D20—24no—
286D20—432no—
287D20—42no—
288D20—42no—
289D20—48no—
290C4×D5—42no—
291C4×D5—42no—
292C4×D5—42no—
293C4×D5—42no—
294C4×D5—48no—
295C5×C8—42no—
296#168—24no—
297C25—51no—
298C25—101no—
299C22×D4—54no—
300C22×D4—52no—
301C22×D4—104no—
302C22×D4—108no—
303C22×D4—102no—
304C22×D4—102no—
305C22×D4—102no—
306C22×D4—102no—
307C22×D4—101no—
308C22×D4—102no—
309C22×D4—204no—
310C22×D4—204no—
311C23×C4—21no—
312C23×C4—21no—
313C23×C4—51no—
314C23×C4—52no—
315C23×C4—52no—
316C23×C4—102no—
317C23×C4—102no—
318C23×C4—102no—
319C23×C4—102no—
320C23×C4—102no—
321C23×C4—102no—
322C23×C4—101no—
323C23×C4C22×D511yescharacteristic
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—54no—
328C22×C8—52no—
329C22×C8—102no—
330C22×C8—102no—
331C22×C8C22×D512yes—
332#121—108no—
333#121—1016no—
334#121—108no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—52no—
341C2×C4⋊C4—102no—
342C2×C4⋊C4—102no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4D2014yes—
345C2×C4⋊C4C22×D512yes—
346C2×C4⋊C4C22×D512yes—
347C2×C22⋊C4—104no—
348C2×C22⋊C4—108no—
349C2×C22⋊C4—104no—
350C2×C22⋊C4—204no—
351#107—108no—
352#102—108no—
353#102—108no—
354C22⋊C8—108no—
355#95—104no—
356C22×C5#39414yes—
357C22×C5#44714yes—
358C22×C5#45214yes—
359C22×C5#46614yes—
360C22×C5#46814yes—
361C22×C5#48014yes—
362C22×C5#48214yes—
363C22×C5C2×#12011yescharacteristic
364C22×C5C2×#12111yescharacteristic
365C22×C5C2×#12311yescharacteristic
366C22×C5C22×D811yescharacteristic
367C22×C5C2×#13511yescharacteristic
368C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C5C2×#13711yescharacteristic
370C2×D5—24no—
371C2×D5—24no—
372C2×D5—24no—
373C2×D5—42no—
374C2×D5—42no—
375C2×D5—42no—
376C2×D5—42no—
377C2×D5—416no—
378C2×D5—44no—
379C2×D5—44no—
380C2×D5—44no—
381C2×D5—82no—
382C2×D5—82no—
383C2×D5—82no—
384C2×D5—82no—
385C2×D5—816no—
386C4×C5—44no—
387C4×C5—82no—
388C4×C5#39414yes—
389C4×C5C2×#12111yescharacteristic
390C4×C5C2×#12111yescharacteristic
391C4×C5C2×#12311yescharacteristic
392C4×C5C2×#12411yescharacteristic
393Dic5—42no—
394Dic5—82no—
395C24—52no—
396C24—54no—
397C24—102no—
398C24—102no—
399C24—102no—
400C24—102no—
401C24—102no—
402C24—102no—
403C24—102no—
404C24—104no—
405C24—202no—
406C24—202no—
407C24—202no—
408C24—202no—
409C24—202no—
410C24—202no—
411C24D4×D511yescharacteristic
412C2×D4—54no—
413C2×D4—1016no—
414C2×D4—102no—
415C2×D4—102no—
416C2×D4—102no—
417C2×D4—102no—
418C2×D4—102no—
419C2×D4—104no—
420C2×D4—108no—
421C2×D4—108no—
422C2×D4—208no—
423C2×D4—2032no—
424C2×D4—208no—
425C2×D4—204no—
426C2×D4—202no—
427C2×D4—202no—
428C2×D4—204no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—52no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—104no—
448C22×C4—104no—
449C22×C4—104no—
450C22×C4—102no—
451C22×C4—204no—
452C22×C4—204no—
453C22×C4—204no—
454C22×C4—204no—
455C22×C4—202no—
456C22×C4—202no—
457C22×C4—202no—
458C22×C4C2×D2012yes—
459C22×C4#70912yes—
460C22×C4#70912yes—
461C22×C4D4×D512yes—
462C22×C4D4×D512yes—
463C22×C4D4×D511yescharacteristic
464C22×C4#71312yes—
465C22×C4C23×D511yescharacteristic
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—44no—
470C2×C8—54no—
471C2×C8—102no—
472C2×C8—102no—
473C2×C8—108no—
474C4⋊C4—22no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—102no—
480C4⋊C4—102no—
481C4⋊C4—202no—
482C4⋊C4C2×D2014yes—
483C22⋊C4—1016no—
484C22⋊C4—208no—
485C2×C5#203318yescomplemented
486C2×C5C2×#39411yescharacteristic
487C2×C5C2×#44711yescharacteristic
488C2×C5C2×#45211yescharacteristic
489C2×C5C2×#46611yescharacteristic
490C2×C5C2×#46811yescharacteristic
491C2×C5C2×#48011yescharacteristic
492C2×C5C2×#48211yescharacteristic
493D5—44no—
494D5—84no—
495C23—54no—
496C23—102no—
497C23—102no—
498C23—108no—
499C23—108no—
500C23—102no—
501C23—102no—
502C23—102no—
503C23—102no—
504C23—108no—
505C23—104no—
506C23—204no—
507C23—204no—
508C23—204no—
509C23—204no—
510C23—202no—
511C23—208no—
512C23—202no—
513C23—202no—
514C23—202no—
515C23—202no—
516C23—202no—
517C23—208no—
518C23—208no—
519C23—404no—
520C23—404no—
521C23—404no—
522C23—404no—
523C23#402812yes—
524C23#403012yes—
525C23#404012yes—
526C23D5×D812yes—
527C23#406012yes—
528C23#406212yes—
529C23#406412yes—
530C23C2×D4×D511yescharacteristic
531D4—104no—
532D4—104no—
533D4—2032no—
534D4—202no—
535D4—202no—
536D4—208no—
537C2×C4—24no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—102no—
548C2×C4—204no—
549C2×C4—202no—
550C2×C4—202no—
551C2×C4—202no—
552C2×C4—202no—
553C2×C4—208no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—404no—
558C2×C4#402114yes—
559C2×C4#402812yes—
560C2×C4#403014yes—
561C2×C4#403012yes—
562C2×C4#404014yes—
563C2×C4#404012yes—
564C2×C4#404114yes—
565C2×C4C22×D2011yescharacteristic
566C2×C4C2×#70911yescharacteristic
567C2×C4C2×#70911yescharacteristic
568C2×C4C2×D4×D511yescharacteristic
569C2×C4C2×D4×D511yescharacteristic
570C2×C4C2×#71311yescharacteristic
571C8—42no—
572C8—104no—
573C5C2×#203311yescharacteristic, complemented, Sylow
574C22—104no—
575C22—104no—
576C22—104no—
577C22—202no—
578C22—202no—
579C22—202no—
580C22—202no—
581C22—2016no—
582C22—204no—
583C22—204no—
584C22—204no—
585C22—402no—
586C22—402no—
587C22—402no—
588C22—4016no—
589C22—402no—
590C22#6496114yes—
591C22#6506214yes—
592C22#6506414yes—
593C22#6509914yes—
594C22#6510114yes—
595C22#6515514yes—
596C22#6517114yes—
597C22C2×#402811yescharacteristic
598C22C2×#403011yescharacteristic
599C22C2×#404011yescharacteristic
600C22C2×D5×D811yescharacteristic
601C22C2×#406011yescharacteristic
602C22C2×#406211yescharacteristic
603C22C2×#406411yescharacteristic
604C4—44no—
605C4—82no—
606C4—202no—
607C4—402no—
608C4#6496114yes—
609C4C2×#402111yescharacteristic
610C4C2×#403011yescharacteristic
611C4C2×#404011yescharacteristic
612C4C2×#404111yescharacteristic
613C2—204no—
614C2—404no—
615C2#1059961518yesdirect product factor
616C2C2×#6496111yescharacteristic
617C2C2×#6506211yescharacteristic
618C2C2×#6506411yescharacteristic
619C2C2×#6509911yescharacteristic
620C2C2×#6510111yescharacteristic
621C2C2×#6515511yescharacteristic
622C2C2×#6517111yescharacteristic
subgroupG/H
centerC24D4×D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC2×C5×#340C2
socleC24×C5C2×D4
prime radicalC22×#4041C2
hypercenterC2×#340D5
hypocenterC5C2×#2033
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#3953C2semidirect
3. C22×#3952C2semidirect
4. C2×#65276C2semidirect
5. C22×#3941C2semidirect
6. C22×#3939C2semidirect
7. C2×C5×#340C2semidirect
8. #10599615C2direct (N × H)
25. C2×#3953C22semidirect
27. C2×#3952C22semidirect
29. #65276C22semidirect
31. C2×#3941C22semidirect
33. C2×#3939C22semidirect
34. C5×#340C22semidirect
85. C22×#168D4semidirect
102. C2×#340D5semidirect
192. C2×#168C2×D4semidirect
218. #340C2×D5semidirect
485. C2×C5#2033semidirect
573. C5C2×#2033semidirect
615. C2#10599615direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40412
C22×#39532
C22×#39522
C2×#652762
C22×#39412
C22×#39392
C2×C5×#3402
#105996152
C2×#20335