Finite Group Databasebeta

← D5×A4×C4⋊C4 #14513997

Subgroups — D5×A4×C4⋊C4 #14513997

Order 1920.

1136 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1136 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
1C2×C4×D5×A4C212yesmaximal
2C2×C4×D5×A4C211yesmaximal, characteristic
3C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4A4×C4⋊Dic5C211yesmaximal, characteristic, complemented
5A4×#683C212yesmaximal, complemented
6C22×D5×C4⋊C4C311yesmaximal, characteristic, complemented, Hall
7C22×D5×A4C2211yescharacteristic
8C2×C4×C5×A4C2212yes—
9C2×C4×C5×A4C2211yescharacteristic
10C2×A4×Dic5C2212yes—
11C2×A4×Dic5C2211yescharacteristic
12C4×D5×A4—24no—
13C4×D5×A4C414yescomplemented
14C3×D5×C4⋊C4—41nomaximal
15C2×A4×C4⋊C4—51nomaximal, Hall
16C23×C4×D5C2×C312yes—
17C23×C4×D5C2×C311yescharacteristic
18C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
19C22×C4⋊Dic5C2×C311yescharacteristic, complemented
20C22×#683C2×C312yescomplemented
21C2×D5×C4⋊C4—31no—
22C2×D5×C4⋊C4—31no—
23C2×D5×C4⋊C4—31no—
24C2×D5×C4⋊C4—32no—
25C2×D5×C4⋊C4—31no—
26C2×D5×C4⋊C4—32no—
27C22×C5×A4C2311yescharacteristic
28C2×D5×A4C2×C412yes—
29C2×D5×A4D412yes—
30C2×D5×A4Q812yes—
31C2×C3×C4×D5—41no—
32C2×C3×C4×D5—42no—
33C4×C5×A4—22no—
34C4×C5×A4C2×C412yescomplemented
35A4×Dic5—22no—
36A4×Dic5C2×C412yescomplemented
37C3×C5×C4⋊C4—41no—
38C3×C4⋊Dic5—41no—
39C3×#683—42no—
40C22×C4×A4—51no—
41C22×C4×A4—52no—
42A4×C4⋊C4—52no—
43A4×C4⋊C4—51no—
44A4×C4⋊C4D511yescharacteristic, direct product factor
45C24×D5C22×C311yescharacteristic
46C23×C4×C5C22×C312yes—
47C23×C4×C5C22×C311yescharacteristic
48C23×Dic5C22×C312yes—
49C23×Dic5C22×C311yescharacteristic
50C22×C4×D5—24no—
51C22×C4×D5—31no—
52C22×C4×D5—31no—
53C22×C4×D5—31no—
54C22×C4×D5—31no—
55C22×C4×D5—34no—
56C22×C4×D5—32no—
57C22×C4×D5—32no—
58C22×C4×D5—32no—
59C22×C4×D5—32no—
60C22×C4×D5—64no—
61C22×C4×D5C3×C414yescomplemented
62C2×C5×C4⋊C4—31no—
63C2×C5×C4⋊C4—31no—
64C2×C5×C4⋊C4—32no—
65C2×C4⋊Dic5—31no—
66C2×C4⋊Dic5—31no—
67C2×C4⋊Dic5—32no—
68C2×#683—32no—
69C2×#683—32no—
70C2×#683—32no—
71C2×#683—32no—
72D5×C4⋊C4—32no—
73D5×C4⋊C4—32no—
74D5×C4⋊C4—34no—
75D5×C4⋊C4—34no—
76D5×C4⋊C4—32no—
77D5×C4⋊C4—32no—
78D5×C4⋊C4—31no—
79D5×C4⋊C4—31no—
80D5×C4⋊C4—31no—
81D5×C4⋊C4—32no—
82D5×C4⋊C4A411yescharacteristic, direct product factor
83C23×C4⋊C4—51noSylow
84C22×C3×D5—41no—
85C2×C5×A4C22×C411yescharacteristic
86C2×C5×A4C2×D411yescharacteristic
87C2×C5×A4C2×Q811yescharacteristic
88D5×A4C4⋊C414yesdirect product factor
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—42no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5—42no—
93C3×C4×D5—44no—
94C3×C4×D5—84no—
95C23×A4—51no—
96C2×C4×A4—51no—
97C2×C4×A4—54no—
98C2×C4×A4—52no—
99C2×C4×A4—104no—
100C2×C4×A4C2×D512yes—
101C2×C4×A4C2×D511yescharacteristic
102C2×C3×C4⋊C4—201no—
103C24×C5C23×C311yescharacteristic
104C23×D5—31no—
105C23×D5—31no—
106C23×D5—32no—
107C23×D5—32no—
108C23×D5—32no—
109C23×D5C2×C3×C412yes—
110C23×D5C3×D412yes—
111C23×D5C3×Q812yes—
112C22×C4×C5—22no—
113C22×C4×C5—31no—
114C22×C4×C5—31no—
115C22×C4×C5—32no—
116C22×C4×C5—32no—
117C22×C4×C5—32no—
118C22×C4×C5—62no—
119C22×C4×C5C2×C3×C412yescomplemented
120C22×Dic5—22no—
121C22×Dic5—31no—
122C22×Dic5—32no—
123C22×Dic5—31no—
124C22×Dic5—32no—
125C22×Dic5—32no—
126C22×Dic5—62no—
127C22×Dic5C2×C3×C412yescomplemented
128C2×C4×D5—34no—
129C2×C4×D5—34no—
130C2×C4×D5—34no—
131C2×C4×D5—32no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—34no—
136C2×C4×D5—34no—
137C2×C4×D5—34no—
138C2×C4×D5—34no—
139C2×C4×D5—34no—
140C2×C4×D5—34no—
141C2×C4×D5—32no—
142C2×C4×D5—32no—
143C2×C4×D5—32no—
144C2×C4×D5—64no—
145C2×C4×D5—64no—
146C2×C4×D5—64no—
147C2×C4×D5—64no—
148C2×C4×D5—64no—
149C2×C4×D5—64no—
150C2×C4×D5—64no—
151C2×C4×D5—64no—
152C2×C4×D5C2×A412yes—
153C2×C4×D5C2×A411yescharacteristic
154C5×C4⋊C4—32no—
155C5×C4⋊C4—32no—
156C5×C4⋊C4—31no—
157C5×C4⋊C4C2×A411yescharacteristic, complemented
158C4⋊Dic5—32no—
159C4⋊Dic5—31no—
160C4⋊Dic5—32no—
161C4⋊Dic5C2×A411yescharacteristic, complemented
162#683—34no—
163#683—32no—
164#683—32no—
165#683—32no—
166#683C2×A412yescomplemented
167C24×C4—51no—
168C24×C4—52no—
169C22×C4⋊C4—52no—
170C22×C4⋊C4—51no—
171C22×C4⋊C4—151no—
172C22×C4⋊C4—151no—
173C22×C4⋊C4—152no—
174C22×C4⋊C4—151no—
175C22×C4⋊C4—151no—
176C22×C4⋊C4—152no—
177C22×C4⋊C4C3×D511yescharacteristic, complemented
178C22×C3×C5—41no—
179C2×C3×D5—42no—
180C2×C3×D5—42no—
181C2×C3×D5—42no—
182C5×A4C2×C4⋊C411yescharacteristic, complemented
183C3×C4×C5—42no—
184C3×C4×C5—82no—
185C3×Dic5—42no—
186C3×Dic5—82no—
187C22×A4—52no—
188C22×A4—52no—
189C22×A4—52no—
190C22×A4C22×D511yescharacteristic
191C22×C3×C4—201no—
192C22×C3×C4—202no—
193C4×A4—22no—
194C4×A4—52no—
195C4×A4—102no—
196C4×A4C4×D512yescomplemented
197C3×C4⋊C4—41no—
198C3×C4⋊C4—202no—
199C3×C4⋊C4—201no—
200C23×C5—31no—
201C23×C5—31no—
202C23×C5—31no—
203C23×C5—31no—
204C23×C5C22×C3×C411yescharacteristic
205C23×C5C2×C3×D411yescharacteristic
206C23×C5C2×C3×Q811yescharacteristic
207C22×D5—32no—
208C22×D5—32no—
209C22×D5—32no—
210C22×D5—38no—
211C22×D5—31no—
212C22×D5—32no—
213C22×D5—32no—
214C22×D5—32no—
215C22×D5—32no—
216C22×D5—32no—
217C22×D5—32no—
218C22×D5—32no—
219C22×D5—32no—
220C22×D5—34no—
221C22×D5—34no—
222C22×D5—32no—
223C22×D5—34no—
224C22×D5C3×C4⋊C414yescomplemented
225C22×D5C22×A411yescharacteristic
226C2×C4×C5—32no—
227C2×C4×C5—31no—
228C2×C4×C5—32no—
229C2×C4×C5—32no—
230C2×C4×C5—32no—
231C2×C4×C5—32no—
232C2×C4×C5—62no—
233C2×C4×C5—62no—
234C2×C4×C5—62no—
235C2×C4×C5—62no—
236C2×C4×C5C22×A412yes—
237C2×C4×C5C22×A411yescharacteristic
238C2×Dic5—32no—
239C2×Dic5—31no—
240C2×Dic5—32no—
241C2×Dic5—32no—
242C2×Dic5—32no—
243C2×Dic5—32no—
244C2×Dic5—62no—
245C2×Dic5—62no—
246C2×Dic5—62no—
247C2×Dic5—62no—
248C2×Dic5C22×A412yes—
249C2×Dic5C22×A411yescharacteristic
250C4×D5—24no—
251C4×D5—38no—
252C4×D5—34no—
253C4×D5—34no—
254C4×D5—34no—
255C4×D5—64no—
256C4×D5—64no—
257C4×D5—68no—
258C4×D5—64no—
259C4×D5C4×A414yescomplemented
260C25—51no—
261C23×C4—51no—
262C23×C4—54no—
263C23×C4—52no—
264C23×C4—104no—
265C23×C4—151no—
266C23×C4—152no—
267C23×C4—151no—
268C23×C4—151no—
269C23×C4—151no—
270C23×C4—154no—
271C23×C4—152no—
272C23×C4—152no—
273C23×C4—152no—
274C23×C4—304no—
275C23×C4C2×C3×D512yes—
276C23×C4C2×C3×D511yescharacteristic
277C2×C4⋊C4—31no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—32no—
280C2×C4⋊C4—51no—
281C2×C4⋊C4—152no—
282C2×C4⋊C4—151no—
283C2×C4⋊C4—151no—
284C2×C4⋊C4—152no—
285C2×C4⋊C4—152no—
286C2×C4⋊C4—154no—
287C2×C4⋊C4—152no—
288C2×C4⋊C4—152no—
289C2×C4⋊C4—154no—
290C2×C4⋊C4—152no—
291C2×C4⋊C4—151no—
292C2×C4⋊C4—151no—
293C2×C4⋊C4—152no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4—152no—
296C2×C4⋊C4—152no—
297C2×C4⋊C4—151no—
298C2×C3×C5—41no—
299C2×C3×C5—41no—
300C2×C3×C5—41no—
301C3×D5—44no—
302C23×C3—201no—
303C2×A4—54no—
304C2×A4C2×C4×D511yescharacteristic
305C2×A4D4×D511yescharacteristic
306C2×A4Q8×D511yescharacteristic
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—204no—
310C2×C3×C4—201no—
311C2×C3×C4—202no—
312C2×C3×C4—404no—
313C22×C5—31no—
314C22×C5—31no—
315C22×C5—31no—
316C22×C5—32no—
317C22×C5—31no—
318C22×C5—31no—
319C22×C5—31no—
320C22×C5—31no—
321C22×C5—31no—
322C22×C5—31no—
323C22×C5C2×C3×C4⋊C411yescharacteristic, complemented
324C22×C5C23×A411yescharacteristic
325C2×D5—34no—
326C2×D5—34no—
327C2×D5—34no—
328C2×D5—32no—
329C2×D5—32no—
330C2×D5—32no—
331C2×D5—34no—
332C2×D5—34no—
333C2×D5—34no—
334C2×D5—34no—
335C2×D5—34no—
336C2×D5C2×C4×A412yes—
337C2×D5D4×A412yes—
338C2×D5Q8×A412yes—
339C4×C5—22no—
340C4×C5—32no—
341C4×C5—62no—
342C4×C5C2×C4×A412yescomplemented
343Dic5—22no—
344Dic5—32no—
345Dic5—62no—
346Dic5C2×C4×A412yescomplemented
347C24—52no—
348C24—52no—
349C24—52no—
350C24—151no—
351C24—151no—
352C24—152no—
353C24—152no—
354C24—152no—
355C24C22×C3×D511yescharacteristic
356C22×C4—22no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—32no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—51no—
363C22×C4—52no—
364C22×C4—52no—
365C22×C4—62no—
366C22×C4—102no—
367C22×C4—151no—
368C22×C4—154no—
369C22×C4—154no—
370C22×C4—152no—
371C22×C4—151no—
372C22×C4—152no—
373C22×C4—154no—
374C22×C4—154no—
375C22×C4—154no—
376C22×C4—154no—
377C22×C4—154no—
378C22×C4—154no—
379C22×C4—152no—
380C22×C4—154no—
381C22×C4—151no—
382C22×C4—152no—
383C22×C4—151no—
384C22×C4—151no—
385C22×C4—152no—
386C22×C4—152no—
387C22×C4—152no—
388C22×C4—304no—
389C22×C4—304no—
390C22×C4—304no—
391C22×C4—304no—
392C22×C4—304no—
393C22×C4—304no—
394C22×C4—304no—
395C22×C4—304no—
396C22×C4—302no—
397C22×C4C3×C4×D512yescomplemented
398C4⋊C4—32no—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—52no—
402C4⋊C4—51no—
403C4⋊C4—152no—
404C4⋊C4—152no—
405C4⋊C4—152no—
406C4⋊C4—154no—
407C4⋊C4—152no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4D5×A411yescharacteristic, direct product factor
411C3×C5—41noHall
412C22×C3—41no—
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416A4D5×C4⋊C411yescharacteristic, direct product factor
417C3×C4—42no—
418C3×C4—82no—
419C3×C4—202no—
420C3×C4—402no—
421C2×C5—31no—
422C2×C5—31no—
423C2×C5—31no—
424C2×C5—31no—
425C2×C5C22×C4×A411yescharacteristic
426C2×C5C2×D4×A411yescharacteristic
427C2×C5C2×Q8×A411yescharacteristic
428D5—34no—
429D5A4×C4⋊C414yesdirect product factor
430C23—31no—
431C23—31no—
432C23—31no—
433C23—31no—
434C23—51no—
435C23—54no—
436C23—152no—
437C23—152no—
438C23—152no—
439C23—152no—
440C23—152no—
441C23—152no—
442C23—152no—
443C23—152no—
444C23—154no—
445C23—154no—
446C23—154no—
447C23—152no—
448C23—152no—
449C23—152no—
450C23—158no—
451C23—152no—
452C23—151no—
453C23C2×C3×C4×D511yescharacteristic
454C23C3×D4×D511yescharacteristic
455C23C3×Q8×D511yescharacteristic
456C2×C4—32no—
457C2×C4—31no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—51no—
463C2×C4—54no—
464C2×C4—52no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—104no—
470C2×C4—154no—
471C2×C4—154no—
472C2×C4—158no—
473C2×C4—152no—
474C2×C4—152no—
475C2×C4—152no—
476C2×C4—151no—
477C2×C4—154no—
478C2×C4—152no—
479C2×C4—152no—
480C2×C4—304no—
481C2×C4—304no—
482C2×C4—304no—
483C2×C4—308no—
484C2×C4—302no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4—302no—
488C2×C4C2×D5×A412yes—
489C2×C4C2×D5×A411yescharacteristic
490C2×C3—41no—
491C2×C3—41no—
492C2×C3—41no—
493C2×C3—204no—
494C5C2×A4×C4⋊C411yescharacteristic, complemented, Sylow
495C22—31no—
496C22—31no—
497C22—31no—
498C22—32no—
499C22—31no—
500C22—31no—
501C22—31no—
502C22—31no—
503C22—31no—
504C22—31no—
505C22—52no—
506C22—52no—
507C22—52no—
508C22—154no—
509C22—154no—
510C22—154no—
511C22—154no—
512C22—154no—
513C22—154no—
514C22—154no—
515C22—154no—
516C22—152no—
517C22—152no—
518C22—152no—
519C22C3×D5×C4⋊C411yescharacteristic, complemented
520C22C22×D5×A411yescharacteristic
521C4—22no—
522C4—32no—
523C4—52no—
524C4—62no—
525C4—102no—
526C4—152no—
527C4—302no—
528C4C4×D5×A412yescomplemented
529C3—41noSylow
530C2—31no—
531C2—31no—
532C2—31no—
533C2—31no—
534C2—54no—
535C2—154no—
536C2C2×C4×D5×A411yescharacteristic
537C2D4×D5×A411yescharacteristic
538C2Q8×D5×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C4⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC22×D5×A4C22
hypercenterC4⋊C4D5×A4
hypocenterC22×C5C2×C3×C4⋊C4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×A4×C4⋊C4C2semidirect
4. A4×C4⋊Dic5C2semidirect
5. A4×#683C2semidirect
6. C22×D5×C4⋊C4C3semidirect
13. C4×D5×A4C4semidirect
18. C22×C5×C4⋊C4C2×C3semidirect
19. C22×C4⋊Dic5C2×C3semidirect
20. C22×#683C2×C3semidirect
34. C4×C5×A4C2×C4semidirect
36. A4×Dic5C2×C4semidirect
44. A4×C4⋊C4D5direct (N × H)
61. C22×C4×D5C3×C4semidirect
82. D5×C4⋊C4A4direct (N × H)
88. D5×A4C4⋊C4direct (N × H)
119. C22×C4×C5C2×C3×C4semidirect
127. C22×Dic5C2×C3×C4semidirect
157. C5×C4⋊C4C2×A4semidirect
161. C4⋊Dic5C2×A4semidirect
166. #683C2×A4semidirect
177. C22×C4⋊C4C3×D5semidirect
182. C5×A4C2×C4⋊C4semidirect
196. C4×A4C4×D5semidirect
224. C22×D5C3×C4⋊C4semidirect
259. C4×D5C4×A4semidirect
323. C22×C5C2×C3×C4⋊C4semidirect
342. C4×C5C2×C4×A4semidirect
346. Dic5C2×C4×A4semidirect
397. C22×C4C3×C4×D5semidirect
410. C4⋊C4D5×A4direct (N × H)
416. A4D5×C4⋊C4direct (N × H)
429. D5A4×C4⋊C4direct (N × H)
494. C5C2×A4×C4⋊C4semidirect
519. C22C3×D5×C4⋊C4semidirect
528. C4C4×D5×A4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C5×A4×C4⋊C42
A4×C4⋊Dic52
A4×#6832
C22×D5×C4⋊C43
C3×D5×C4⋊C44
C2×A4×C4⋊C45