Finite Group Databasebeta

← C5×#85297 #14511035

Subgroups — C5×#85297 #14511035

Order 1920.

1304 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 96 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×C5×S4C211yesmaximal, characteristic, complemented
2C2×C5×GL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊S4C212yesmaximal, complemented
4C5×A4×C22⋊C4C211yesmaximal, characteristic, complemented
5C5×(C2×S4)⋊C4C212yesmaximal, complemented
6C5×#2410—31nomaximal, Hall
7C23×C5×A4C2211yescharacteristic
8C22×C5×S4—22no—
9C22×C5×S4—24no—
10C22×C5×S4C2212yes—
11C22×C5×S4C2211yescharacteristic, complemented
12C2×C4×C5×A4C2212yescomplemented
13C5×GL(2,ℤ/4)—22no—
14C2×C5×SL(2,ℤ/4)C2211yescharacteristic, complemented
15C5×C4⋊S4—24no—
16C5×#882—41nomaximal
17#85297C511yesmaximal, characteristic, direct product factor, Hall
18C23×C5×D4—31no—
19C2×C5×#121—32no—
20C2×C5×#120—31no—
21C2×C5×#120—31no—
22C22×C5×C22⋊C4D311yescharacteristic, complemented
23C5×#394—32no—
24C5×#392—32no—
25C5×#386—31no—
26C5×#386—32no—
27C5×#385—31no—
28C5×#379—31no—
29C23×C5×D3—41no—
30C22×C5×A4—22no—
31C22×C5×A4D412yescomplemented
32C22×C5×A4C2311yescharacteristic
33C2×C5×S4—28no—
34C2×C5×S4—22no—
35C2×C5×S4—22no—
36C2×C5×S4—22no—
37C2×C5×S4—21no—
38C2×C5×S4D414yescomplemented
39C2×C5×#67—41no—
40C2×C5×D12—42no—
41C4×C5×A4—22no—
42C5×SL(2,ℤ/4)—21no—
43C3×C5×C22⋊C4—41no—
44C5×(C2×D3)⋊C4—42no—
45C23×S4C2×C511yescharacteristic, complemented
46C2×GL(2,ℤ/4)C2×C511yescharacteristic, complemented
47C2×C4⋊S4C2×C512yescomplemented
48A4×C22⋊C4C2×C511yescharacteristic, complemented
49(C2×S4)⋊C4C2×C512yescomplemented
50C25×C5—31no—
51C25×C5C2×D311yescharacteristic
52C22×C5×D4—32no—
53C22×C5×D4—31no—
54C22×C5×D4—32no—
55C22×C5×D4—31no—
56C22×C5×D4—32no—
57C22×C5×D4—31no—
58C22×C5×D4—64no—
59C22×C5×D4—64no—
60C22×C5×D4—62no—
61C22×C5×D4—62no—
62C23×C4×C5—31no—
63C23×C4×C5C2×D312yescomplemented
64C5×#121—64no—
65C5×#121—64no—
66C5×#120—61no—
67C5×#120—62no—
68C5×#120—62no—
69C5×#120—62no—
70C5×#120—61no—
71C2×C5×C4⋊C4—32no—
72C2×C5×C22⋊C4—31no—
73C2×C5×C22⋊C4—31no—
74C2×C5×C22⋊C4—32no—
75C2×C5×C22⋊C4—31no—
76C2×C5×C22⋊C4—32no—
77C2×C5×C22⋊C4—32no—
78C2×C5×C22⋊C4—32no—
79C2×C5×C22⋊C4—31no—
80C2×C5×C22⋊C4—31no—
81C2×C5×C22⋊C4—32no—
82C5×#95—32no—
83C5×#95—32no—
84#2410—31noSylow
85C23×C3×C5—41no—
86C22×C5×D3—42no—
87C22×C5×D3—41no—
88C22×C5×D3—84no—
89C22×C5×D3—82no—
90C2×C5×A4—22no—
91C2×C5×A4C2×D411yescharacteristic
92C2×C5×A4C2×D412yes—
93C5×S4—24no—
94C5×S4—41no—
95C2×C3×C4×C5—42no—
96C5×#67—82no—
97C2×C5×Dic3—41no—
98C5×D12—84no—
99C23×A4C22×C511yescharacteristic
100C22×S4—22no—
101C22×S4—24no—
102C22×S4C22×C512yes—
103C22×S4C22×C511yescharacteristic, complemented
104C2×C4×A4C22×C512yescomplemented
105GL(2,ℤ/4)—22no—
106C2×SL(2,ℤ/4)C22×C511yescharacteristic, complemented
107C4⋊S4—24no—
108#882—41no—
109C24×C5—22no—
110C24×C5—31no—
111C24×C5—31no—
112C24×C5—32no—
113C24×C5—32no—
114C24×C5—31no—
115C24×C5—62no—
116C24×C5—62no—
117C24×C5—64no—
118C24×C5—61no—
119C24×C5—62no—
120C24×C5—61no—
121C24×C5—122no—
122C24×C5D1212yescomplemented
123C24×C5C22×D311yescharacteristic
124C2×C5×D4—34no—
125C2×C5×D4—34no—
126C2×C5×D4—64no—
127C2×C5×D4—62no—
128C2×C5×D4—68no—
129C2×C5×D4—62no—
130C2×C5×D4—62no—
131C2×C5×D4—64no—
132C2×C5×D4—64no—
133C2×C5×D4—68no—
134C2×C5×D4—616no—
135C2×C5×D4—62no—
136C2×C5×D4—62no—
137C2×C5×D4—61no—
138C2×C5×D4—62no—
139C2×C5×D4—62no—
140C2×C5×D4—61no—
141C2×C5×D4—64no—
142C2×C5×D4—62no—
143C2×C5×D4—62no—
144C2×C5×D4—61no—
145C2×C5×D4—62no—
146C2×C5×D4—61no—
147C2×C5×D4—62no—
148C2×C5×D4—122no—
149C2×C5×D4—122no—
150C22×C4×C5—22no—
151C22×C4×C5—32no—
152C22×C4×C5—32no—
153C22×C4×C5—32no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—64no—
158C22×C4×C5—62no—
159C22×C4×C5—62no—
160C5×C4⋊C4—64no—
161C5×C22⋊C4—31no—
162C5×C22⋊C4—32no—
163C5×C22⋊C4—61no—
164C5×C22⋊C4—62no—
165C5×C22⋊C4—64no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—62no—
168C5×C22⋊C4—62no—
169C5×C22⋊C4—64no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—62no—
172C5×C22⋊C4—122no—
173C5×C22⋊C4S411yescharacteristic, complemented
174C23×D4—31no—
175C2×#121—32no—
176C2×#120—31no—
177C2×#120—31no—
178C22×C22⋊C4C5×D311yescharacteristic, complemented
179#394—32no—
180#392—32no—
181#386—31no—
182#386—32no—
183#385—31no—
184#379—31no—
185C22×C3×C5—42no—
186C22×C3×C5—41no—
187C22×C3×C5—82no—
188C2×C5×D3—44no—
189C2×C5×D3—82no—
190C2×C5×D3—82no—
191C2×C5×D3—88no—
192C2×C5×D3—82no—
193C2×C5×D3—81no—
194C5×A4#12011yescharacteristic, complemented
195C3×C4×C5—82no—
196C5×Dic3—81no—
197C23×D3—41no—
198C22×A4—22no—
199C22×A4C5×D412yescomplemented
200C22×A4C23×C511yescharacteristic
201C2×S4—28no—
202C2×S4—22no—
203C2×S4—22no—
204C2×S4—22no—
205C2×S4—21no—
206C2×S4C5×D414yescomplemented
207C2×#67—41no—
208C2×D12—42no—
209C4×A4—22no—
210SL(2,ℤ/4)—21no—
211C3×C22⋊C4—41no—
212(C2×D3)⋊C4—42no—
213C23×C5—22no—
214C23×C5—31no—
215C23×C5—31no—
216C23×C5—32no—
217C23×C5—32no—
218C23×C5—32no—
219C23×C5—32no—
220C23×C5—31no—
221C23×C5—34no—
222C23×C5—62no—
223C23×C5—62no—
224C23×C5—61no—
225C23×C5—62no—
226C23×C5—64no—
227C23×C5—62no—
228C23×C5—62no—
229C23×C5—62no—
230C23×C5—62no—
231C23×C5—62no—
232C23×C5—62no—
233C23×C5—62no—
234C23×C5—62no—
235C23×C5—61no—
236C23×C5—61no—
237C23×C5—62no—
238C23×C5—68no—
239C23×C5—62no—
240C23×C5—61no—
241C23×C5—124no—
242C23×C5—122no—
243C23×C5—122no—
244C23×C5—128no—
245C23×C5—124no—
246C23×C5—124no—
247C23×C5—122no—
248C23×C5C2×D1211yescharacteristic
249C23×C5D3×D412yes—
250C23×C5C2×S411yescharacteristic
251C5×D4—64no—
252C5×D4—64no—
253C5×D4—64no—
254C5×D4—616no—
255C5×D4—64no—
256C5×D4—124no—
257C5×D4—124no—
258C5×D4—121no—
259C5×D4—122no—
260C5×D4—122no—
261C5×D4—124no—
262C5×D4—121no—
263C5×D4—122no—
264C2×C4×C5—34no—
265C2×C4×C5—32no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—68no—
271C2×C4×C5—62no—
272C2×C4×C5—62no—
273C2×C4×C5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—62no—
277C2×C4×C5—62no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5C2×S412yescomplemented
281C25—31no—
282C25C2×C5×D311yescharacteristic
283C22×D4—32no—
284C22×D4—31no—
285C22×D4—32no—
286C22×D4—31no—
287C22×D4—32no—
288C22×D4—31no—
289C22×D4—64no—
290C22×D4—64no—
291C22×D4—62no—
292C22×D4—62no—
293C23×C4—31no—
294C23×C4C2×C5×D312yescomplemented
295#121—64no—
296#121—64no—
297#120—61no—
298#120—62no—
299#120—62no—
300#120—62no—
301#120—61no—
302C2×C4⋊C4—32no—
303C2×C22⋊C4—31no—
304C2×C22⋊C4—31no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—31no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—32no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—32no—
313#95—32no—
314#95—32no—
315C2×C3×C5—41no—
316C2×C3×C5—42no—
317C2×C3×C5—82no—
318C5×D3—84no—
319C5×D3—161no—
320C23×C3—41no—
321C22×D3—42no—
322C22×D3—41no—
323C22×D3—84no—
324C22×D3—82no—
325C2×A4—22no—
326C2×A4C2×C5×D411yescharacteristic
327C2×A4C2×C5×D412yes—
328S4—24no—
329S4—41no—
330C2×C3×C4—42no—
331#67—82no—
332C2×Dic3—41no—
333D12—84no—
334C22×C5—22no—
335C22×C5—31no—
336C22×C5—32no—
337C22×C5—31no—
338C22×C5—31no—
339C22×C5—32no—
340C22×C5—32no—
341C22×C5—32no—
342C22×C5—62no—
343C22×C5—62no—
344C22×C5—64no—
345C22×C5—61no—
346C22×C5—62no—
347C22×C5—62no—
348C22×C5—64no—
349C22×C5—64no—
350C22×C5—62no—
351C22×C5—64no—
352C22×C5—128no—
353C22×C5—122no—
354C22×C5—122no—
355C22×C5—122no—
356C22×C5—121no—
357C22×C5—121no—
358C22×C5—122no—
359C22×C5—128no—
360C22×C5—122no—
361C22×C5—122no—
362C22×C5—121no—
363C22×C5—122no—
364C22×C5#88211yescharacteristic, complemented
365C22×C5C4⋊S412yescomplemented
366C22×C5C22×S411yescharacteristic
367C4×C5—22no—
368C4×C5—64no—
369C4×C5—62no—
370C4×C5—121no—
371C4×C5—121no—
372C4×C5—121no—
373C24—22no—
374C24—31no—
375C24—31no—
376C24—32no—
377C24—32no—
378C24—31no—
379C24—62no—
380C24—62no—
381C24—64no—
382C24—61no—
383C24—62no—
384C24—61no—
385C24—122no—
386C24C5×D1212yescomplemented
387C24C22×C5×D311yescharacteristic
388C2×D4—34no—
389C2×D4—34no—
390C2×D4—64no—
391C2×D4—62no—
392C2×D4—68no—
393C2×D4—62no—
394C2×D4—62no—
395C2×D4—64no—
396C2×D4—64no—
397C2×D4—68no—
398C2×D4—616no—
399C2×D4—62no—
400C2×D4—62no—
401C2×D4—61no—
402C2×D4—62no—
403C2×D4—62no—
404C2×D4—61no—
405C2×D4—64no—
406C2×D4—62no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4—62no—
410C2×D4—61no—
411C2×D4—62no—
412C2×D4—122no—
413C2×D4—122no—
414C22×C4—22no—
415C22×C4—32no—
416C22×C4—32no—
417C22×C4—32no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—64no—
422C22×C4—62no—
423C22×C4—62no—
424C4⋊C4—64no—
425C22⋊C4—31no—
426C22⋊C4—32no—
427C22⋊C4—61no—
428C22⋊C4—62no—
429C22⋊C4—64no—
430C22⋊C4—61no—
431C22⋊C4—62no—
432C22⋊C4—62no—
433C22⋊C4—64no—
434C22⋊C4—61no—
435C22⋊C4—62no—
436C22⋊C4—122no—
437C22⋊C4C5×S411yescharacteristic, complemented
438C3×C5—41noHall
439C22×C3—42no—
440C22×C3—41no—
441C22×C3—82no—
442C2×D3—44no—
443C2×D3—82no—
444C2×D3—82no—
445C2×D3—88no—
446C2×D3—82no—
447C2×D3—81no—
448A4C5×#12011yescharacteristic, complemented
449C3×C4—82no—
450Dic3—81no—
451C2×C5—22no—
452C2×C5—31no—
453C2×C5—31no—
454C2×C5—32no—
455C2×C5—62no—
456C2×C5—124no—
457C2×C5—241no—
458C2×C5C2×C4⋊S411yescharacteristic
459C2×C5D4×S412yes—
460C23—22no—
461C23—31no—
462C23—31no—
463C23—32no—
464C23—32no—
465C23—32no—
466C23—32no—
467C23—31no—
468C23—34no—
469C23—62no—
470C23—62no—
471C23—61no—
472C23—62no—
473C23—64no—
474C23—62no—
475C23—62no—
476C23—62no—
477C23—62no—
478C23—62no—
479C23—62no—
480C23—62no—
481C23—62no—
482C23—61no—
483C23—61no—
484C23—62no—
485C23—68no—
486C23—62no—
487C23—61no—
488C23—124no—
489C23—122no—
490C23—122no—
491C23—128no—
492C23—124no—
493C23—124no—
494C23—122no—
495C23C2×C5×D1211yescharacteristic
496C23C5×D3×D412yes—
497C23C2×C5×S411yescharacteristic
498D4—64no—
499D4—64no—
500D4—64no—
501D4—616no—
502D4—64no—
503D4—124no—
504D4—124no—
505D4—121no—
506D4—122no—
507D4—122no—
508D4—124no—
509D4—122no—
510D4—121no—
511C2×C4—34no—
512C2×C4—32no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—68no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4C2×C5×S412yescomplemented
528C2×C3—41no—
529C2×C3—42no—
530C2×C3—82no—
531D3—84no—
532D3—161no—
533C5#8529711yescharacteristic, direct product factor, Sylow
534C22—22no—
535C22—31no—
536C22—32no—
537C22—31no—
538C22—31no—
539C22—32no—
540C22—32no—
541C22—32no—
542C22—62no—
543C22—62no—
544C22—64no—
545C22—61no—
546C22—62no—
547C22—62no—
548C22—64no—
549C22—64no—
550C22—62no—
551C22—64no—
552C22—128no—
553C22—122no—
554C22—122no—
555C22—122no—
556C22—121no—
557C22—121no—
558C22—122no—
559C22—128no—
560C22—122no—
561C22—122no—
562C22—121no—
563C22—122no—
564C22C5×#88211yescharacteristic, complemented
565C22C5×C4⋊S412yescomplemented
566C22C22×C5×S411yescharacteristic
567C4—22no—
568C4—64no—
569C4—62no—
570C4—121no—
571C4—121no—
572C4—121no—
573C3—41noSylow
574C2—22no—
575C2—31no—
576C2—31no—
577C2—32no—
578C2—62no—
579C2—124no—
580C2—241no—
581C2C2×C5×C4⋊S411yescharacteristic
582C2C5×D4×S412yes—
subgroupG/H
centerC22×C5C22×S4
commutator, cosocleC22×A4C23×C5
FrattiniC22C22×C5×S4
FittingC22×C5×C22⋊C4D3
socleC24×C5C22×D3
hypercenterC5×C22⋊C4S4
hypocenterA4C5×#120
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C5×S4C2semidirect
2. C2×C5×GL(2,ℤ/4)C2semidirect
3. C2×C5×C4⋊S4C2semidirect
4. C5×A4×C22⋊C4C2semidirect
5. C5×(C2×S4)⋊C4C2semidirect
11. C22×C5×S4C22semidirect
12. C2×C4×C5×A4C22semidirect
14. C2×C5×SL(2,ℤ/4)C22semidirect
17. #85297C5direct (N × H)
22. C22×C5×C22⋊C4D3semidirect
31. C22×C5×A4D4semidirect
38. C2×C5×S4D4semidirect
45. C23×S4C2×C5semidirect
46. C2×GL(2,ℤ/4)C2×C5semidirect
47. C2×C4⋊S4C2×C5semidirect
48. A4×C22⋊C4C2×C5semidirect
49. (C2×S4)⋊C4C2×C5semidirect
63. C23×C4×C5C2×D3semidirect
103. C22×S4C22×C5semidirect
104. C2×C4×A4C22×C5semidirect
106. C2×SL(2,ℤ/4)C22×C5semidirect
122. C24×C5D12semidirect
173. C5×C22⋊C4S4semidirect
178. C22×C22⋊C4C5×D3semidirect
194. C5×A4#120semidirect
199. C22×A4C5×D4semidirect
206. C2×S4C5×D4semidirect
280. C2×C4×C5C2×S4semidirect
294. C23×C4C2×C5×D3semidirect
364. C22×C5#882semidirect
365. C22×C5C4⋊S4semidirect
386. C24C5×D12semidirect
437. C22⋊C4C5×S4semidirect
448. A4C5×#120semidirect
527. C2×C4C2×C5×S4semidirect
533. C5#85297direct (N × H)
564. C22C5×#882semidirect
565. C22C5×C4⋊S4semidirect

Maximal subgroups

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

subgroupindex
C23×C5×S42
C2×C5×GL(2,ℤ/4)2
C2×C5×C4⋊S42
C5×A4×C22⋊C42
C5×(C2×S4)⋊C42
C5×#24103
C5×#8824
#852975