Finite Group Databasebeta

← C2×#10612840 #12966830

Subgroups — C2×#10612840 #12966830

Order 1280.

2358 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×#713C211yesmaximal, characteristic
3C2×C5×#477C211yesmaximal, characteristic, complemented
4C2×#65373C211yesmaximal, characteristic, complemented
5C2×#65310C211yesmaximal, characteristic, complemented
6#10612840C2116yesmaximal, direct product factor
7C2×#65179C212yesmaximal, complemented
8C2×#65170C212yesmaximal, complemented
9C2×#65131C211yesmaximal, characteristic, complemented
10C2×#65126C211yesmaximal, characteristic, complemented
11C2×#65092C212yesmaximal
12C2×#65080C212yesmaximal, complemented
13C22×#713C2211yescharacteristic
14C22×Q8×D5—21no—
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C4×C5×Q8C2211yescharacteristic
17C2×Q8×Dic5C2211yescharacteristic
18C2×#4090—21no—
19C22×#676C2212yes—
20D5×C4⋊Q8—24no—
21D5×C4⋊Q8C2218yescomplemented
22C4×#713—24no—
23C4×#713C2218yes—
24C2×#4039—21no—
25C2×#4039C2211yescharacteristic
26C2×#4038—21no—
27C2×#4038C2211yescharacteristic
28C2×D5×C4⋊C4—21no—
29C2×D5×C4⋊C4C2212yes—
30C2×#4034—21no—
31C2×#4034C2212yes—
32C2×C4×D20—21no—
33C2×C4×D20C2211yescharacteristic
34C2×C42×D5—21no—
35C2×C42×D5C2211yescharacteristic
36C2×#4015C2211yescharacteristic
37C5×#477C2218yescomplemented
38C2×C5×#107C2212yes—
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2212yes—
41C2×#3967C2212yes—
42C2×#3953C2212yes—
43C2×#3949C2212yes—
44C2×#3946C2212yes—
45#65373C2218yescomplemented
46#65310C2218yescomplemented
47C2×#3941C2212yes—
48C2×#3940C2212yes—
49C2×#3939C2212yes—
50C2×C4⋊#168C2211yescharacteristic
51#65179C22116yescomplemented
52#65170C22116yescomplemented
53#65131C2218yescomplemented
54#65126C2218yescomplemented
55#65092C22116yes—
56#65080C22116yescomplemented
57C2×#3079—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C5×Q8C2311yescharacteristic
60C2×#713—22no—
61C2×#713—24no—
62C2×#713Q818yescomplemented
63C2×#713C2314yes—
64C2×Q8×D5—28no—
65C2×Q8×D5—48no—
66C22×D20—21no—
67C22×D20C2311yescharacteristic
68C22×C4×D5—21no—
69C22×C4×D5—22no—
70C22×C4×D5—21no—
71C22×C4×D5—21no—
72C22×C4×D5D411yescharacteristic
73C22×C4×D5D411yescharacteristic
74C22×C4×D5C2311yescharacteristic
75C22×Dic10—21no—
76C22×Dic10—22no—
77C22×C5×C8C2312yes—
78C5×C4⋊Q8—22no—
79C5×C4⋊Q8C2314yes—
80C4×C5×Q8—22no—
81C4×C5×Q8C2314yes—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4C2312yes—
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C42×C5—21no—
87C2×C42×C5C2311yescharacteristic
88Q8×Dic5—22no—
89Q8×Dic5C2314yes—
90#4090—28no—
91C2×#685—21no—
92C2×#685—21no—
93C2×#685—21no—
94C2×C4⋊Dic5—21no—
95C2×C4⋊Dic5—21no—
96C2×C4⋊Dic5C2312yes—
97C2×C4⋊Dic5C2311yescharacteristic
98C2×#683—22no—
99C2×#683—22no—
100C2×C4×Dic5—21no—
101C2×C4×Dic5—21no—
102C2×C4×Dic5D411yescharacteristic
103C2×C4×Dic5D411yescharacteristic
104C2×C4×Dic5C2311yescharacteristic
105C22×#168C2312yes—
106C2×#676—28no—
107C2×#676C2318yes—
108#4039—28no—
109#4039—22no—
110#4039C2314yes—
111#4038—22no—
112#4038—28no—
113#4038C2314yes—
114D5×C4⋊C4—24no—
115D5×C4⋊C4—28no—
116D5×C4⋊C4C2318yes—
117#4034—24no—
118#4034—28no—
119#4034C2318yes—
120C4×D20—28no—
121C4×D20—22no—
122C4×D20C2314yes—
123C42×D5—28no—
124C42×D5D414yes—
125C42×D5C2314yes—
126#4015—22no—
127#4015C2314yes—
128C5×#107C2318yes—
129C5×C4⋊C8C2314yes—
130C5×#103C2318yes—
131#3967C2318yes—
132#3953C2318yes—
133#3949C2318yes—
134#3946C2318yes—
135#3941C2318yes—
136#3940C2318yes—
137#3939C2318yes—
138C4⋊#168C2314yes—
139C22×C4⋊Q8—51no—
140C2×C4×#41—51no—
141#3079—516no—
142C2×#477—51no—
143C2×#477D511yescharacteristic, complemented
144C2×#475—52no—
145C2×#476—51no—
146C2×#476—51no—
147C2×#474—52no—
148C2×#428—52no—
149C2×#423—51no—
150C2×#417—52no—
151C23×D5—21no—
152C23×D5C2×D411yescharacteristic
153C2×C5×Q8—21no—
154C2×C5×Q8—24no—
155C2×C5×Q8—22no—
156C2×C5×Q8—44no—
157C2×C5×Q8C2×Q814yescomplemented
158C2×C5×Q8C2412yes—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2411yescharacteristic
165C22×Dic5—22no—
166C22×Dic5—21no—
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C22×Dic5C2×D411yescharacteristic
170#713—216no—
171#713—28no—
172#713C2×Q8116yescomplemented
173Q8×D5—432no—
174C2×D20—28no—
175C2×D20—24no—
176C2×D20—21no—
177C2×D20—22no—
178C2×D20C2×Q814yescomplemented
179C2×D20C2412yes—
180C2×C4×D5—24no—
181C2×C4×D5—28no—
182C2×C4×D5—24no—
183C2×C4×D5—24no—
184C2×C4×D5—28no—
185C2×C4×D5—24no—
186C2×C4×D5—24no—
187C2×C4×D5—48no—
188C2×C4×D5—44no—
189C2×C4×D5—44no—
190C2×C4×D5C2×D414yes—
191C2×C4×D5C2×D414yes—
192C2×C4×D5C2×D412yes—
193C2×C4×D5C2×Q814yes—
194C2×C4×D5#4114yes—
195C2×C4×D5C2412yes—
196C2×Dic10—24no—
197C2×Dic10—28no—
198C2×Dic10—44no—
199C2×Dic10—48no—
200C2×C5×C8—24no—
201C2×C5×C8C2414yes—
202C5×C4⋊C4—24no—
203C5×C4⋊C4—24no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4C2412yes—
207C5×C4⋊C4C2414yes—
208C42×C5—24no—
209C42×C5C2×D412yes—
210C42×C5C2412yes—
211#685—24no—
212#685—24no—
213#685—24no—
214C4⋊Dic5—22no—
215C4⋊Dic5—24no—
216C4⋊Dic5—21no—
217C4⋊Dic5—24no—
218C4⋊Dic5C2414yes—
219C4⋊Dic5C2412yes—
220#683—28no—
221#683—28no—
222C4×Dic5—24no—
223C4×Dic5—24no—
224C4×Dic5C2×D414yes—
225C4×Dic5C2×D412yes—
226C4×Dic5C2×D414yes—
227C4×Dic5C2412yes—
228C2×#168—24no—
229C2×#168C2414yes—
230#676—216no—
231C22×#41—51no—
232C23×Q8—101no—
233C22×M16—52no—
234C2×C4⋊Q8—58no—
235C2×C4⋊Q8—52no—
236C2×C4⋊Q8—51no—
237C2×C4⋊Q8—101no—
238C2×C4⋊Q8—104no—
239C2×C4⋊Q8—101no—
240C2×C4⋊Q8C2×D511yescharacteristic
241C4×#41—58no—
242C4×#41—104no—
243C2×C4×Q8—51no—
244C2×C4×Q8C2×D511yescharacteristic
245C2×C4×D4—51no—
246C2×C4×D4—51no—
247C2×C4×D4—101no—
248C2×C4×D4—101no—
249C2×#117—51no—
250C2×#117—101no—
251C22×C4⋊C4—52no—
252C22×C4⋊C4—101no—
253C22×C42—51no—
254C22×C42—101no—
255#477—58no—
256#477C2×D518yescomplemented
257#476—58no—
258#476—58no—
259#475—516no—
260#474—516no—
261#428—516no—
262C2×#107—52no—
263C2×#107C2×D512yes—
264C2×#106—52no—
265C2×#106—52no—
266#423—58no—
267C2×C4⋊C8—52no—
268C2×C4⋊C8—51no—
269C2×C4⋊C8C2×D511yescharacteristic
270#417—516no—
271C2×#103—52no—
272C2×#103C2×D512yes—
273C2×#102—52no—
274C2×#102—52no—
275C23×C5C22×D411yescharacteristic
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—24no—
279C22×D5—22no—
280C22×D5—42no—
281C22×D5—42no—
282C22×D5C22⋊Q814yes—
283C22×D5C22×D412yes—
284C5×Q8—24no—
285C5×Q8—22no—
286C5×Q8—48no—
287C5×Q8C22×Q814yescomplemented
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—22no—
291C2×C4×C5—22no—
292C2×C4×C5—24no—
293C2×C4×C5—44no—
294C2×C4×C5—42no—
295C2×C4×C5#13714yes—
296C2×C4×C5C22×D412yes—
297C2×C4×C5C22×D411yescharacteristic
298C2×C4×C5C22×D412yes—
299C2×C4×C5C22×Q812yes—
300C2×C4×C5C2×#4112yes—
301C2×C4×C5C2511yescharacteristic
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—24no—
305C2×Dic5—44no—
306C2×Dic5—42no—
307C2×Dic5C22⋊Q814yes—
308C2×Dic5AGL(1,ℤ/8)14yes—
309C2×Dic5C22×D412yes—
310C2×Dic5C22×D412yes—
311C2×Dic5C22×D412yes—
312D20—216no—
313D20—24no—
314D20—22no—
315D20C22×Q814yescomplemented
316C4×D5—28no—
317C4×D5—216no—
318C4×D5—28no—
319C4×D5—416no—
320C4×D5—48no—
321C4×D5—48no—
322C4×D5C22⋊Q818yes—
323C4×D5C22×Q814yes—
324C4×D5C2×#4114yes—
325Dic10—48no—
326Dic10—416no—
327C5×C8—24no—
328#168—24no—
329C2×#41—58no—
330C2×#41—54no—
331C2×#41—102no—
332C2×#41—104no—
333C22×Q8—21no—
334C22×Q8—102no—
335C22×Q8—108no—
336C22×Q8—101no—
337C22×Q8—208no—
338C22×Q8C22×D511yescharacteristic
339C22×D4—51no—
340C22×D4—101no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—51no—
344C23×C4—101no—
345C23×C4—101no—
346C23×C4—102no—
347C23×C4—101no—
348C2×M16—58no—
349C2×M16—108no—
350C22×C8—52no—
351C22×C8C22×D512yes—
352C4⋊Q8—22no—
353C4⋊Q8—58no—
354C4⋊Q8—54no—
355C4⋊Q8—108no—
356C4⋊Q8—104no—
357C4⋊Q8—108no—
358C4⋊Q8—102no—
359C4⋊Q8C22×D514yes—
360C4×Q8—22no—
361C4×Q8—54no—
362C4×Q8—102no—
363C4×Q8C22×D514yes—
364C4×D4—54no—
365C4×D4—54no—
366C4×D4—108no—
367C4×D4—102no—
368C4×D4—108no—
369C4×D4—102no—
370#117—54no—
371#117—108no—
372#117—102no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—58no—
378C2×C4⋊C4—104no—
379C2×C4⋊C4—108no—
380C2×C4⋊C4—102no—
381C2×C4⋊C4—102no—
382C2×C4⋊C4—101no—
383C2×C4⋊C4—101no—
384C2×C4⋊C4C22×D512yes—
385C2×C4⋊C4C22×D511yescharacteristic
386C2×C22⋊C4—101no—
387C2×C22⋊C4—101no—
388C2×C22⋊C4—101no—
389C2×C42—21no—
390C2×C42—51no—
391C2×C42—51no—
392C2×C42—51no—
393C2×C42—54no—
394C2×C42—54no—
395C2×C42—108no—
396C2×C42—101no—
397C2×C42—101no—
398C2×C42C22×D511yescharacteristic
399#107—58no—
400#107C22×D518yes—
401#106—58no—
402#106—58no—
403C4⋊C8—58no—
404C4⋊C8—54no—
405C4⋊C8C22×D514yes—
406#103—58no—
407#103C22×D518yes—
408#102—58no—
409#102—58no—
410C22×C5C2×C22⋊Q812yes—
411C22×C5C2×AGL(1,ℤ/8)12yes—
412C22×C5C2×#13712yes—
413C22×C5C23×D411yescharacteristic
414C2×D5—28no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—24no—
418C2×D5—48no—
419C2×D5—42no—
420C2×D5—42no—
421C2×D5C2×C22⋊Q814yes—
422C4×C5—24no—
423C4×C5—22no—
424C4×C5—44no—
425C4×C5—42no—
426C4×C5C2×C22⋊Q812yes—
427C4×C5C2×#13714yes—
428C4×C5C23×Q811yescharacteristic
429C4×C5C22×#4111yescharacteristic
430Dic5—22no—
431Dic5—44no—
432Dic5—42no—
433Dic5C2×C22⋊Q814yes—
434Dic5C2×AGL(1,ℤ/8)14yes—
435C24—51no—
436C24—101no—
437#41—516no—
438#41—1016no—
439#41—108no—
440C2×Q8—21no—
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—44no—
444C2×Q8—108no—
445C2×Q8—104no—
446C2×Q8—204no—
447C2×Q8—208no—
448C2×Q8—2032no—
449C2×Q8Q8×D514yescomplemented
450C2×Q8C23×D512yes—
451C2×D4—54no—
452C2×D4—52no—
453C2×D4—104no—
454C2×D4—108no—
455C2×D4—101no—
456C2×D4—102no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—51no—
461C22×C4—51no—
462C22×C4—52no—
463C22×C4—54no—
464C22×C4—54no—
465C22×C4—52no—
466C22×C4—51no—
467C22×C4—54no—
468C22×C4—54no—
469C22×C4—104no—
470C22×C4—104no—
471C22×C4—108no—
472C22×C4—104no—
473C22×C4—108no—
474C22×C4—104no—
475C22×C4—101no—
476C22×C4—102no—
477C22×C4—104no—
478C22×C4—204no—
479C22×C4—208no—
480C22×C4—204no—
481C22×C4D4×D511yescharacteristic
482C22×C4D4×D511yescharacteristic
483C22×C4C23×D511yescharacteristic
484M16—1016no—
485C2×C8—24no—
486C2×C8—54no—
487C2×C8—104no—
488C2×C8C23×D514yes—
489C4⋊C4—24no—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—54no—
494C4⋊C4—52no—
495C4⋊C4—108no—
496C4⋊C4—108no—
497C4⋊C4—104no—
498C4⋊C4—102no—
499C4⋊C4—101no—
500C4⋊C4—104no—
501C4⋊C4C23×D514yes—
502C4⋊C4C23×D512yes—
503C22⋊C4—104no—
504C22⋊C4—104no—
505C22⋊C4—104no—
506C42—24no—
507C42—54no—
508C42—54no—
509C42—52no—
510C42—52no—
511C42—104no—
512C42—104no—
513C42D4×D512yes—
514C42C23×D512yes—
515C2×C5#307914yescomplemented
516C2×C5C22×C22⋊Q811yescharacteristic
517C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
518C2×C5C22×#13711yescharacteristic
519D5—24no—
520D5—44no—
521C23—54no—
522C23—52no—
523C23—102no—
524C23—102no—
525C23—104no—
526C23—102no—
527C23—202no—
528C23—202no—
529C23C2×D4×D511yescharacteristic
530Q8—24no—
531Q8—22no—
532Q8—48no—
533Q8—208no—
534Q8—2016no—
535Q8C2×Q8×D514yescomplemented
536D4—54no—
537D4—1016no—
538D4—104no—
539D4—102no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—54no—
548C2×C4—54no—
549C2×C4—52no—
550C2×C4—52no—
551C2×C4—58no—
552C2×C4—54no—
553C2×C4—54no—
554C2×C4—52no—
555C2×C4—108no—
556C2×C4—1016no—
557C2×C4—102no—
558C2×C4—108no—
559C2×C4—102no—
560C2×C4—104no—
561C2×C4—208no—
562C2×C4—2016no—
563C2×C4—202no—
564C2×C4—204no—
565C2×C4—208no—
566C2×C4#406414yes—
567C2×C4C2×D4×D512yes—
568C2×C4C2×D4×D512yes—
569C2×C4C2×D4×D511yescharacteristic
570C2×C4C2×Q8×D512yes—
571C2×C4D5×#4112yes—
572C2×C4C24×D511yescharacteristic
573C8—24no—
574C8—104no—
575C5C2×#307911yescharacteristic, complemented, Sylow
576C22—54no—
577C22—108no—
578C22—102no—
579C22—102no—
580C22—104no—
581C22—208no—
582C22—202no—
583C22—202no—
584C22D5×C22⋊Q812yes—
585C22C2×#406412yes—
586C22D5×AGL(1,ℤ/8)12yes—
587C22C22×D4×D511yescharacteristic
588C4—24no—
589C4—22no—
590C4—44no—
591C4—42no—
592C4—54no—
593C4—54no—
594C4—102no—
595C4—202no—
596C4—204no—
597C4D5×C22⋊Q812yes—
598C4C2×#406414yes—
599C4C22×Q8×D511yescharacteristic
600C4C2×D5×#4111yescharacteristic
601C2—104no—
602C2—204no—
603C2#1061284014yesdirect product factor
604C2C2×D5×C22⋊Q811yescharacteristic
605C2C22×#406411yescharacteristic
606C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#477C2
socleC23×C5C22×D4
prime radicalC22×#713C22
hypercenterC2×#477D5
hypocenterC5C2×#3079
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×D5×C4⋊Q8C2semidirect
3. C2×C5×#477C2semidirect
4. C2×#65373C2semidirect
5. C2×#65310C2semidirect
6. #10612840C2direct (N × H)
7. C2×#65179C2semidirect
8. C2×#65170C2semidirect
9. C2×#65131C2semidirect
10. C2×#65126C2semidirect
12. C2×#65080C2semidirect
21. D5×C4⋊Q8C22semidirect
37. C5×#477C22semidirect
45. #65373C22semidirect
46. #65310C22semidirect
51. #65179C22semidirect
52. #65170C22semidirect
53. #65131C22semidirect
54. #65126C22semidirect
56. #65080C22semidirect
62. C2×#713Q8semidirect
143. C2×#477D5semidirect
157. C2×C5×Q8C2×Q8semidirect
172. #713C2×Q8semidirect
178. C2×D20C2×Q8semidirect
256. #477C2×D5semidirect
287. C5×Q8C22×Q8semidirect
315. D20C22×Q8semidirect
449. C2×Q8Q8×D5semidirect
515. C2×C5#3079semidirect
535. Q8C2×Q8×D5semidirect
575. C5C2×#3079semidirect
603. C2#10612840direct (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×C4×#7132
C2×C5×#4772
C2×#653732
C2×#653102
#106128402
C2×#651792
C2×#651702
C2×#651312
C2×#651262
C2×#650922
C2×#650802
C2×#30795