Finite Group Databasebeta

← C2×#10613159 #12967101

Subgroups — C2×#10613159 #12967101

Order 1280.

2326 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×C22⋊Q8C211yesmaximal, characteristic
2C22×#4038C211yesmaximal, characteristic
3C2×C5×#483C211yesmaximal, characteristic, complemented
4C2×#65333C211yesmaximal, characteristic, complemented
5C2×#65260C211yesmaximal, characteristic, complemented
6#10613159C2116yesmaximal, direct product factor
7C2×#65150C212yesmaximal, complemented
8C2×#65156C212yesmaximal, complemented
9C2×#65091C212yesmaximal, complemented
10C2×#65103C212yesmaximal, complemented
11C2×#65015C211yesmaximal, characteristic
12C2×#65011C211yesmaximal, characteristic, complemented
13C22×Q8×D5C2211yescharacteristic
14C23×C4×D5C2211yescharacteristic
15C2×C5×C22⋊Q8C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C2×#4092C2211yescharacteristic
18C22×#685—21no—
19C22×C4⋊Dic5C2211yescharacteristic
20C2×#4070C2211yescharacteristic
21C22×C4×Dic5—21no—
22C22×#676C2212yes—
23D5×C22⋊Q8—24no—
24D5×C22⋊Q8C2218yes—
25C2×#4043C2211yescharacteristic
26C2×#4042—21no—
27C2×#4038—21no—
28C2×#4038—21no—
29C2×#4038—24no—
30C2×#4038C2212yes—
31C2×#4038C2212yes—
32C2×#4038C2218yes—
33C2×D5×C4⋊C4—21no—
34C2×D5×C4⋊C4C2211yescharacteristic
35C2×D5×C22⋊C4—21no—
36C2×#4024—21no—
37C5×#483C2218yescomplemented
38C2×C5×#106C2212yescomplemented
39C2×C5×#103C2212yescomplemented
40C2×C5×C22⋊C8C2211yescharacteristic
41C2×#3967C2212yescomplemented
42C2×C22⋊#168C2211yescharacteristic
43C2×#3952C2212yes—
44C2×#3950C2212yescomplemented
45C2×#3948C2212yescomplemented
46#65333C2218yescomplemented
47#65260C2218yescomplemented
48C2×#3942C2212yescomplemented
49C2×#3940C2212yescomplemented
50C2×#3939C2212yescomplemented
51#65156C22116yescomplemented
52#65150C22116yescomplemented
53#65103C22116yescomplemented
54#65091C22116yescomplemented
55#65015C2218yes—
56#65011C2218yescomplemented
57C2×#3095—51nomaximal, Sylow
58C24×D5D411yescharacteristic
59C22×C5×Q8C2311yescharacteristic
60C23×C4×C5—21no—
61C23×C4×C5C2311yescharacteristic
62C23×Dic5—21no—
63C23×Dic5D411yescharacteristic
64C2×Q8×D5—22no—
65C2×Q8×D5—28no—
66C2×Q8×D5C2314yes—
67C22×C4×D5—28no—
68C22×C4×D5—21no—
69C22×C4×D5—21no—
70C22×C4×D5D411yescharacteristic
71C22×C4×D5D411yescharacteristic
72C22×C4×D5D414yes—
73C22×C4×D5C2311yescharacteristic
74C22×C4×D5C2314yes—
75C22×C4×D5C2311yescharacteristic
76C22×Dic10—21no—
77C22×Dic10C2311yescharacteristic
78C22×C5×C8C2312yes—
79C5×C22⋊Q8—22no—
80C5×C22⋊Q8C2314yes—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4C2312yes—
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2314yes—
87C2×C5×C22⋊C4—21no—
88C2×C22⋊Dic5—21no—
89#4092—22no—
90#4092C2314yes—
91C2×#685—21no—
92C2×#685—21no—
93C2×#685—22no—
94C2×#685—28no—
95C2×#685—22no—
96C2×C4⋊Dic5—21no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—21no—
99C2×C4⋊Dic5C2311yescharacteristic
100C2×C4⋊Dic5C2314yes—
101C2×C4⋊Dic5C2312yes—
102#4070—22no—
103#4070C2314yes—
104C2×#683—21no—
105C2×#683—21no—
106C2×#683—21no—
107C2×C4×Dic5—28no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C22×#168C2312yes—
111C2×#676—28no—
112C2×#676C2318yes—
113#4043—22no—
114#4043C2314yes—
115#4042—28no—
116#4038—28no—
117#4038—28no—
118#4038—24no—
119#4038—24no—
120#4038C2318yes—
121#4038C2318yes—
122D5×C4⋊C4—28no—
123D5×C4⋊C4—22no—
124D5×C4⋊C4C2314yes—
125D5×C22⋊C4—28no—
126#4024—28no—
127C5×#106C2318yescomplemented
128C5×#103C2318yescomplemented
129C5×C22⋊C8C2314yes—
130#3967C2318yescomplemented
131C22⋊#168C2314yes—
132#3952C2318yes—
133#3950C2318yescomplemented
134#3948C2318yescomplemented
135#3942C2318yescomplemented
136#3940C2318yescomplemented
137#3939C2318yescomplemented
138C22×C22⋊Q8—51no—
139C22×#117—51no—
140#3095—516no—
141C2×#484—51no—
142C2×#484—51no—
143C2×#485—52no—
144C2×#485—52no—
145C2×#483—51no—
146C2×#483D511yescharacteristic, complemented
147C2×#428—52no—
148C2×#419—52no—
149C2×#407—51no—
150C24×C5C2×D411yescharacteristic
151C23×D5—24no—
152C23×D5—24no—
153C23×D5—42no—
154C23×D5C2×D411yescharacteristic
155C23×D5C2×D414yes—
156C23×D5C2×D411yescharacteristic
157C2×C5×Q8—21no—
158C2×C5×Q8—24no—
159C2×C5×Q8C2412yes—
160C22×C4×C5—24no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—24no—
164C22×C4×C5—22no—
165C22×C4×C5—44no—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D412yes—
168C22×C4×C5C2412yes—
169C22×C4×C5C2411yescharacteristic
170C22×Dic5—24no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—24no—
174C22×Dic5—22no—
175C22×Dic5—44no—
176C22×Dic5C2×D414yes—
177C22×Dic5C2×D411yescharacteristic
178C22×Dic5C2×D411yescharacteristic
179Q8×D5—216no—
180Q8×D5—48no—
181C2×C4×D5—24no—
182C2×C4×D5—24no—
183C2×C4×D5—24no—
184C2×C4×D5—216no—
185C2×C4×D5—216no—
186C2×C4×D5—24no—
187C2×C4×D5—24no—
188C2×C4×D5—44no—
189C2×C4×D5—44no—
190C2×C4×D5C2×D414yes—
191C2×C4×D5C2×D414yes—
192C2×C4×D5C2×D412yes—
193C2×C4×D5C2×D412yes—
194C2×C4×D5#4118yes—
195C2×C4×D5C2412yes—
196C2×C4×D5C2412yes—
197C2×Dic10—24no—
198C2×Dic10—21no—
199C2×Dic10—24no—
200C2×Dic10—44no—
201C2×Dic10C2412yes—
202C2×C5×C8—24no—
203C2×C5×C8C2414yes—
204C5×C4⋊C4—24no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—24no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4C2414yes—
209C5×C4⋊C4C2412yes—
210C5×C22⋊C4—24no—
211C22⋊Dic5—24no—
212#685—24no—
213#685—24no—
214#685—28no—
215#685—28no—
216C4⋊Dic5—21no—
217C4⋊Dic5—24no—
218C4⋊Dic5—22no—
219C4⋊Dic5—24no—
220C4⋊Dic5C2414yes—
221C4⋊Dic5C2412yes—
222#683—24no—
223#683—24no—
224#683—24no—
225C4×Dic5—28no—
226C4×Dic5—28no—
227C2×#168—24no—
228C2×#168C2414yes—
229#676—216no—
230C23×Q8—51no—
231C24×C4—51no—
232C22×M16—52no—
233C2×C22⋊Q8—51no—
234C2×C22⋊Q8—51no—
235C2×C22⋊Q8—58no—
236C2×C22⋊Q8—51no—
237C2×C22⋊Q8—101no—
238C2×C22⋊Q8—101no—
239C2×C22⋊Q8—104no—
240C2×C22⋊Q8C2×D511yescharacteristic
241C2×#117—52no—
242C2×#117—58no—
243C2×#117—52no—
244C2×#117—101no—
245C2×#117—104no—
246C2×#117—101no—
247C22×C4⋊C4—51no—
248C22×C4⋊C4—51no—
249C22×C4⋊C4—101no—
250C22×C4⋊C4C2×D511yescharacteristic
251C22×C22⋊C4—101no—
252C22×C22⋊C4—101no—
253C22×C42—101no—
254#485—516no—
255#485—516no—
256#484—58no—
257#484—58no—
258#483—58no—
259#483C2×D518yescomplemented
260#428—516no—
261C2×#107—52no—
262C2×#107—52no—
263C2×#106—52no—
264C2×#106C2×D512yescomplemented
265#419—516no—
266C2×#103—52no—
267C2×#103—52no—
268C2×#103—52no—
269C2×#103C2×D512yescomplemented
270#407—58no—
271C2×C22⋊C8—51no—
272C2×C22⋊C8—52no—
273C2×C22⋊C8C2×D511yescharacteristic
274C23×C5—22no—
275C23×C5—22no—
276C23×C5#13714yes—
277C23×C5C22×D412yes—
278C23×C5C22×D411yescharacteristic
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—28no—
283C22×D5—22no—
284C22×D5—22no—
285C22×D5—28no—
286C22×D5—44no—
287C22×D5—416no—
288C22×D5#12314yes—
289C22×D5C22×D412yes—
290C22×D5C22×D412yes—
291C5×Q8—24no—
292C5×Q8—42no—
293C2×C4×C5—22no—
294C2×C4×C5—24no—
295C2×C4×C5—24no—
296C2×C4×C5—24no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—42no—
300C2×C4×C5—48no—
301C2×C4×C5—44no—
302C2×C4×C5—42no—
303C2×C4×C5C22×D412yes—
304C2×C4×C5C22×D411yescharacteristic
305C2×C4×C5C2×#4114yes—
306C2×C4×C5C2511yescharacteristic
307C2×Dic5—22no—
308C2×Dic5—28no—
309C2×Dic5—24no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—48no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—44no—
316C2×Dic5#12314yes—
317C2×Dic5C22×D412yes—
318C2×Dic5C22×D412yes—
319C4×D5—28no—
320C4×D5—24no—
321C4×D5—24no—
322C4×D5—28no—
323C4×D5—48no—
324C4×D5—48no—
325C4×D5#12318yes—
326C4×D5C2×#4118yes—
327Dic10—24no—
328Dic10—42no—
329Dic10—48no—
330C5×C8—24no—
331#168—24no—
332C25—51no—
333C22×Q8—54no—
334C22×Q8—51no—
335C22×Q8—101no—
336C22×Q8—102no—
337C22×Q8—108no—
338C22×Q8C22×D511yescharacteristic
339C23×C4—21no—
340C23×C4—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—54no—
345C23×C4—51no—
346C23×C4—54no—
347C23×C4—108no—
348C23×C4—101no—
349C23×C4—101no—
350C23×C4—101no—
351C23×C4C22×D511yescharacteristic
352C2×M16—58no—
353C2×M16—108no—
354C22×C8—52no—
355C22×C8C22×D512yes—
356C22⋊Q8—22no—
357C22⋊Q8—54no—
358C22⋊Q8—54no—
359C22⋊Q8—54no—
360C22⋊Q8—108no—
361C22⋊Q8—108no—
362C22⋊Q8—102no—
363C22⋊Q8—102no—
364C22⋊Q8—102no—
365C22⋊Q8C22×D514yes—
366#117—58no—
367#117—58no—
368#117—104no—
369#117—108no—
370#117—104no—
371#117—108no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4—54no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—54no—
379C2×C4⋊C4—102no—
380C2×C4⋊C4—108no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4—101no—
383C2×C4⋊C4—101no—
384C2×C4⋊C4—102no—
385C2×C4⋊C4—101no—
386C2×C4⋊C4—101no—
387C2×C4⋊C4C22×D511yescharacteristic
388C2×C4⋊C4C22×D512yes—
389C2×C4⋊C4C22×D514yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—108no—
392C2×C22⋊C4—108no—
393C2×C22⋊C4—102no—
394C2×C22⋊C4—102no—
395C2×C22⋊C4—101no—
396C2×C22⋊C4—101no—
397C2×C22⋊C4—101no—
398C2×C42—108no—
399C2×C42—102no—
400C2×C42—102no—
401#107—58no—
402#107—58no—
403#106—58no—
404#106C22×D518yescomplemented
405#103—58no—
406#103—58no—
407#103—58no—
408#103C22×D518yescomplemented
409C22⋊C8—54no—
410C22⋊C8—58no—
411C22⋊C8C22×D514yes—
412C22×C5—28no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5C2×#12312yes—
416C22×C5C2×#13714yes—
417C22×C5C2×#13712yes—
418C22×C5#57512yes—
419C22×C5C23×D411yescharacteristic
420C2×D5—28no—
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—22no—
424C2×D5—22no—
425C2×D5—22no—
426C2×D5—416no—
427C2×D5—44no—
428C2×D5C2×#12314yes—
429C4×C5—22no—
430C4×C5—42no—
431C4×C5—44no—
432C4×C5—42no—
433C4×C5C2×#12312yes—
434C4×C5C22×#4112yes—
435Dic5—22no—
436Dic5—42no—
437Dic5—42no—
438Dic5—44no—
439Dic5C2×#12314yes—
440C24—51no—
441C24—51no—
442C24—54no—
443C24—104no—
444C24—104no—
445C24—202no—
446C24D4×D511yescharacteristic
447C2×Q8—21no—
448C2×Q8—24no—
449C2×Q8—52no—
450C2×Q8—104no—
451C2×Q8—1016no—
452C2×Q8—101no—
453C2×Q8—104no—
454C2×Q8—204no—
455C2×Q8—208no—
456C2×Q8C23×D512yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—44no—
463C22×C4—51no—
464C22×C4—52no—
465C22×C4—58no—
466C22×C4—52no—
467C22×C4—54no—
468C22×C4—51no—
469C22×C4—54no—
470C22×C4—54no—
471C22×C4—52no—
472C22×C4—52no—
473C22×C4—104no—
474C22×C4—1016no—
475C22×C4—1016no—
476C22×C4—104no—
477C22×C4—104no—
478C22×C4—104no—
479C22×C4—104no—
480C22×C4—104no—
481C22×C4—104no—
482C22×C4—102no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—204no—
486C22×C4—204no—
487C22×C4—204no—
488C22×C4D4×D512yes—
489C22×C4D4×D511yescharacteristic
490C22×C4C23×D512yes—
491C22×C4C23×D511yescharacteristic
492M16—1016no—
493C2×C8—24no—
494C2×C8—54no—
495C2×C8—104no—
496C2×C8C23×D514yes—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—24no—
500C4⋊C4—21no—
501C4⋊C4—54no—
502C4⋊C4—52no—
503C4⋊C4—104no—
504C4⋊C4—104no—
505C4⋊C4—104no—
506C4⋊C4—104no—
507C4⋊C4—102no—
508C4⋊C4—101no—
509C4⋊C4—104no—
510C4⋊C4C23×D514yes—
511C4⋊C4C23×D512yes—
512C22⋊C4—24no—
513C22⋊C4—108no—
514C22⋊C4—108no—
515C22⋊C4—104no—
516C22⋊C4—104no—
517C22⋊C4—104no—
518C42—108no—
519C42—108no—
520C2×C5—24no—
521C2×C5#309514yescomplemented
522C2×C5C22×#12311yescharacteristic
523C2×C5C22×#13711yescharacteristic
524C2×C5C2×#57511yescharacteristic
525D5—24no—
526D5—42no—
527C23—22no—
528C23—22no—
529C23—54no—
530C23—52no—
531C23—52no—
532C23—108no—
533C23—102no—
534C23—102no—
535C23—108no—
536C23—102no—
537C23—102no—
538C23—102no—
539C23—204no—
540C23—2016no—
541C23#406114yes—
542C23C2×D4×D512yes—
543C23C2×D4×D511yescharacteristic
544Q8—24no—
545Q8—42no—
546Q8—104no—
547Q8—208no—
548Q8—202no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—48no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—54no—
560C2×C4—52no—
561C2×C4—58no—
562C2×C4—58no—
563C2×C4—52no—
564C2×C4—108no—
565C2×C4—108no—
566C2×C4—108no—
567C2×C4—102no—
568C2×C4—104no—
569C2×C4—104no—
570C2×C4—104no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—208no—
574C2×C4—208no—
575C2×C4—208no—
576C2×C4—204no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4C2×D4×D512yes—
580C2×C4C2×D4×D511yescharacteristic
581C2×C4D5×#4114yes—
582C2×C4C24×D511yescharacteristic
583C8—24no—
584C8—104no—
585C5C2×#309511yescharacteristic, complemented, Sylow
586C22—22no—
587C22—28no—
588C22—22no—
589C22—54no—
590C22—108no—
591C22—102no—
592C22—102no—
593C22—102no—
594C22—102no—
595C22—102no—
596C22—2016no—
597C22—204no—
598C22D5×#12312yes—
599C22C2×#406114yes—
600C22C2×#406112yes—
601C22#6611112yes—
602C22C22×D4×D511yescharacteristic
603C4—22no—
604C4—42no—
605C4—44no—
606C4—42no—
607C4—54no—
608C4—102no—
609C4—202no—
610C4—204no—
611C4—202no—
612C4D5×#12312yes—
613C4C2×D5×#4112yes—
614C2—24no—
615C2—104no—
616C2—202no—
617C2#1061315914yesdirect product factor
618C2C2×D5×#12311yescharacteristic
619C2C22×#406111yescharacteristic
620C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#483C2
socleC23×C5C22×D4
prime radicalC24×D5D4
hypercenterC2×#483D5
hypocenterC5C2×#3095
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. C2×C5×#483C2semidirect
4. C2×#65333C2semidirect
5. C2×#65260C2semidirect
6. #10613159C2direct (N × H)
7. C2×#65150C2semidirect
8. C2×#65156C2semidirect
9. C2×#65091C2semidirect
10. C2×#65103C2semidirect
12. C2×#65011C2semidirect
37. C5×#483C22semidirect
38. C2×C5×#106C22semidirect
39. C2×C5×#103C22semidirect
41. C2×#3967C22semidirect
44. C2×#3950C22semidirect
45. C2×#3948C22semidirect
46. #65333C22semidirect
47. #65260C22semidirect
48. C2×#3942C22semidirect
49. C2×#3940C22semidirect
50. C2×#3939C22semidirect
51. #65156C22semidirect
52. #65150C22semidirect
53. #65103C22semidirect
54. #65091C22semidirect
56. #65011C22semidirect
127. C5×#106C23semidirect
128. C5×#103C23semidirect
130. #3967C23semidirect
133. #3950C23semidirect
134. #3948C23semidirect
135. #3942C23semidirect
136. #3940C23semidirect
137. #3939C23semidirect
146. C2×#483D5semidirect
259. #483C2×D5semidirect
264. C2×#106C2×D5semidirect
269. C2×#103C2×D5semidirect
404. #106C22×D5semidirect
408. #103C22×D5semidirect
521. C2×C5#3095semidirect
585. C5C2×#3095semidirect
617. C2#10613159direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊Q82
C22×#40382
C2×C5×#4832
C2×#653332
C2×#652602
#106131592
C2×#651502
C2×#651562
C2×#650912
C2×#651032
C2×#650152
C2×#650112
C2×#30955