Finite Group Databasebeta

← C2×D5⋊#328 #13030184

Subgroups — C2×D5⋊#328 #13030184

Order 1280.

1846 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊Q8C211yesmaximal, characteristic
2C22×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic
3C2×D5⋊(C22⋊C8)C211yesmaximal, characteristic
4C2×#64926C212yesmaximal, complemented
5D5⋊#328C218yesmaximal, direct product factor
6C2×#64869C212yesmaximal, complemented
7C24×AGL(1,𝔽5)—21no—
8C22×Q8×D5C411yescharacteristic, complemented
9C23×C4×D5C2211yescharacteristic
10C22×D5⋊C8—21no—
11C2×C5×C22⋊Q8C411yescharacteristic, complemented
12C2×#4092C2211yescharacteristic
13C2×#4070C411yescharacteristic, complemented
14D5×C22⋊Q8—22no—
15D5×C22⋊Q8—22no—
16D5×C22⋊Q8C414yescomplemented
17D5×C22⋊Q8C2214yes—
18C2×#4043C2211yescharacteristic
19C2×#4042—21no—
20C2×D5×C4⋊C4—21no—
21C2×D5×C4⋊C4C411yescharacteristic, complemented
22C2×D5×C22⋊C4—21no—
23C2×#4024—21no—
24C2×C22⋊#170—21no—
25C2×(C2×AGL(1,𝔽5))⋊C4—21no—
26C2×(C2×AGL(1,𝔽5))⋊C4—22no—
27C2×(C2×AGL(1,𝔽5))⋊C4C2212yes—
28C2×(C2×AGL(1,𝔽5))⋊C4C2214yes—
29D5⋊(C22⋊C8)—22no—
30D5⋊(C22⋊C8)C2214yes—
31C2×#4003C2212yes—
32#64926C2218yescomplemented
33#64869C2218yescomplemented
34C22×#328—51nomaximal, Sylow
35C24×D5D411yescharacteristic
36C23×AGL(1,𝔽5)—28no—
37C23×AGL(1,𝔽5)—24no—
38C23×AGL(1,𝔽5)—22no—
39C23×AGL(1,𝔽5)—44no—
40C23×AGL(1,𝔽5)—44no—
41C22×C5×Q8C2×C411yescharacteristic, complemented
42C23×C4×C5C2×C411yescharacteristic
43C23×Dic5D411yescharacteristic
44C2×Q8×D5—22no—
45C2×Q8×D5—44no—
46C2×Q8×D5C2×C414yescomplemented
47C22×C4×D5—21no—
48C22×C4×D5—21no—
49C22×C4×D5—44no—
50C22×C4×D5C2×C411yescharacteristic
51C22×C4×D5C2×C412yes—
52C22×C4×D5D411yescharacteristic
53C22×C4×D5D411yescharacteristic
54C22×C4×D5D412yes—
55C22×C4×D5D412yes—
56C22×C4×D5C2311yescharacteristic
57C22×C4×D5C2312yes—
58C22×Dic10—21no—
59C22×Dic10C2×C411yescharacteristic, complemented
60C22×#170—22no—
61C2×D5⋊C8—24no—
62C2×D5⋊C8—44no—
63C5×C22⋊Q8—22no—
64C5×C22⋊Q8C2×C414yescomplemented
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
67C2×C5×C22⋊C4—21no—
68C2×C22⋊Dic5—21no—
69#4092—21no—
70#4092—21no—
71#4092C2×C412yescomplemented
72#4092C2312yes—
73C2×#685—21no—
74C2×#685—21no—
75C2×C4⋊Dic5—21no—
76C2×C4⋊Dic5C2×C411yescharacteristic, complemented
77#4070—22no—
78#4070C2×C414yescomplemented
79C2×#683—21no—
80C2×#683—21no—
81C2×#683—21no—
82#4043—21no—
83#4043—21no—
84#4043C2×C412yescomplemented
85#4043C2312yes—
86#4042—24no—
87#4042—24no—
88D5×C4⋊C4—24no—
89D5×C4⋊C4—22no—
90D5×C4⋊C4—24no—
91D5×C4⋊C4C2×C414yescomplemented
92D5×C22⋊C4—24no—
93D5×C22⋊C4—24no—
94#4024—24no—
95#4024—24no—
96C22⋊#170—24no—
97(C2×AGL(1,𝔽5))⋊C4—24no—
98(C2×AGL(1,𝔽5))⋊C4—22no—
99(C2×AGL(1,𝔽5))⋊C4C2314yes—
100#4003—22no—
101#4003C2314yes—
102C22×C22⋊Q8—51no—
103C22×C22⋊C8—51no—
104C22×#95—51no—
105C2×#328—52no—
106C2×#328—58no—
107C2×#328—52no—
108C24×C5C22⋊C411yescharacteristic
109C23×D5—24no—
110C23×D5—24no—
111C23×D5C22⋊C412yes—
112C23×D5C22⋊C411yescharacteristic
113C23×D5SD1614yes—
114C23×D5Q1614yes—
115C23×D5C2×D412yes—
116C23×D5C2×D411yescharacteristic
117C22×AGL(1,𝔽5)—28no—
118C22×AGL(1,𝔽5)—216no—
119C22×AGL(1,𝔽5)—24no—
120C22×AGL(1,𝔽5)—44no—
121C22×AGL(1,𝔽5)—432no—
122C22×AGL(1,𝔽5)—48no—
123C22×AGL(1,𝔽5)—44no—
124C22×AGL(1,𝔽5)—48no—
125C2×C5×Q8—21no—
126C2×C5×Q8—42no—
127C2×C5×Q8C22×C412yescomplemented
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—42no—
131C22×C4×C5C22⋊C411yescharacteristic
132C22×C4×C5C22⋊C412yes—
133C22×C4×C5C22×C411yescharacteristic
134C22×C4×C5C22×C412yes—
135C22×Dic5—21no—
136C22×Dic5—21no—
137C22×Dic5—42no—
138C22×Dic5C22⋊C411yescharacteristic
139C22×Dic5C22⋊C412yes—
140C22×Dic5C2×D411yescharacteristic
141C22×Dic5C2×D412yes—
142Q8×D5—48no—
143Q8×D5—48no—
144C2×C4×D5—24no—
145C2×C4×D5—24no—
146C2×C4×D5—24no—
147C2×C4×D5—24no—
148C2×C4×D5—44no—
149C2×C4×D5—44no—
150C2×C4×D5—44no—
151C2×C4×D5—44no—
152C2×C4×D5—42no—
153C2×C4×D5—42no—
154C2×C4×D5—44no—
155C2×C4×D5—44no—
156C2×C4×D5C22⋊C412yes—
157C2×C4×D5C22⋊C412yes—
158C2×C4×D5C22⋊C412yes—
159C2×C4×D5C22×C412yes—
160C2×C4×D5C22×C411yescharacteristic
161C2×C4×D5C2×D412yes—
162C2×C4×D5C2×D412yes—
163C2×C4×D5C2×D411yescharacteristic
164C2×C4×D5C2×D411yescharacteristic
165C2×C4×D5C2411yescharacteristic
166C2×Dic10—21no—
167C2×Dic10—24no—
168C2×Dic10—44no—
169C2×Dic10—42no—
170C2×Dic10C22×C412yescomplemented
171C2×#170—24no—
172C2×#170—44no—
173D5⋊C8—48no—
174C5×C4⋊C4—24no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4C22×C412yescomplemented
177C5×C22⋊C4—24no—
178C22⋊Dic5—24no—
179#685—22no—
180#685—22no—
181#685—22no—
182#685—22no—
183C4⋊Dic5—21no—
184C4⋊Dic5—22no—
185C4⋊Dic5—22no—
186C4⋊Dic5C22×C412yescomplemented
187#683—24no—
188#683—22no—
189#683—24no—
190#683—22no—
191C23×Q8—51no—
192C24×C4—51no—
193C24×C4—101no—
194C23×C8—101no—
195C2×C22⋊Q8—51no—
196C2×C22⋊Q8—51no—
197C2×C22⋊Q8—54no—
198C2×C22⋊Q8—54no—
199C2×C22⋊Q8—51no—
200C2×C22⋊Q8—101no—
201C2×C22⋊Q8—101no—
202C2×C22⋊Q8—102no—
203C2×C22⋊Q8—102no—
204C2×C22⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
205C22×C4⋊C4—51no—
206C22×C4⋊C4—101no—
207C22×C22⋊C4—101no—
208C2×C22⋊C8—52no—
209C2×C22⋊C8—54no—
210C2×C22⋊C8—101no—
211C2×C22⋊C8—102no—
212C2×#95—52no—
213C2×#95—54no—
214C2×#95—101no—
215C2×#95—102no—
216#328—58no—
217#328—58no—
218C23×C5—22no—
219C23×C5—22no—
220C23×C5#10314yes—
221C23×C5C2×C22⋊C412yes—
222C23×C5C2×C22⋊C411yescharacteristic
223C22×D5—22no—
224C22×D5—22no—
225C22×D5—216no—
226C22×D5—216no—
227C22×D5—24no—
228C22×D5—24no—
229C22×D5—24no—
230C22×D5—24no—
231C22×D5#9914yes—
232C22×D5#10318yes—
233C22×D5#10314yes—
234C22×D5#10414yes—
235C22×D5C2×C22⋊C411yescharacteristic
236C22×D5C2×C22⋊C412yes—
237C22×D5C2×SD1612yes—
238C22×D5C2×SD1614yes—
239C22×D5C2×Q1612yes—
240C22×D5C2×Q1614yes—
241C22×D5C22×D411yescharacteristic
242C2×AGL(1,𝔽5)—28no—
243C2×AGL(1,𝔽5)—44no—
244C2×AGL(1,𝔽5)—416no—
245C2×AGL(1,𝔽5)—432no—
246C2×AGL(1,𝔽5)—44no—
247C5×Q8—42no—
248C5×Q8—42no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5C2×C22⋊C412yes—
258C2×C4×C5C2×C22⋊C411yescharacteristic
259C2×C4×C5C23×C411yescharacteristic
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5C2×C22⋊C411yescharacteristic
269C2×Dic5C2×C22⋊C412yes—
270C2×Dic5C22×D411yescharacteristic
271C4×D5—24no—
272C4×D5—24no—
273C4×D5—24no—
274C4×D5—24no—
275C4×D5—42no—
276C4×D5—41no—
277C4×D5—41no—
278C4×D5—42no—
279C4×D5—41no—
280C4×D5—41no—
281C4×D5—48no—
282C4×D5—48no—
283Dic10—48no—
284Dic10—42no—
285Dic10—42no—
286#170—44no—
287C25—51no—
288C22×Q8—54no—
289C22×Q8—51no—
290C22×Q8—101no—
291C22×Q8—102no—
292C22×Q8—204no—
293C22×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
294C23×C4—51no—
295C23×C4—51no—
296C23×C4—51no—
297C23×C4—51no—
298C23×C4—52no—
299C23×C4—52no—
300C23×C4—52no—
301C23×C4—51no—
302C23×C4—52no—
303C23×C4—101no—
304C23×C4—101no—
305C23×C4—104no—
306C23×C4—102no—
307C23×C4—108no—
308C23×C4—204no—
309C23×C4—204no—
310C23×C4—204no—
311C23×C4C2×AGL(1,𝔽5)11yescharacteristic
312C22×C8—104no—
313C22×C8—102no—
314C22×C8—204no—
315C22⋊Q8—22no—
316C22⋊Q8—52no—
317C22⋊Q8—52no—
318C22⋊Q8—54no—
319C22⋊Q8—52no—
320C22⋊Q8—52no—
321C22⋊Q8—104no—
322C22⋊Q8—104no—
323C22⋊Q8—104no—
324C22⋊Q8—104no—
325C22⋊Q8—101no—
326C22⋊Q8—101no—
327C22⋊Q8—101no—
328C22⋊Q8—101no—
329C22⋊Q8—102no—
330C22⋊Q8C2×AGL(1,𝔽5)14yescomplemented
331C2×C4⋊C4—21no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—54no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—104no—
336C2×C4⋊C4—104no—
337C2×C4⋊C4—101no—
338C2×C4⋊C4—101no—
339C2×C4⋊C4—101no—
340C2×C4⋊C4—101no—
341C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
342C2×C22⋊C4—21no—
343C2×C22⋊C4—104no—
344C2×C22⋊C4—104no—
345C2×C22⋊C4—101no—
346C2×C22⋊C4—101no—
347C2×C22⋊C4—101no—
348C22⋊C8—54no—
349C22⋊C8—102no—
350C22⋊C8—104no—
351#95—54no—
352#95—102no—
353#95—104no—
354C22×C5—22no—
355C22×C5—22no—
356C22×C5—28no—
357C22×C5C2×#9912yes—
358C22×C5C2×#10314yes—
359C22×C5C2×#10312yes—
360C22×C5C2×#10412yes—
361C22×C5C22×C22⋊C411yescharacteristic
362C2×D5—21no—
363C2×D5—21no—
364C2×D5—21no—
365C2×D5—21no—
366C2×D5—24no—
367C2×D5—24no—
368C2×D5—28no—
369C2×D5—216no—
370C2×D5—28no—
371C2×D5#328116yescomplemented
372C2×D5C2×#9914yes—
373C2×D5C2×#10312yes—
374C2×D5C2×#10314yes—
375C2×D5C2×#10414yes—
376C2×D5C22×SD1611yescharacteristic
377C2×D5C22×Q1611yescharacteristic
378AGL(1,𝔽5)—48no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—22no—
382C4×C5—42no—
383C4×C5—42no—
384Dic5—21no—
385Dic5—22no—
386Dic5—21no—
387Dic5—42no—
388Dic5—42no—
389C24—51no—
390C24—52no—
391C24—52no—
392C24—51no—
393C24—54no—
394C24—54no—
395C24—104no—
396C24—104no—
397C24C22⋊AGL(1,𝔽5)11yescharacteristic
398C2×Q8—21no—
399C2×Q8—42no—
400C2×Q8—52no—
401C2×Q8—104no—
402C2×Q8—101no—
403C2×Q8—202no—
404C2×Q8—204no—
405C2×Q8—208no—
406C2×Q8—208no—
407C2×Q8C22×AGL(1,𝔽5)12yescomplemented
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—42no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—52no—
416C22×C4—52no—
417C22×C4—52no—
418C22×C4—52no—
419C22×C4—51no—
420C22×C4—52no—
421C22×C4—51no—
422C22×C4—52no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—104no—
426C22×C4—104no—
427C22×C4—104no—
428C22×C4—104no—
429C22×C4—104no—
430C22×C4—1016no—
431C22×C4—108no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—202no—
435C22×C4—202no—
436C22×C4—204no—
437C22×C4—204no—
438C22×C4—204no—
439C22×C4—204no—
440C22×C4—204no—
441C22×C4—204no—
442C22×C4—202no—
443C22×C4—208no—
444C22×C4—204no—
445C22×C4—208no—
446C22×C4—2032no—
447C22×C4—204no—
448C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
449C22×C4C22⋊AGL(1,𝔽5)12yes—
450C22×C4C22×AGL(1,𝔽5)11yescharacteristic
451C22×C4C22×AGL(1,𝔽5)12yes—
452C2×C8—104no—
453C2×C8—208no—
454C2×C8—204no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—52no—
458C4⋊C4—104no—
459C4⋊C4—102no—
460C4⋊C4—102no—
461C4⋊C4—102no—
462C4⋊C4—102no—
463C4⋊C4—101no—
464C4⋊C4—104no—
465C4⋊C4C22×AGL(1,𝔽5)12yescomplemented
466C22⋊C4—24no—
467C22⋊C4—102no—
468C22⋊C4—102no—
469C22⋊C4—102no—
470C22⋊C4—102no—
471C22⋊C4—104no—
472C2×C5—24no—
473C2×C5C2×#32814yescomplemented
474C2×C5C22×#9911yescharacteristic
475C2×C5C22×#10311yescharacteristic
476C2×C5C22×#10411yescharacteristic
477D5—21no—
478D5—21no—
479D5—22no—
480D5C2×#32818yescomplemented
481C23—22no—
482C23—22no—
483C23—54no—
484C23—52no—
485C23—54no—
486C23—54no—
487C23—51no—
488C23—51no—
489C23—54no—
490C23—52no—
491C23—58no—
492C23—54no—
493C23—52no—
494C23—104no—
495C23—104no—
496C23—104no—
497C23—1016no—
498C23—104no—
499C23—1016no—
500C23—102no—
501C23—102no—
502C23#400914yes—
503C23C2×C22⋊AGL(1,𝔽5)12yes—
504C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
505Q8—42no—
506Q8—42no—
507Q8—202no—
508Q8—202no—
509Q8—208no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—51no—
519C2×C4—51no—
520C2×C4—52no—
521C2×C4—104no—
522C2×C4—104no—
523C2×C4—104no—
524C2×C4—104no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—108no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—202no—
533C2×C4—202no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—208no—
537C2×C4—208no—
538C2×C4—202no—
539C2×C4—202no—
540C2×C4—204no—
541C2×C4—2032no—
542C2×C4—204no—
543C2×C4—2016no—
544C2×C4—202no—
545C2×C4—202no—
546C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
547C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
548C2×C4C23×AGL(1,𝔽5)11yescharacteristic
549C8—204no—
550C5C22×#32811yescharacteristic, complemented, Sylow
551C22—22no—
552C22—22no—
553C22—28no—
554C22—54no—
555C22—54no—
556C22—54no—
557C22—516no—
558C22—51no—
559C22—51no—
560C22—52no—
561C22—108no—
562C22—1016no—
563C22—108no—
564C22—101no—
565C22—101no—
566C22—101no—
567C22—101no—
568C22—104no—
569C22—104no—
570C22D5⋊#9912yes—
571C22C2×#400914yes—
572C22C2×#400912yes—
573C22D5⋊#10412yes—
574C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
575C4—21no—
576C4—22no—
577C4—21no—
578C4—42no—
579C4—42no—
580C4—101no—
581C4—102no—
582C4—101no—
583C4—208no—
584C4—202no—
585C4—202no—
586C2—24no—
587C2—58no—
588C2—101no—
589C2—101no—
590C2—102no—
591C2D5⋊#32814yesdirect product factor
592C2C2×D5⋊#9911yescharacteristic
593C2C22×#400911yescharacteristic
594C2C2×D5⋊#10411yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C22⋊Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC24×D5D4
cosocleC2×C4×D5C24
hypercenterC2×C22⋊Q8AGL(1,𝔽5)
hypocenterC5C22×#328
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. C2×#64926C2semidirect
5. D5⋊#328C2direct (N × H)
6. C2×#64869C2semidirect
8. C22×Q8×D5C4semidirect
11. C2×C5×C22⋊Q8C4semidirect
13. C2×#4070C4semidirect
16. D5×C22⋊Q8C4semidirect
21. C2×D5×C4⋊C4C4semidirect
32. #64926C22semidirect
33. #64869C22semidirect
41. C22×C5×Q8C2×C4semidirect
46. C2×Q8×D5C2×C4semidirect
59. C22×Dic10C2×C4semidirect
64. C5×C22⋊Q8C2×C4semidirect
66. C2×C5×C4⋊C4C2×C4semidirect
71. #4092C2×C4semidirect
76. C2×C4⋊Dic5C2×C4semidirect
78. #4070C2×C4semidirect
84. #4043C2×C4semidirect
91. D5×C4⋊C4C2×C4semidirect
127. C2×C5×Q8C22×C4semidirect
170. C2×Dic10C22×C4semidirect
176. C5×C4⋊C4C22×C4semidirect
186. C4⋊Dic5C22×C4semidirect
204. C2×C22⋊Q8AGL(1,𝔽5)semidirect
293. C22×Q8C2×AGL(1,𝔽5)semidirect
330. C22⋊Q8C2×AGL(1,𝔽5)semidirect
341. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
371. C2×D5#328semidirect
407. C2×Q8C22×AGL(1,𝔽5)semidirect
465. C4⋊C4C22×AGL(1,𝔽5)semidirect
473. C2×C5C2×#328semidirect
480. D5C2×#328semidirect
550. C5C22×#328semidirect
591. C2D5⋊#328direct (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×(C2×AGL(1,𝔽5))⋊C42
C2×D5⋊(C22⋊C8)2
C2×#649262
D5⋊#3282
C2×#648692
C22×#3285