Finite Group Databasebeta

← D5×A4×C22⋊C4 #14513986

Subgroups — D5×A4×C22⋊C4 #14513986

Order 1920.

1984 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D5×A4C211yesmaximal, characteristic
2C2×C4×D5×A4C212yesmaximal, complemented
3C5×A4×C22⋊C4C211yesmaximal, characteristic, complemented
4A4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5A4×#685C212yesmaximal, complemented
6C22×D5×C22⋊C4C311yesmaximal, characteristic, complemented, Hall
7C23×C5×A4C2211yescharacteristic
8C22×D5×A4—24no—
9C22×D5×A4C414yescomplemented
10C22×D5×A4C2211yescharacteristic
11C22×D5×A4C2211yescharacteristic
12C2×C4×C5×A4C2212yescomplemented
13C2×A4×Dic5C2212yescomplemented
14C4×D5×A4—24no—
15C3×D5×C22⋊C4—41nomaximal
16C2×A4×C22⋊C4—51nomaximal, Hall
17C25×D5C2×C311yescharacteristic
18C23×C4×D5C2×C312yescomplemented
19C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
20C22×C22⋊Dic5C2×C311yescharacteristic, complemented
21C22×#685C2×C312yescomplemented
22C2×D5×C22⋊C4—31no—
23C2×D5×C22⋊C4—31no—
24C2×D5×C22⋊C4—31no—
25C2×D5×C22⋊C4—32no—
26C2×D5×C22⋊C4—31no—
27C2×D5×C22⋊C4—32no—
28C23×C3×D5—41no—
29C22×C5×A4—22no—
30C22×C5×A4C2×C412yescomplemented
31C22×C5×A4C2311yescharacteristic
32C2×D5×A4—22no—
33C2×D5×A4—28no—
34C2×D5×A4C2×C412yes—
35C2×D5×A4C2×C412yescomplemented
36C2×D5×A4D414yes—
37C2×C3×C4×D5—42no—
38C4×C5×A4—22no—
39A4×Dic5—22no—
40C3×C5×C22⋊C4—41no—
41C3×C22⋊Dic5—41no—
42C3×#685—42no—
43C24×A4—51no—
44C22×C4×A4—52no—
45A4×C22⋊C4—51no—
46A4×C22⋊C4—52no—
47A4×C22⋊C4D511yescharacteristic, direct product factor
48C25×C5C22×C311yescharacteristic
49C24×D5—24no—
50C24×D5—31no—
51C24×D5—31no—
52C24×D5—31no—
53C24×D5—31no—
54C24×D5—34no—
55C24×D5—64no—
56C24×D5C3×C414yescomplemented
57C24×D5C22×C311yescharacteristic
58C24×D5C22×C311yescharacteristic
59C23×C4×C5C22×C312yescomplemented
60C23×Dic5C22×C312yescomplemented
61C22×C4×D5—24no—
62C22×C4×D5—32no—
63C22×C4×D5—32no—
64C22×C4×D5—32no—
65C22×C4×D5—32no—
66C22×C4×D5—64no—
67C2×C5×C22⋊C4—31no—
68C2×C5×C22⋊C4—31no—
69C2×C5×C22⋊C4—32no—
70C2×C22⋊Dic5—31no—
71C2×C22⋊Dic5—31no—
72C2×C22⋊Dic5—32no—
73C2×#685—32no—
74C2×#685—32no—
75C2×#685—32no—
76C2×#685—32no—
77D5×C22⋊C4—32no—
78D5×C22⋊C4—32no—
79D5×C22⋊C4—34no—
80D5×C22⋊C4—34no—
81D5×C22⋊C4—32no—
82D5×C22⋊C4—31no—
83D5×C22⋊C4—32no—
84D5×C22⋊C4—31no—
85D5×C22⋊C4—31no—
86D5×C22⋊C4—32no—
87D5×C22⋊C4A411yescharacteristic, direct product factor
88C23×C22⋊C4—51noSylow
89C23×C3×C5—41no—
90C22×C3×D5—41no—
91C22×C3×D5—44no—
92C22×C3×D5—41no—
93C22×C3×D5—84no—
94C2×C5×A4—22no—
95C2×C5×A4C22×C411yescharacteristic
96C2×C5×A4C2×D412yes—
97D5×A4—22no—
98D5×A4C22⋊C414yesdirect product factor
99C2×C3×C4×C5—42no—
100C2×C3×Dic5—42no—
101C3×C4×D5—84no—
102C23×A4—51no—
103C23×A4—54no—
104C23×A4—51no—
105C23×A4—104no—
106C23×A4C2×D511yescharacteristic
107C2×C4×A4—52no—
108C2×C4×A4—104no—
109C2×C4×A4C2×D512yescomplemented
110C2×C3×C22⋊C4—201no—
111C24×C5—22no—
112C24×C5—31no—
113C24×C5—32no—
114C24×C5—31no—
115C24×C5—62no—
116C24×C5C2×C3×C412yescomplemented
117C24×C5C23×C311yescharacteristic
118C23×D5—22no—
119C23×D5—28no—
120C23×D5—31no—
121C23×D5—31no—
122C23×D5—34no—
123C23×D5—32no—
124C23×D5—34no—
125C23×D5—34no—
126C23×D5—34no—
127C23×D5—32no—
128C23×D5—31no—
129C23×D5—34no—
130C23×D5—34no—
131C23×D5—31no—
132C23×D5—31no—
133C23×D5—31no—
134C23×D5—34no—
135C23×D5—34no—
136C23×D5—34no—
137C23×D5—32no—
138C23×D5—31no—
139C23×D5—64no—
140C23×D5—64no—
141C23×D5—64no—
142C23×D5—64no—
143C23×D5—616no—
144C23×D5—64no—
145C23×D5—64no—
146C23×D5—64no—
147C23×D5—616no—
148C23×D5—64no—
149C23×D5—68no—
150C23×D5—62no—
151C23×D5C2×C3×C412yes—
152C23×D5C2×C3×C412yescomplemented
153C23×D5C3×D414yes—
154C23×D5C2×A411yescharacteristic
155C22×C4×C5—22no—
156C22×C4×C5—32no—
157C22×C4×C5—32no—
158C22×C4×C5—62no—
159C22×Dic5—22no—
160C22×Dic5—32no—
161C22×Dic5—32no—
162C22×Dic5—62no—
163C2×C4×D5—34no—
164C2×C4×D5—32no—
165C2×C4×D5—32no—
166C2×C4×D5—32no—
167C2×C4×D5—64no—
168C2×C4×D5—64no—
169C2×C4×D5—64no—
170C2×C4×D5—64no—
171C2×C4×D5—64no—
172C2×C4×D5—64no—
173C2×C4×D5—64no—
174C2×C4×D5—64no—
175C2×C4×D5C2×A412yescomplemented
176C5×C22⋊C4—32no—
177C5×C22⋊C4—31no—
178C5×C22⋊C4—32no—
179C5×C22⋊C4C2×A411yescharacteristic, complemented
180C22⋊Dic5—32no—
181C22⋊Dic5—31no—
182C22⋊Dic5—32no—
183C22⋊Dic5C2×A411yescharacteristic, complemented
184#685—34no—
185#685—32no—
186#685—32no—
187#685—32no—
188#685C2×A412yescomplemented
189C26—51no—
190C24×C4—52no—
191C22×C22⋊C4—51no—
192C22×C22⋊C4—52no—
193C22×C22⋊C4—151no—
194C22×C22⋊C4—151no—
195C22×C22⋊C4—152no—
196C22×C22⋊C4—151no—
197C22×C22⋊C4—152no—
198C22×C22⋊C4—151no—
199C22×C22⋊C4C3×D511yescharacteristic, complemented
200C22×C3×C5—42no—
201C22×C3×C5—41no—
202C22×C3×C5—82no—
203C2×C3×D5—42no—
204C2×C3×D5—42no—
205C2×C3×D5—44no—
206C2×C3×D5—88no—
207C2×C3×D5—82no—
208C5×A4C2×C22⋊C411yescharacteristic, complemented
209C3×C4×C5—82no—
210C3×Dic5—82no—
211C24×C3—201no—
212C22×A4—22no—
213C22×A4—52no—
214C22×A4—54no—
215C22×A4—52no—
216C22×A4—108no—
217C22×A4—102no—
218C22×A4C4×D512yescomplemented
219C22×A4C22×D511yescharacteristic
220C22×C3×C4—202no—
221C4×A4—22no—
222C4×A4—102no—
223C3×C22⋊C4—41no—
224C3×C22⋊C4—202no—
225C3×C22⋊C4—201no—
226C23×C5—22no—
227C23×C5—32no—
228C23×C5—31no—
229C23×C5—31no—
230C23×C5—32no—
231C23×C5—32no—
232C23×C5—32no—
233C23×C5—32no—
234C23×C5—31no—
235C23×C5—62no—
236C23×C5—62no—
237C23×C5—62no—
238C23×C5—64no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—64no—
242C23×C5C22×C3×C411yescharacteristic
243C23×C5C2×C3×D412yes—
244C23×C5C22×A411yescharacteristic
245C22×D5—24no—
246C22×D5—22no—
247C22×D5—34no—
248C22×D5—32no—
249C22×D5—38no—
250C22×D5—31no—
251C22×D5—32no—
252C22×D5—32no—
253C22×D5—34no—
254C22×D5—34no—
255C22×D5—34no—
256C22×D5—32no—
257C22×D5—34no—
258C22×D5—38no—
259C22×D5—38no—
260C22×D5—32no—
261C22×D5—34no—
262C22×D5—31no—
263C22×D5—34no—
264C22×D5—34no—
265C22×D5—32no—
266C22×D5—32no—
267C22×D5—32no—
268C22×D5—68no—
269C22×D5—64no—
270C22×D5—616no—
271C22×D5—68no—
272C22×D5—62no—
273C22×D5—62no—
274C22×D5—64no—
275C22×D5—68no—
276C22×D5—616no—
277C22×D5—616no—
278C22×D5—68no—
279C22×D5—68no—
280C22×D5—616no—
281C22×D5—68no—
282C22×D5—68no—
283C22×D5—68no—
284C22×D5—68no—
285C22×D5—64no—
286C22×D5—64no—
287C22×D5—64no—
288C22×D5—62no—
289C22×D5—62no—
290C22×D5—62no—
291C22×D5C3×C22⋊C414yescomplemented
292C22×D5C4×A414yescomplemented
293C22×D5C22×A411yescharacteristic
294C22×D5C22×A411yescharacteristic
295C2×C4×C5—32no—
296C2×C4×C5—62no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5—62no—
300C2×C4×C5C22×A412yescomplemented
301C2×Dic5—32no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5C22×A412yescomplemented
307C4×D5—24no—
308C4×D5—64no—
309C4×D5—64no—
310C4×D5—68no—
311C4×D5—64no—
312C25—51no—
313C25—54no—
314C25—51no—
315C25—104no—
316C25—151no—
317C25—151no—
318C25—151no—
319C25—151no—
320C25—154no—
321C25—304no—
322C25C2×C3×D511yescharacteristic
323C23×C4—52no—
324C23×C4—104no—
325C23×C4—152no—
326C23×C4—152no—
327C23×C4—152no—
328C23×C4—152no—
329C23×C4—304no—
330C23×C4C2×C3×D512yescomplemented
331C2×C22⋊C4—31no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—32no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—152no—
337C2×C22⋊C4—152no—
338C2×C22⋊C4—151no—
339C2×C22⋊C4—154no—
340C2×C22⋊C4—152no—
341C2×C22⋊C4—152no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—154no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—151no—
346C2×C22⋊C4—151no—
347C2×C22⋊C4—152no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—151no—
352C2×C3×C5—41no—
353C2×C3×C5—42no—
354C2×C3×C5—82no—
355C3×D5—44no—
356C3×D5—82no—
357C23×C3—41no—
358C23×C3—201no—
359C23×C3—201no—
360C23×C3—204no—
361C23×C3—404no—
362C2×A4—22no—
363C2×A4—54no—
364C2×A4—102no—
365C2×A4C2×C4×D511yescharacteristic
366C2×A4D4×D512yes—
367C2×C3×C4—42no—
368C2×C3×C4—202no—
369C2×C3×C4—404no—
370C22×C5—22no—
371C22×C5—31no—
372C22×C5—32no—
373C22×C5—32no—
374C22×C5—31no—
375C22×C5—31no—
376C22×C5—32no—
377C22×C5—32no—
378C22×C5—32no—
379C22×C5—62no—
380C22×C5—64no—
381C22×C5—62no—
382C22×C5—62no—
383C22×C5—62no—
384C22×C5—64no—
385C22×C5—62no—
386C22×C5C2×C3×C22⋊C411yescharacteristic, complemented
387C22×C5C2×C4×A412yescomplemented
388C22×C5C23×A411yescharacteristic
389C2×D5—22no—
390C2×D5—28no—
391C2×D5—34no—
392C2×D5—38no—
393C2×D5—32no—
394C2×D5—34no—
395C2×D5—38no—
396C2×D5—34no—
397C2×D5—34no—
398C2×D5—34no—
399C2×D5—32no—
400C2×D5—68no—
401C2×D5—62no—
402C2×D5—64no—
403C2×D5—62no—
404C2×D5—68no—
405C2×D5—616no—
406C2×D5—64no—
407C2×D5—62no—
408C2×D5—68no—
409C2×D5—62no—
410C2×D5—62no—
411C2×D5C2×C4×A412yes—
412C2×D5C2×C4×A412yescomplemented
413C2×D5D4×A414yes—
414C4×C5—22no—
415C4×C5—62no—
416Dic5—22no—
417Dic5—62no—
418C24—22no—
419C24—31no—
420C24—32no—
421C24—31no—
422C24—51no—
423C24—52no—
424C24—54no—
425C24—52no—
426C24—62no—
427C24—108no—
428C24—102no—
429C24—151no—
430C24—151no—
431C24—151no—
432C24—151no—
433C24—154no—
434C24—154no—
435C24—151no—
436C24—154no—
437C24—152no—
438C24—152no—
439C24—154no—
440C24—154no—
441C24—154no—
442C24—151no—
443C24—152no—
444C24—154no—
445C24—154no—
446C24—154no—
447C24—151no—
448C24—302no—
449C24—304no—
450C24—304no—
451C24—308no—
452C24—304no—
453C24—304no—
454C24—304no—
455C24—3016no—
456C24—304no—
457C24—304no—
458C24—304no—
459C24—3016no—
460C24C3×C4×D512yescomplemented
461C24C22×C3×D511yescharacteristic
462C22×C4—22no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4—52no—
466C22×C4—62no—
467C22×C4—102no—
468C22×C4—152no—
469C22×C4—152no—
470C22×C4—154no—
471C22×C4—152no—
472C22×C4—152no—
473C22×C4—152no—
474C22×C4—304no—
475C22×C4—304no—
476C22×C4—304no—
477C22×C4—304no—
478C22×C4—304no—
479C22×C4—304no—
480C22×C4—304no—
481C22×C4—304no—
482C22×C4—302no—
483C22⋊C4—32no—
484C22⋊C4—31no—
485C22⋊C4—32no—
486C22⋊C4—51no—
487C22⋊C4—52no—
488C22⋊C4—152no—
489C22⋊C4—152no—
490C22⋊C4—154no—
491C22⋊C4—152no—
492C22⋊C4—152no—
493C22⋊C4—151no—
494C22⋊C4—152no—
495C22⋊C4D5×A411yescharacteristic, direct product factor
496C3×C5—41noHall
497C22×C3—42no—
498C22×C3—41no—
499C22×C3—82no—
500C22×C3—204no—
501C22×C3—202no—
502C22×C3—202no—
503C22×C3—402no—
504C22×C3—408no—
505A4D5×C22⋊C411yescharacteristic, direct product factor
506C3×C4—82no—
507C3×C4—402no—
508C2×C5—22no—
509C2×C5—32no—
510C2×C5—31no—
511C2×C5—31no—
512C2×C5—62no—
513C2×C5C22×C4×A411yescharacteristic
514C2×C5C2×D4×A412yes—
515D5—22no—
516D5—34no—
517D5—62no—
518D5A4×C22⋊C414yesdirect product factor
519C23—22no—
520C23—32no—
521C23—31no—
522C23—31no—
523C23—32no—
524C23—32no—
525C23—32no—
526C23—32no—
527C23—31no—
528C23—51no—
529C23—54no—
530C23—51no—
531C23—54no—
532C23—62no—
533C23—62no—
534C23—62no—
535C23—64no—
536C23—62no—
537C23—62no—
538C23—64no—
539C23—104no—
540C23—102no—
541C23—154no—
542C23—154no—
543C23—152no—
544C23—152no—
545C23—152no—
546C23—152no—
547C23—154no—
548C23—154no—
549C23—154no—
550C23—152no—
551C23—154no—
552C23—158no—
553C23—154no—
554C23—152no—
555C23—158no—
556C23—152no—
557C23—158no—
558C23—152no—
559C23—151no—
560C23—154no—
561C23—151no—
562C23—304no—
563C23—302no—
564C23—302no—
565C23—302no—
566C23—304no—
567C23—302no—
568C23—302no—
569C23—304no—
570C23—304no—
571C23—308no—
572C23—308no—
573C23—3016no—
574C23—304no—
575C23—308no—
576C23—308no—
577C23—308no—
578C23—308no—
579C23—308no—
580C23—3016no—
581C23—308no—
582C23—3016no—
583C23—3016no—
584C23—308no—
585C23C2×C3×C4×D511yescharacteristic
586C23C3×D4×D512yes—
587C23C2×D5×A411yescharacteristic
588C2×C4—32no—
589C2×C4—52no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—104no—
595C2×C4—152no—
596C2×C4—304no—
597C2×C4—304no—
598C2×C4—304no—
599C2×C4—308no—
600C2×C4—302no—
601C2×C4—302no—
602C2×C4—302no—
603C2×C4—302no—
604C2×C4C2×D5×A412yescomplemented
605C2×C3—41no—
606C2×C3—42no—
607C2×C3—82no—
608C2×C3—204no—
609C2×C3—402no—
610C5C2×A4×C22⋊C411yescharacteristic, complemented, Sylow
611C22—22no—
612C22—31no—
613C22—32no—
614C22—32no—
615C22—31no—
616C22—31no—
617C22—32no—
618C22—32no—
619C22—32no—
620C22—52no—
621C22—54no—
622C22—52no—
623C22—62no—
624C22—62no—
625C22—64no—
626C22—62no—
627C22—62no—
628C22—64no—
629C22—62no—
630C22—108no—
631C22—102no—
632C22—154no—
633C22—158no—
634C22—154no—
635C22—154no—
636C22—158no—
637C22—154no—
638C22—152no—
639C22—154no—
640C22—152no—
641C22—308no—
642C22—302no—
643C22—302no—
644C22—304no—
645C22—302no—
646C22—302no—
647C22—304no—
648C22—308no—
649C22—308no—
650C22—3016no—
651C22—302no—
652C22C3×D5×C22⋊C411yescharacteristic, complemented
653C22C4×D5×A412yescomplemented
654C22C22×D5×A411yescharacteristic
655C4—22no—
656C4—62no—
657C4—102no—
658C4—302no—
659C3—41noSylow
660C2—22no—
661C2—31no—
662C2—31no—
663C2—32no—
664C2—54no—
665C2—62no—
666C2—102no—
667C2—154no—
668C2—302no—
669C2C2×C4×D5×A411yescharacteristic
670C2D4×D5×A412yes—
subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C22⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC23×D5×A4C2
hypercenterC22⋊C4D5×A4
hypocenterC22×C5C2×C3×C22⋊C4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D5×A4C2semidirect
3. C5×A4×C22⋊C4C2semidirect
4. A4×C22⋊Dic5C2semidirect
5. A4×#685C2semidirect
6. C22×D5×C22⋊C4C3semidirect
9. C22×D5×A4C4semidirect
12. C2×C4×C5×A4C22semidirect
13. C2×A4×Dic5C22semidirect
18. C23×C4×D5C2×C3semidirect
19. C22×C5×C22⋊C4C2×C3semidirect
20. C22×C22⋊Dic5C2×C3semidirect
21. C22×#685C2×C3semidirect
30. C22×C5×A4C2×C4semidirect
35. C2×D5×A4C2×C4semidirect
47. A4×C22⋊C4D5direct (N × H)
56. C24×D5C3×C4semidirect
59. C23×C4×C5C22×C3semidirect
60. C23×Dic5C22×C3semidirect
87. D5×C22⋊C4A4direct (N × H)
98. D5×A4C22⋊C4direct (N × H)
109. C2×C4×A4C2×D5semidirect
116. C24×C5C2×C3×C4semidirect
152. C23×D5C2×C3×C4semidirect
175. C2×C4×D5C2×A4semidirect
179. C5×C22⋊C4C2×A4semidirect
183. C22⋊Dic5C2×A4semidirect
188. #685C2×A4semidirect
199. C22×C22⋊C4C3×D5semidirect
208. C5×A4C2×C22⋊C4semidirect
218. C22×A4C4×D5semidirect
291. C22×D5C3×C22⋊C4semidirect
292. C22×D5C4×A4semidirect
300. C2×C4×C5C22×A4semidirect
306. C2×Dic5C22×A4semidirect
330. C23×C4C2×C3×D5semidirect
386. C22×C5C2×C3×C22⋊C4semidirect
387. C22×C5C2×C4×A4semidirect
412. C2×D5C2×C4×A4semidirect
460. C24C3×C4×D5semidirect
495. C22⋊C4D5×A4direct (N × H)
505. A4D5×C22⋊C4direct (N × H)
518. D5A4×C22⋊C4direct (N × H)
604. C2×C4C2×D5×A4semidirect
610. C5C2×A4×C22⋊C4semidirect
652. C22C3×D5×C22⋊C4semidirect
653. C22C4×D5×A4semidirect

Maximal subgroups

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

subgroupindex
C23×D5×A42
C2×C4×D5×A42
C5×A4×C22⋊C42
A4×C22⋊Dic52
A4×#6852
C22×D5×C22⋊C43
C3×D5×C22⋊C44
C2×A4×C22⋊C45