Finite Group Databasebeta

← C5×A4×#123 #14511324

Subgroups — C5×A4×#123 #14511324

Order 1920.

916 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 916 conjugacy classes of subgroups — too many to draw. Only its 132 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×C5×D4×A4C211yesmaximal, characteristic
2C22×C4×C5×A4C211yesmaximal, characteristic, complemented
3C5×A4×C4⋊C4C212yesmaximal, complemented
4C5×A4×C22⋊C4C212yesmaximal, complemented
5C5×A4×C22⋊C4C211yesmaximal, characteristic, complemented
6C22×C5×#123C311yesmaximal, characteristic, complemented, Hall
7C23×C5×A4C2211yescharacteristic
8C23×C5×A4C2211yescharacteristic
9C5×D4×A4—22no—
10C2×C4×C5×A4—22no—
11C2×C4×C5×A4C2212yes—
12C2×C4×C5×A4C2211yescharacteristic
13C2×C4×C5×A4C2212yes—
14C3×C5×#123—41nomaximal
15A4×#123C511yesmaximal, characteristic, direct product factor, Hall
16C23×C5×D4C2×C311yescharacteristic
17C24×C4×C5C2×C311yescharacteristic, complemented
18C2×C5×#123—31no—
19C2×C5×#123—31no—
20C2×C5×#123—32no—
21C2×C5×#123—32no—
22C2×C5×#123—31no—
23C2×C5×#123—31no—
24C22×C5×C4⋊C4C2×C312yescomplemented
25C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
26C22×C5×C22⋊C4C2×C312yescomplemented
27C22×C5×A4—22no—
28C22×C5×A4—21no—
29C22×C5×A4—22no—
30C22×C5×A4D412yes—
31C22×C5×A4C2311yescharacteristic
32C2×C3×C5×D4—41no—
33C22×C3×C4×C5—41no—
34C4×C5×A4—22no—
35C4×C5×A4—21no—
36C4×C5×A4—22no—
37C3×C5×C4⋊C4—42no—
38C3×C5×C22⋊C4—41no—
39C3×C5×C22⋊C4—42no—
40C2×D4×A4C2×C511yescharacteristic
41C22×C4×A4C2×C511yescharacteristic, complemented
42A4×C4⋊C4C2×C512yescomplemented
43A4×C22⋊C4C2×C512yescomplemented
44A4×C22⋊C4C2×C511yescharacteristic, complemented
45C25×C5C22×C311yescharacteristic
46C25×C5C22×C311yescharacteristic
47C22×C5×D4—22no—
48C22×C5×D4—31no—
49C22×C5×D4—31no—
50C22×C5×D4—31no—
51C22×C5×D4—31no—
52C22×C5×D4—62no—
53C23×C4×C5—22no—
54C23×C4×C5—31no—
55C23×C4×C5—31no—
56C23×C4×C5—32no—
57C23×C4×C5—62no—
58C23×C4×C5C22×C312yes—
59C23×C4×C5C22×C312yes—
60C23×C4×C5C22×C311yescharacteristic
61C5×#123—32no—
62C5×#123—32no—
63C5×#123—34no—
64C5×#123—32no—
65C5×#123—34no—
66C5×#123—31no—
67C5×#123—31no—
68C5×#123—32no—
69C5×#123—32no—
70C5×#123—31no—
71C5×#123A411yescharacteristic, direct product factor
72C2×C5×C4⋊C4—32no—
73C2×C5×C4⋊C4—32no—
74C2×C5×C4⋊C4—32no—
75C2×C5×C4⋊C4—32no—
76C2×C5×C22⋊C4—31no—
77C2×C5×C22⋊C4—32no—
78C2×C5×C22⋊C4—31no—
79C2×C5×C22⋊C4—32no—
80C2×C5×C22⋊C4—32no—
81C2×C5×C22⋊C4—32no—
82C2×C5×C22⋊C4—32no—
83C22×#123C3×C511yescharacteristic, complemented, Sylow
84C23×C3×C5—41no—
85C23×C3×C5—41no—
86C2×C5×A4—22no—
87C2×C5×A4—41no—
88C2×C5×A4C2×D411yescharacteristic
89C2×C5×A4#4112yes—
90C3×C5×D4—82no—
91C2×C3×C4×C5—42no—
92C2×C3×C4×C5—42no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—82no—
95C23×A4C22×C511yescharacteristic
96C23×A4C22×C511yescharacteristic
97D4×A4—22no—
98C2×C4×A4—22no—
99C2×C4×A4C22×C512yes—
100C2×C4×A4C22×C511yescharacteristic
101C2×C4×A4C22×C512yes—
102C3×#123—41no—
103C24×C5—22no—
104C24×C5—21no—
105C24×C5—22no—
106C24×C5—31no—
107C24×C5—32no—
108C24×C5—31no—
109C24×C5—31no—
110C24×C5—31no—
111C24×C5—62no—
112C24×C5—61no—
113C24×C5—62no—
114C24×C5C3×D412yes—
115C24×C5C23×C311yescharacteristic
116C2×C5×D4—32no—
117C2×C5×D4—31no—
118C2×C5×D4—31no—
119C2×C5×D4—31no—
120C2×C5×D4—62no—
121C2×C5×D4—62no—
122C2×C5×D4—62no—
123C2×C5×D4—62no—
124C2×C5×D4—62no—
125C2×C5×D4—62no—
126C2×C5×D4—62no—
127C2×C5×D4—62no—
128C2×C5×D4C2×A411yescharacteristic
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C22×C4×C5—22no—
132C22×C4×C5—32no—
133C22×C4×C5—31no—
134C22×C4×C5—32no—
135C22×C4×C5—32no—
136C22×C4×C5—31no—
137C22×C4×C5—32no—
138C22×C4×C5—32no—
139C22×C4×C5—32no—
140C22×C4×C5—31no—
141C22×C4×C5—62no—
142C22×C4×C5—62no—
143C22×C4×C5—64no—
144C22×C4×C5—64no—
145C22×C4×C5—62no—
146C22×C4×C5—62no—
147C22×C4×C5—62no—
148C22×C4×C5—62no—
149C22×C4×C5—61no—
150C22×C4×C5C2×A411yescharacteristic, complemented
151C5×C4⋊C4—34no—
152C5×C4⋊C4—32no—
153C5×C4⋊C4—32no—
154C5×C4⋊C4—32no—
155C5×C4⋊C4C2×A412yescomplemented
156C5×C22⋊C4—32no—
157C5×C22⋊C4—34no—
158C5×C22⋊C4—31no—
159C5×C22⋊C4—32no—
160C5×C22⋊C4—32no—
161C5×C22⋊C4—32no—
162C5×C22⋊C4—32no—
163C5×C22⋊C4C2×A411yescharacteristic, complemented
164C5×C22⋊C4C2×A412yescomplemented
165C23×D4C2×C3×C511yescharacteristic
166C24×C4C2×C3×C511yescharacteristic, complemented
167C2×#123—31no—
168C2×#123—31no—
169C2×#123—32no—
170C2×#123—32no—
171C2×#123—31no—
172C2×#123—31no—
173C22×C4⋊C4C2×C3×C512yescomplemented
174C22×C22⋊C4C2×C3×C511yescharacteristic, complemented
175C22×C22⋊C4C2×C3×C512yescomplemented
176C22×C3×C5—42no—
177C22×C3×C5—41no—
178C22×C3×C5—82no—
179C22×C3×C5—81no—
180C22×C3×C5—82no—
181C5×A4#12311yescharacteristic, direct product factor
182C3×C4×C5—82no—
183C3×C4×C5—82no—
184C3×C4×C5—81no—
185C22×A4—22no—
186C22×A4—21no—
187C22×A4—22no—
188C22×A4C5×D412yes—
189C22×A4C23×C511yescharacteristic
190C2×C3×D4—41no—
191C22×C3×C4—41no—
192C4×A4—22no—
193C4×A4—21no—
194C4×A4—22no—
195C3×C4⋊C4—42no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—42no—
198C23×C5—22no—
199C23×C5—31no—
200C23×C5—32no—
201C23×C5—31no—
202C23×C5—32no—
203C23×C5—32no—
204C23×C5—32no—
205C23×C5—32no—
206C23×C5—31no—
207C23×C5—31no—
208C23×C5—41no—
209C23×C5—62no—
210C23×C5—62no—
211C23×C5—61no—
212C23×C5—61no—
213C23×C5—62no—
214C23×C5—62no—
215C23×C5—62no—
216C23×C5—64no—
217C23×C5—62no—
218C23×C5—62no—
219C23×C5—64no—
220C23×C5—61no—
221C23×C5—61no—
222C23×C5—62no—
223C23×C5—62no—
224C23×C5—121no—
225C23×C5—122no—
226C23×C5—122no—
227C23×C5C2×C3×D411yescharacteristic
228C23×C5C3×#4112yes—
229C23×C5C22×A411yescharacteristic
230C23×C5C22×A411yescharacteristic
231C5×D4—22no—
232C5×D4—62no—
233C5×D4—62no—
234C5×D4—64no—
235C5×D4—62no—
236C2×C4×C5—22no—
237C2×C4×C5—32no—
238C2×C4×C5—32no—
239C2×C4×C5—31no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5—61no—
243C2×C4×C5—62no—
244C2×C4×C5—62no—
245C2×C4×C5—64no—
246C2×C4×C5—61no—
247C2×C4×C5—64no—
248C2×C4×C5—62no—
249C2×C4×C5—62no—
250C2×C4×C5—62no—
251C2×C4×C5—61no—
252C2×C4×C5—62no—
253C2×C4×C5—62no—
254C2×C4×C5—61no—
255C2×C4×C5C22×A412yes—
256C2×C4×C5C22×A412yes—
257C2×C4×C5C22×A411yescharacteristic
258C25C22×C3×C511yescharacteristic
259C25C22×C3×C511yescharacteristic
260C22×D4—22no—
261C22×D4—31no—
262C22×D4—31no—
263C22×D4—31no—
264C22×D4—31no—
265C22×D4—62no—
266C23×C4—22no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—32no—
270C23×C4—62no—
271C23×C4C22×C3×C512yes—
272C23×C4C22×C3×C512yes—
273C23×C4C22×C3×C511yescharacteristic
274#123—32no—
275#123—32no—
276#123—34no—
277#123—32no—
278#123—34no—
279#123—31no—
280#123—31no—
281#123—32no—
282#123—32no—
283#123—31no—
284#123C5×A411yescharacteristic, direct product factor
285C2×C4⋊C4—32no—
286C2×C4⋊C4—32no—
287C2×C4⋊C4—32no—
288C2×C4⋊C4—32no—
289C2×C22⋊C4—31no—
290C2×C22⋊C4—32no—
291C2×C22⋊C4—31no—
292C2×C22⋊C4—32no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—32no—
296C2×C3×C5—41no—
297C2×C3×C5—42no—
298C2×C3×C5—82no—
299C2×C3×C5—161no—
300C23×C3—41no—
301C23×C3—41no—
302C2×A4—22no—
303C2×A4—41no—
304C2×A4C2×C5×D411yescharacteristic
305C2×A4C5×#4112yes—
306C3×D4—82no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—41no—
310C2×C3×C4—82no—
311C22×C5—22no—
312C22×C5—21no—
313C22×C5—22no—
314C22×C5—31no—
315C22×C5—32no—
316C22×C5—32no—
317C22×C5—31no—
318C22×C5—31no—
319C22×C5—32no—
320C22×C5—32no—
321C22×C5—32no—
322C22×C5—62no—
323C22×C5—64no—
324C22×C5—62no—
325C22×C5—62no—
326C22×C5—62no—
327C22×C5—64no—
328C22×C5—62no—
329C22×C5—61no—
330C22×C5—62no—
331C22×C5—121no—
332C22×C5—121no—
333C22×C5—122no—
334C22×C5—121no—
335C22×C5—121no—
336C22×C5—122no—
337C22×C5C3×#12311yescharacteristic, complemented
338C22×C5D4×A412yes—
339C22×C5C23×A411yescharacteristic
340C4×C5—22no—
341C4×C5—21no—
342C4×C5—22no—
343C4×C5—62no—
344C4×C5—61no—
345C4×C5—62no—
346C24—22no—
347C24—21no—
348C24—22no—
349C24—31no—
350C24—32no—
351C24—31no—
352C24—31no—
353C24—31no—
354C24—62no—
355C24—61no—
356C24—62no—
357C24C3×C5×D412yes—
358C24C23×C3×C511yescharacteristic
359C2×D4—32no—
360C2×D4—31no—
361C2×D4—31no—
362C2×D4—31no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—62no—
367C2×D4—62no—
368C2×D4—62no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4C2×C5×A411yescharacteristic
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—32no—
376C22×C4—31no—
377C22×C4—32no—
378C22×C4—32no—
379C22×C4—31no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—31no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—64no—
387C22×C4—64no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—61no—
392C22×C4—62no—
393C22×C4C2×C5×A411yescharacteristic, complemented
394C4⋊C4—34no—
395C4⋊C4—32no—
396C4⋊C4—32no—
397C4⋊C4—32no—
398C4⋊C4C2×C5×A412yescomplemented
399C22⋊C4—32no—
400C22⋊C4—34no—
401C22⋊C4—31no—
402C22⋊C4—32no—
403C22⋊C4—32no—
404C22⋊C4—32no—
405C22⋊C4—32no—
406C22⋊C4C2×C5×A411yescharacteristic, complemented
407C22⋊C4C2×C5×A412yescomplemented
408C3×C5—41noHall
409C22×C3—42no—
410C22×C3—41no—
411C22×C3—82no—
412C22×C3—81no—
413C22×C3—82no—
414A4C5×#12311yescharacteristic, direct product factor
415C3×C4—82no—
416C3×C4—81no—
417C3×C4—82no—
418C2×C5—22no—
419C2×C5—31no—
420C2×C5—32no—
421C2×C5—31no—
422C2×C5—41no—
423C2×C5—62no—
424C2×C5—121no—
425C2×C5C2×D4×A411yescharacteristic
426C2×C5A4×#4112yes—
427C23—22no—
428C23—31no—
429C23—32no—
430C23—31no—
431C23—32no—
432C23—32no—
433C23—32no—
434C23—32no—
435C23—31no—
436C23—31no—
437C23—41no—
438C23—62no—
439C23—62no—
440C23—61no—
441C23—61no—
442C23—62no—
443C23—62no—
444C23—62no—
445C23—64no—
446C23—62no—
447C23—62no—
448C23—64no—
449C23—61no—
450C23—61no—
451C23—62no—
452C23—62no—
453C23—121no—
454C23—122no—
455C23—122no—
456C23C2×C3×C5×D411yescharacteristic
457C23C3×C5×#4112yes—
458C23C22×C5×A411yescharacteristic
459C23C22×C5×A411yescharacteristic
460D4—22no—
461D4—62no—
462D4—62no—
463D4—64no—
464D4—62no—
465C2×C4—22no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—31no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—64no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—64no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4C22×C5×A412yes—
485C2×C4C22×C5×A412yes—
486C2×C4C22×C5×A411yescharacteristic
487C2×C3—41no—
488C2×C3—42no—
489C2×C3—82no—
490C2×C3—161no—
491C5A4×#12311yescharacteristic, direct product factor, Sylow
492C22—22no—
493C22—21no—
494C22—22no—
495C22—31no—
496C22—32no—
497C22—32no—
498C22—31no—
499C22—31no—
500C22—32no—
501C22—32no—
502C22—32no—
503C22—62no—
504C22—62no—
505C22—64no—
506C22—62no—
507C22—62no—
508C22—64no—
509C22—62no—
510C22—61no—
511C22—62no—
512C22—121no—
513C22—121no—
514C22—122no—
515C22—121no—
516C22—121no—
517C22—122no—
518C22C3×C5×#12311yescharacteristic, complemented
519C22C5×D4×A412yes—
520C22C23×C5×A411yescharacteristic
521C4—22no—
522C4—21no—
523C4—22no—
524C4—62no—
525C4—61no—
526C4—62no—
527C3—41noSylow
528C2—22no—
529C2—31no—
530C2—31no—
531C2—32no—
532C2—41no—
533C2—62no—
534C2—121no—
535C2C2×C5×D4×A411yescharacteristic
536C2C5×A4×#4112yes—
subgroupG/H
centerC22×C5C23×A4
commutator, cosocleC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#123C3
socleC24×C5C23×C3
prime radicalC2×C5×D4×A4C2
hypercenterC5×#123A4
hypocenterC22C3×C5×#123
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C5 ◁ C5×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×C5×A4C2semidirect
3. C5×A4×C4⋊C4C2semidirect
4. C5×A4×C22⋊C4C2semidirect
5. C5×A4×C22⋊C4C2semidirect
6. C22×C5×#123C3semidirect
15. A4×#123C5direct (N × H)
17. C24×C4×C5C2×C3semidirect
24. C22×C5×C4⋊C4C2×C3semidirect
25. C22×C5×C22⋊C4C2×C3semidirect
26. C22×C5×C22⋊C4C2×C3semidirect
41. C22×C4×A4C2×C5semidirect
42. A4×C4⋊C4C2×C5semidirect
43. A4×C22⋊C4C2×C5semidirect
44. A4×C22⋊C4C2×C5semidirect
71. C5×#123A4direct (N × H)
83. C22×#123C3×C5semidirect
150. C22×C4×C5C2×A4semidirect
155. C5×C4⋊C4C2×A4semidirect
163. C5×C22⋊C4C2×A4semidirect
164. C5×C22⋊C4C2×A4semidirect
166. C24×C4C2×C3×C5semidirect
173. C22×C4⋊C4C2×C3×C5semidirect
174. C22×C22⋊C4C2×C3×C5semidirect
175. C22×C22⋊C4C2×C3×C5semidirect
181. C5×A4#123direct (N × H)
284. #123C5×A4direct (N × H)
337. C22×C5C3×#123semidirect
393. C22×C4C2×C5×A4semidirect
398. C4⋊C4C2×C5×A4semidirect
406. C22⋊C4C2×C5×A4semidirect
407. C22⋊C4C2×C5×A4semidirect
414. A4C5×#123direct (N × H)
491. C5A4×#123direct (N × H)
518. C22C3×C5×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×A42
C22×C4×C5×A42
C5×A4×C4⋊C42
C5×A4×C22⋊C42
C22×C5×#1233
C3×C5×#1234
A4×#1235