Finite Group Databasebeta

← C2×#10599676 #12100968

Subgroups — C2×#10599676 #12100968

Order 1280.

2438 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D5C211yesmaximal, characteristic, complemented
2C22×#4041C211yesmaximal, characteristic
3C22×#3953C211yesmaximal, characteristic, complemented
4C2×#65276C211yesmaximal, characteristic, complemented
5C22×#3941C211yesmaximal, characteristic, complemented
6C2×C5×#340C211yesmaximal, characteristic, complemented
7C2×#64749C211yesmaximal, characteristic, complemented
8#10599676C218yesmaximal, 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
19C22×C8×D5—24no—
20C22×C8×D5—24no—
21C22×C8×D5—24no—
22C22×C8×D5C2214yescomplemented
23C2×#4041—22no—
24C2×#4041—24no—
25C2×#4041C418yescomplemented
26C2×#4041C2214yes—
27C2×#3963—21no—
28C2×#3953—24no—
29C2×#3953C2214yescomplemented
30#65276—22no—
31#65276C2214yescomplemented
32C2×#3941—24no—
33C2×#3941C2214yescomplemented
34C5×#340C2214yescomplemented
35#64749C2214yescomplemented
36C2×#1893—51nomaximal, Sylow
37C24×D5—21no—
38C24×D5D411yescharacteristic
39C23×C4×C5—21no—
40C23×C4×C5—21no—
41C23×C4×C5C2311yescharacteristic
42C23×Dic5—21no—
43C23×Dic5D411yescharacteristic
44C22×D20—22no—
45C22×D20—22no—
46C22×D20—22no—
47C22×D20—22no—
48C22×D20—28no—
49C22×D20—24no—
50C22×D20—21no—
51C22×D20—22no—
52C22×D20—44no—
53C22×D20—44no—
54C22×D20C2×C414yes—
55C22×D20C2312yes—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—22no—
60C22×C4×D5C2×C414yes—
61C22×C4×D5D412yes—
62C22×C4×D5D414yes—
63C22×C4×D5C2312yes—
64C22×C5×C8—22no—
65C22×C5×C8—22no—
66C22×C5×C8D414yescomplemented
67C22×C5×C8C2312yes—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4C2×C414yes—
74C2×C5×C4⋊C4C2312yes—
75C2×C5×C4⋊C4C2312yes—
76C2×#685—28no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—44no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5C2312yes—
84C22×#168—22no—
85C22×#168—22no—
86C22×#168D414yescomplemented
87C22×#168C2312yes—
88C2×C8×D5—232no—
89C2×C8×D5—28no—
90C2×C8×D5—28no—
91C2×C8×D5—28no—
92#4041—216no—
93#4041—28no—
94#4041C2×C4116yescomplemented
95#3963—24no—
96#3953—28no—
97#3941—28no—
98C24×C8—51no—
99C22×#121—51no—
100C22×#102—51no—
101C22×#102—51no—
102C2×#380—51no—
103#1893—58no—
104C2×#340—51no—
105C2×#340D511yescharacteristic, complemented
106C24×C5C2×D411yescharacteristic
107C23×D5—22no—
108C23×D5—22no—
109C23×D5—22no—
110C23×D5—22no—
111C23×D5—24no—
112C23×D5—22no—
113C23×D5—42no—
114C23×D5—42no—
115C23×D5—42no—
116C23×D5—42no—
117C23×D5—42no—
118C23×D5—42no—
119C23×D5C22⋊C414yes—
120C23×D5D814yes—
121C23×D5SD1614yes—
122C23×D5C2×D412yes—
123C22×C4×C5—24no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—42no—
127C22×C4×C5—42no—
128C22×C4×C5—42no—
129C22×C4×C5—42no—
130C22×C4×C5—42no—
131C22×C4×C5C22×C412yes—
132C22×C4×C5C2×D412yes—
133C22×C4×C5C2×D411yescharacteristic
134C22×C4×C5C2×D412yes—
135C22×C4×C5C2×D412yes—
136C22×C4×C5#4112yes—
137C22×C4×C5#4112yes—
138C22×C4×C5C2411yescharacteristic
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—42no—
143C22×Dic5—42no—
144C22×Dic5—42no—
145C22×Dic5C22⋊C414yes—
146C22×Dic5C2×D412yes—
147C2×D20—28no—
148C2×D20—28no—
149C2×D20—22no—
150C2×D20—22no—
151C2×D20—22no—
152C2×D20—22no—
153C2×D20—216no—
154C2×D20—24no—
155C2×D20—22no—
156C2×D20—432no—
157C2×D20—48no—
158C2×D20—48no—
159C2×D20—44no—
160C2×D20—42no—
161C2×D20—42no—
162C2×D20—44no—
163C2×D20C22×C414yes—
164C2×C4×D5—28no—
165C2×C4×D5—28no—
166C2×C4×D5—28no—
167C2×C4×D5—24no—
168C2×C4×D5—24no—
169C2×C4×D5—28no—
170C2×C4×D5—22no—
171C2×C4×D5—22no—
172C2×C4×D5—22no—
173C2×C4×D5—22no—
174C2×C4×D5C22⋊C418yes—
175C2×C4×D5C22×C414yes—
176C2×C4×D5C2×D414yes—
177C2×C5×C8—28no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8C2×D414yescomplemented
181C5×C4⋊C4—24no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—42no—
186C5×C4⋊C4C22×C414yes—
187#685—216no—
188#685—48no—
189C4⋊Dic5—22no—
190C4⋊Dic5—22no—
191C4⋊Dic5—42no—
192C2×#168—28no—
193C2×#168—22no—
194C2×#168—22no—
195C2×#168C2×D414yescomplemented
196C8×D5—232no—
197C23×D4—51no—
198C23×D4—101no—
199C24×C4—51no—
200C23×C8—51no—
201C23×C8—54no—
202C23×C8—104no—
203C23×C8—104no—
204C23×C8—104no—
205C23×C8C2×D511yescharacteristic
206C2×#121—58no—
207C2×#121—54no—
208C2×#121—104no—
209C2×#121—102no—
210C22×C4⋊C4—51no—
211C22×C4⋊C4C2×D511yescharacteristic
212C22×C4⋊C4C2×D511yescharacteristic
213C22×C22⋊C4—101no—
214C22×C22⋊C4—101no—
215C2×#102—54no—
216C2×#102—54no—
217C2×#102—104no—
218C2×#102—104no—
219#380—54no—
220#380—102no—
221C2×#95—101no—
222#340—54no—
223#340C2×D514yescomplemented
224C23×C5C2×C22⋊C412yes—
225C23×C5#12112yes—
226C23×C5#12112yes—
227C23×C5C2×D812yes—
228C23×C5C2×SD1612yes—
229C23×C5#13512yes—
230C23×C5#13512yes—
231C23×C5C22×D411yescharacteristic
232C22×D5—22no—
233C22×D5—22no—
234C22×D5—22no—
235C22×D5—22no—
236C22×D5—28no—
237C22×D5—28no—
238C22×D5—28no—
239C22×D5—28no—
240C22×D5—28no—
241C22×D5—28no—
242C22×D5—24no—
243C22×D5—42no—
244C22×D5—42no—
245C22×D5—42no—
246C22×D5—42no—
247C22×D5—42no—
248C22×D5—42no—
249C22×D5—48no—
250C22×D5—48no—
251C22×D5—48no—
252C22×D5—84no—
253C22×D5—84no—
254C22×D5—84no—
255C22×D5—84no—
256C22×D5#102116yescomplemented
257C22×D5C2×C22⋊C414yes—
258C22×D5C2×D814yes—
259C22×D5C2×SD1614yes—
260C2×C4×C5—24no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—48no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—84no—
268C2×C4×C5C2×C22⋊C412yes—
269C2×C4×C5C4×D414yes—
270C2×C4×C5C4×D414yes—
271C2×C4×C5#12014yes—
272C2×C4×C5#12112yes—
273C2×C4×C5#12112yes—
274C2×C4×C5#12314yes—
275C2×C4×C5C23×C411yescharacteristic
276C2×C4×C5C22×D411yescharacteristic
277C2×C4×C5C22×D411yescharacteristic
278C2×C4×C5C22×D411yescharacteristic
279C2×C4×C5C2×#4111yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—28no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—84no—
288C2×Dic5C2×C22⋊C414yes—
289D20—24no—
290D20—24no—
291D20—432no—
292D20—42no—
293D20—42no—
294D20—48no—
295C4×D5—24no—
296C4×D5—24no—
297C4×D5—24no—
298C4×D5—24no—
299C4×D5—216no—
300C5×C8—24no—
301#168—24no—
302C25—51no—
303C25—101no—
304C22×D4—54no—
305C22×D4—52no—
306C22×D4—104no—
307C22×D4—108no—
308C22×D4—102no—
309C22×D4—102no—
310C22×D4—102no—
311C22×D4—102no—
312C22×D4—101no—
313C22×D4—102no—
314C22×D4—204no—
315C22×D4—204no—
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—51no—
319C23×C4—54no—
320C23×C4—54no—
321C23×C4—52no—
322C23×C4—52no—
323C23×C4—102no—
324C23×C4—102no—
325C23×C4—102no—
326C23×C4—102no—
327C23×C4—101no—
328C23×C4C22×D511yescharacteristic
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—54no—
332C22×C8—52no—
333C22×C8—108no—
334C22×C8—108no—
335C22×C8—1032no—
336C22×C8—102no—
337C22×C8—102no—
338C22×C8—108no—
339C22×C8D2014yescomplemented
340C22×C8C22×D512yes—
341#121—516no—
342#121—108no—
343#121—1016no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—52no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—102no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4C4×D514yes—
354C2×C4⋊C4C22×D512yes—
355C2×C4⋊C4C22×D512yes—
356C2×C22⋊C4—104no—
357C2×C22⋊C4—108no—
358C2×C22⋊C4—104no—
359C2×C22⋊C4—204no—
360#102—108no—
361#102—108no—
362#95—104no—
363C22×C5#38614yes—
364C22×C5C2×#10214yes—
365C22×C5#41614yes—
366C22×C5#46514yes—
367C22×C5#46514yes—
368C22×C5#46614yes—
369C22×C5#46614yes—
370C22×C5C22×C22⋊C411yescharacteristic
371C22×C5C2×#12111yescharacteristic
372C22×C5C2×#12111yescharacteristic
373C22×C5C22×D811yescharacteristic
374C22×C5C22×SD1611yescharacteristic
375C22×C5C2×#13511yescharacteristic
376C22×C5C2×#13511yescharacteristic
377C2×D5—24no—
378C2×D5—232no—
379C2×D5—24no—
380C2×D5—24no—
381C2×D5—24no—
382C2×D5—24no—
383C2×D5—24no—
384C2×D5—44no—
385C2×D5—44no—
386C2×D5—44no—
387C2×D5—816no—
388C2×D5—82no—
389C2×D5—82no—
390C2×D5—82no—
391C2×D5—82no—
392C2×D5C2×#10218yescomplemented
393C4×C5—44no—
394C4×C5—82no—
395C4×C5#38614yes—
396C4×C5C2×C4×D411yescharacteristic
397C4×C5C2×C4×D411yescharacteristic
398C4×C5C2×#12011yescharacteristic
399C4×C5C2×#12311yescharacteristic
400Dic5—24no—
401Dic5—82no—
402C24—52no—
403C24—54no—
404C24—54no—
405C24—54no—
406C24—102no—
407C24—102no—
408C24—102no—
409C24—102no—
410C24—102no—
411C24—104no—
412C24—202no—
413C24—202no—
414C24—202no—
415C24—202no—
416C24—202no—
417C24—202no—
418C24D4×D511yescharacteristic
419C2×D4—54no—
420C2×D4—1016no—
421C2×D4—102no—
422C2×D4—102no—
423C2×D4—102no—
424C2×D4—102no—
425C2×D4—102no—
426C2×D4—108no—
427C2×D4—104no—
428C2×D4—108no—
429C2×D4—2032no—
430C2×D4—208no—
431C2×D4—208no—
432C2×D4—204no—
433C2×D4—202no—
434C2×D4—204no—
435C2×D4—202no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—52no—
445C22×C4—54no—
446C22×C4—54no—
447C22×C4—54no—
448C22×C4—58no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—108no—
456C22×C4—108no—
457C22×C4—104no—
458C22×C4—108no—
459C22×C4—108no—
460C22×C4—104no—
461C22×C4—102no—
462C22×C4—202no—
463C22×C4—202no—
464C22×C4—202no—
465C22×C4C2×C4×D512yes—
466C22×C4C2×D2012yes—
467C22×C4#70912yes—
468C22×C4D4×D512yes—
469C22×C4D4×D512yes—
470C22×C4D4×D511yescharacteristic
471C22×C4#71312yes—
472C22×C4C23×D511yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—28no—
476C2×C8—54no—
477C2×C8—1032no—
478C2×C8—102no—
479C2×C8—102no—
480C2×C8—108no—
481C2×C8C2×D2014yescomplemented
482C4⋊C4—22no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—102no—
488C4⋊C4—102no—
489C4⋊C4—202no—
490C4⋊C4C2×C4×D514yes—
491C22⋊C4—1016no—
492C22⋊C4—208no—
493C2×C5#189318yescomplemented
494C2×C5C2×#38611yescharacteristic
495C2×C5C22×#10211yescharacteristic
496C2×C5C2×#41611yescharacteristic
497C2×C5C2×#46511yescharacteristic
498C2×C5C2×#46511yescharacteristic
499C2×C5C2×#46611yescharacteristic
500C2×C5C2×#46611yescharacteristic
501D5—28no—
502D5—84no—
503C23—54no—
504C23—516no—
505C23—54no—
506C23—54no—
507C23—102no—
508C23—108no—
509C23—102no—
510C23—102no—
511C23—102no—
512C23—108no—
513C23—108no—
514C23—108no—
515C23—108no—
516C23—108no—
517C23—104no—
518C23—202no—
519C23—208no—
520C23—202no—
521C23—202no—
522C23—202no—
523C23—202no—
524C23—202no—
525C23—208no—
526C23—208no—
527C23—404no—
528C23—404no—
529C23—404no—
530C23—404no—
531C23D5×C22⋊C412yes—
532C23#403012yes—
533C23#404112yes—
534C23D5×D812yes—
535C23D5×SD1612yes—
536C23#406212yes—
537C23#406512yes—
538C23C2×D4×D511yescharacteristic
539D4—104no—
540D4—104no—
541D4—2032no—
542D4—202no—
543D4—202no—
544D4—208no—
545C2×C4—24no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—54no—
553C2×C4—84no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—108no—
557C2×C4—104no—
558C2×C4—104no—
559C2×C4—104no—
560C2×C4—104no—
561C2×C4—1016no—
562C2×C4—202no—
563C2×C4—202no—
564C2×C4—202no—
565C2×C4—404no—
566C2×C4C4×D2014yes—
567C2×C4D5×C22⋊C412yes—
568C2×C4#402814yes—
569C2×C4#403012yes—
570C2×C4#403914yes—
571C2×C4#404014yes—
572C2×C4#404112yes—
573C2×C4C22×C4×D511yescharacteristic
574C2×C4C22×D2011yescharacteristic
575C2×C4C2×#70911yescharacteristic
576C2×C4C2×D4×D511yescharacteristic
577C2×C4C2×D4×D511yescharacteristic
578C2×C4C2×#71311yescharacteristic
579C8—24no—
580C8—104no—
581C5C2×#189311yescharacteristic, complemented, Sylow
582C22—58no—
583C22—104no—
584C22—104no—
585C22—104no—
586C22—104no—
587C22—104no—
588C22—104no—
589C22—1032no—
590C22—204no—
591C22—204no—
592C22—204no—
593C22—402no—
594C22—402no—
595C22—402no—
596C22—402no—
597C22—4016no—
598C22#6495414yes—
599C22D5×#10214yes—
600C22#6506414yes—
601C22#6509314yes—
602C22#6509614yes—
603C22#6515314yes—
604C22#6517214yes—
605C22C2×D5×C22⋊C411yescharacteristic
606C22C2×#403011yescharacteristic
607C22C2×#404111yescharacteristic
608C22C2×D5×D811yescharacteristic
609C22C2×D5×SD1611yescharacteristic
610C22C2×#406211yescharacteristic
611C22C2×#406511yescharacteristic
612C4—44no—
613C4—82no—
614C4—104no—
615C4—402no—
616C4#6495414yes—
617C4C2×C4×D2011yescharacteristic
618C4C2×#402811yescharacteristic
619C4C2×#403911yescharacteristic
620C4C2×#404011yescharacteristic
621C2—108no—
622C2—404no—
623C2#1059967618yesdirect product factor
624C2C2×#6495411yescharacteristic
625C2C2×D5×#10211yescharacteristic
626C2C2×#6506411yescharacteristic
627C2C2×#6509311yescharacteristic
628C2C2×#6509611yescharacteristic
629C2C2×#6515311yescharacteristic
630C2C2×#6517211yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#340C2
socleC24×C5C2×D4
prime radicalC22×#4041C2
cosocleC22×C4×C5C24
hypercenterC2×#340D5
hypocenterC5C2×#1893
LCSG ▷ C2×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
1. C23×C8×D5C2semidirect
3. C22×#3953C2semidirect
4. C2×#65276C2semidirect
5. C22×#3941C2semidirect
6. C2×C5×#340C2semidirect
7. C2×#64749C2semidirect
8. #10599676C2direct (N × H)
22. C22×C8×D5C22semidirect
25. C2×#4041C4semidirect
29. C2×#3953C22semidirect
31. #65276C22semidirect
33. C2×#3941C22semidirect
34. C5×#340C22semidirect
35. #64749C22semidirect
66. C22×C5×C8D4semidirect
86. C22×#168D4semidirect
94. #4041C2×C4semidirect
105. C2×#340D5semidirect
180. C2×C5×C8C2×D4semidirect
195. C2×#168C2×D4semidirect
223. #340C2×D5semidirect
256. C22×D5#102semidirect
339. C22×C8D20semidirect
392. C2×D5C2×#102semidirect
481. C2×C8C2×D20semidirect
493. C2×C5#1893semidirect
581. C5C2×#1893semidirect
623. C2#10599676direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D52
C22×#40412
C22×#39532
C2×#652762
C22×#39412
C2×C5×#3402
C2×#647492
#105996762
C2×#18935