Finite Group Databasebeta

← C5×SD16×S4 #14511197

Subgroups — C5×SD16×S4 #14511197

Order 1920.

596 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C5×Q8×S4C211yesmaximal, characteristic, complemented
2C5×D4×S4C211yesmaximal, characteristic
3C5×A4×SD16C211yesmaximal, characteristic, complemented
4C5×#5417C211yesmaximal, characteristic, complemented
5C5×#5414C211yesmaximal, characteristic, complemented
6C5×#5401C211yesmaximal, characteristic, complemented
7C5×C8×S4C211yesmaximal, characteristic, complemented
8C5×D4×SD16—31nomaximal, Hall
9C22×C5×S4—21no—
10C5×Q8×A4C2211yescharacteristic, complemented
11C5×D4×A4C2211yescharacteristic
12C5×GL(2,ℤ/4)—21no—
13C5×C4⋊S4C2211yescharacteristic
14C4×C5×S4—21no—
15C4×C5×S4C2211yescharacteristic
16C5×A4⋊Q8—21no—
17C5×A4⋊Q8C2211yescharacteristic, complemented
18C5×D3×SD16—41nomaximal
19C5×C8×A4C2211yescharacteristic, complemented
20C5×A4⋊C8C2211yescharacteristic, complemented
21SD16×S4C511yesmaximal, characteristic, direct product factor, Hall
22C22×C5×SD16—31no—
23C22×C5×SD16D311yescharacteristic, complemented
24C5×D4×Q8—31no—
25C5×D42—31no—
26C5×#492—31no—
27C5×#465—31no—
28C5×#465—31no—
29C5×#461—31no—
30C5×#460—31no—
31C5×#450—31no—
32C5×#450—31no—
33C5×#448—31no—
34C5×#448—31no—
35C4×C5×SD16—31no—
36C5×C8×D4—31no—
37C22×C5×A4—21no—
38C2×C5×S4—21no—
39C2×C5×S4—42no—
40C2×C5×S4D411yescharacteristic
41C5×D3×Q8—41no—
42C5×D3×D4—41no—
43C4×C5×A4—21no—
44C4×C5×A4C2311yescharacteristic
45C5×SL(2,ℤ/4)—21no—
46C5×SL(2,ℤ/4)D411yescharacteristic
47C3×C5×SD16—41no—
48C5×#215—41no—
49C5×#214—41no—
50C5×#204—41no—
51C5×D3×C8—41no—
52Q8×S4C2×C511yescharacteristic, complemented
53D4×S4C2×C511yescharacteristic
54A4×SD16C2×C511yescharacteristic, complemented
55#5417C2×C511yescharacteristic, complemented
56#5414C2×C511yescharacteristic, complemented
57#5401C2×C511yescharacteristic, complemented
58C8×S4C2×C511yescharacteristic, complemented
59C22×C5×Q8—31no—
60C22×C5×Q8C2×D311yescharacteristic, complemented
61C22×C5×D4—31no—
62C22×C5×D4—61no—
63C22×C5×D4C2×D311yescharacteristic
64C2×C5×SD16—31no—
65C2×C5×SD16—31no—
66C2×C5×SD16—31no—
67C2×C5×SD16—31no—
68C2×C5×SD16—31no—
69C2×C5×SD16—31no—
70C2×C5×SD16—31no—
71C2×C5×SD16—31no—
72C2×C5×SD16—31no—
73C2×C5×SD16—61no—
74C2×C5×SD16—61no—
75C2×C5×SD16—61no—
76C2×C5×SD16—61no—
77C22×C5×C8—31no—
78C22×C5×C8C2×D311yescharacteristic, complemented
79C5×C4⋊Q8—31no—
80C5×C4⋊Q8—61no—
81C5×#127—31no—
82C5×C22⋊Q8—31no—
83C5×C22⋊Q8—31no—
84C5×C22⋊Q8—61no—
85C5×C22⋊Q8—61no—
86C5×#121—31no—
87C5×#121—31no—
88C5×#121—61no—
89C5×#120—61no—
90C5×#120—61no—
91C4×C5×Q8—31no—
92C4×C5×D4—31no—
93C4×C5×D4—31no—
94C4×C5×D4—61no—
95C5×#106—31no—
96C5×C4⋊C8—31no—
97C5×#103—31no—
98C5×#103—31no—
99C5×#103—31no—
100C5×#102—31no—
101C5×#102—31no—
102C5×#102—31no—
103C5×C22⋊C8—31no—
104C5×C22⋊C8—31no—
105C4×C5×C8—31no—
106D4×SD16—31noSylow
107C22×C5×D3—81no—
108C2×C5×A4—41no—
109C2×C5×A4C2×D411yescharacteristic
110C5×S4—41no—
111C5×S4SD1612yesdirect product factor
112C3×C5×Q8—41no—
113C3×C5×D4—41no—
114C5×#67—81no—
115C5×D12—41no—
116C4×C5×D3—41no—
117C4×C5×D3—81no—
118C5×Dic6—41no—
119C5×Dic6—81no—
120C3×C5×C8—41no—
121C5×C3⋊C8—41no—
122C22×S4—21no—
123Q8×A4C22×C511yescharacteristic, complemented
124D4×A4C22×C511yescharacteristic
125GL(2,ℤ/4)—21no—
126C4⋊S4C22×C511yescharacteristic
127C4×S4—21no—
128C4×S4C22×C511yescharacteristic
129A4⋊Q8—21no—
130A4⋊Q8C22×C511yescharacteristic, complemented
131D3×SD16—41no—
132C8×A4C22×C511yescharacteristic, complemented
133A4⋊C8C22×C511yescharacteristic, complemented
134C24×C5—21no—
135C24×C5—61no—
136C2×C5×Q8—31no—
137C2×C5×Q8—31no—
138C2×C5×Q8—31no—
139C2×C5×Q8—61no—
140C2×C5×Q8—61no—
141C2×C5×Q8—61no—
142C2×C5×Q8—61no—
143C2×C5×Q8—121no—
144C2×C5×D4—31no—
145C2×C5×D4—31no—
146C2×C5×D4—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—121no—
157C2×C5×D4—122no—
158C2×C5×D4—122no—
159C22×C4×C5—21no—
160C22×C4×C5—31no—
161C22×C4×C5—61no—
162C22×C4×C5—61no—
163C22×C4×C5C22×D311yescharacteristic
164C5×SD16—31no—
165C5×SD16—31no—
166C5×SD16—31no—
167C5×SD16—61no—
168C5×SD16—61no—
169C5×SD16—61no—
170C5×SD16—61no—
171C5×SD16—61no—
172C5×SD16—61no—
173C5×SD16—61no—
174C5×SD16—121no—
175C5×SD16—121no—
176C5×SD16S411yescharacteristic, direct product factor
177C2×C5×C8—31no—
178C2×C5×C8—31no—
179C2×C5×C8—31no—
180C2×C5×C8—31no—
181C2×C5×C8—61no—
182C2×C5×C8—61no—
183C5×C4⋊C4—31no—
184C5×C4⋊C4—31no—
185C5×C4⋊C4—31no—
186C5×C4⋊C4—61no—
187C5×C4⋊C4—61no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4—61no—
191C5×C22⋊C4—31no—
192C5×C22⋊C4—31no—
193C5×C22⋊C4—61no—
194C5×C22⋊C4—61no—
195C5×C22⋊C4—61no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—61no—
198C42×C5—31no—
199C42×C5—61no—
200C22×SD16—31no—
201C22×SD16C5×D311yescharacteristic, complemented
202D4×Q8—31no—
203D42—31no—
204#492—31no—
205#465—31no—
206#465—31no—
207#461—31no—
208#460—31no—
209#450—31no—
210#450—31no—
211#448—31no—
212#448—31no—
213C4×SD16—31no—
214C8×D4—31no—
215C22×C3×C5—81no—
216C2×C5×D3—41no—
217C2×C5×D3—81no—
218C2×C5×D3—162no—
219C5×A4C2×SD1611yescharacteristic, complemented
220C3×C4×C5—41no—
221C3×C4×C5—81no—
222C5×Dic3—41no—
223C5×Dic3—81no—
224C22×A4—21no—
225C2×S4—21no—
226C2×S4—42no—
227C2×S4C5×D411yescharacteristic
228D3×Q8—41no—
229D3×D4—41no—
230C4×A4—21no—
231C4×A4C23×C511yescharacteristic
232SL(2,ℤ/4)—21no—
233SL(2,ℤ/4)C5×D411yescharacteristic
234C3×SD16—41no—
235#215—41no—
236#214—41no—
237#204—41no—
238D3×C8—41no—
239C23×C5—31no—
240C23×C5—41no—
241C23×C5—61no—
242C23×C5—61no—
243C23×C5—61no—
244C23×C5—121no—
245C23×C5—121no—
246C23×C5—122no—
247C23×C5—121no—
248C23×C5—241no—
249C23×C5D3×D411yescharacteristic
250C5×Q8—31no—
251C5×Q8—61no—
252C5×Q8—61no—
253C5×Q8—61no—
254C5×Q8—61no—
255C5×Q8—121no—
256C5×Q8—121no—
257C5×Q8C2×S411yescharacteristic, complemented
258C5×D4—32no—
259C5×D4—32no—
260C5×D4—31no—
261C5×D4—61no—
262C5×D4—61no—
263C5×D4—61no—
264C5×D4—61no—
265C5×D4—122no—
266C5×D4—121no—
267C5×D4—121no—
268C5×D4—121no—
269C5×D4—122no—
270C5×D4—121no—
271C5×D4—241no—
272C5×D4C2×S411yescharacteristic
273C2×C4×C5—31no—
274C2×C4×C5—31no—
275C2×C4×C5—31no—
276C2×C4×C5—31no—
277C2×C4×C5—31no—
278C2×C4×C5—61no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—121no—
286C2×C4×C5—122no—
287C2×C4×C5—121no—
288C5×C8—31no—
289C5×C8—61no—
290C5×C8—61no—
291C5×C8C2×S411yescharacteristic, complemented
292C22×Q8—31no—
293C22×Q8C2×C5×D311yescharacteristic, complemented
294C22×D4—31no—
295C22×D4—61no—
296C22×D4C2×C5×D311yescharacteristic
297C2×SD16—31no—
298C2×SD16—31no—
299C2×SD16—31no—
300C2×SD16—31no—
301C2×SD16—31no—
302C2×SD16—31no—
303C2×SD16—31no—
304C2×SD16—31no—
305C2×SD16—31no—
306C2×SD16—61no—
307C2×SD16—61no—
308C2×SD16—61no—
309C2×SD16—61no—
310C22×C8—31no—
311C22×C8C2×C5×D311yescharacteristic, complemented
312C4⋊Q8—31no—
313C4⋊Q8—61no—
314#127—31no—
315C22⋊Q8—31no—
316C22⋊Q8—31no—
317C22⋊Q8—61no—
318C22⋊Q8—61no—
319#121—31no—
320#121—31no—
321#121—61no—
322#120—61no—
323#120—61no—
324C4×Q8—31no—
325C4×D4—31no—
326C4×D4—31no—
327C4×D4—61no—
328#106—31no—
329C4⋊C8—31no—
330#103—31no—
331#103—31no—
332#103—31no—
333#102—31no—
334#102—31no—
335#102—31no—
336C22⋊C8—31no—
337C22⋊C8—31no—
338C4×C8—31no—
339C2×C3×C5—41no—
340C2×C3×C5—161no—
341C5×D3—42no—
342C5×D3—161no—
343C22×D3—81no—
344C2×A4—41no—
345C2×A4C2×C5×D411yescharacteristic
346S4—41no—
347S4C5×SD1612yesdirect product factor
348C3×Q8—41no—
349C3×D4—41no—
350#67—81no—
351D12—41no—
352C4×D3—41no—
353C4×D3—81no—
354Dic6—41no—
355Dic6—81no—
356C3×C8—41no—
357C3⋊C8—41no—
358C22×C5—21no—
359C22×C5—31no—
360C22×C5—31no—
361C22×C5—32no—
362C22×C5—61no—
363C22×C5—61no—
364C22×C5—61no—
365C22×C5—121no—
366C22×C5—121no—
367C22×C5—121no—
368C22×C5—121no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5—121no—
372C22×C5—242no—
373C22×C5—242no—
374C22×C5D3×SD1611yescharacteristic, complemented
375C4×C5—21no—
376C4×C5—32no—
377C4×C5—31no—
378C4×C5—61no—
379C4×C5—61no—
380C4×C5—61no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5C22×S411yescharacteristic
385C24—21no—
386C24—61no—
387C2×Q8—31no—
388C2×Q8—31no—
389C2×Q8—31no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—121no—
395C2×D4—31no—
396C2×D4—31no—
397C2×D4—31no—
398C2×D4—31no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—121no—
408C2×D4—122no—
409C2×D4—122no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4C22×C5×D311yescharacteristic
415SD16—31no—
416SD16—31no—
417SD16—31no—
418SD16—61no—
419SD16—61no—
420SD16—61no—
421SD16—61no—
422SD16—61no—
423SD16—61no—
424SD16—61no—
425SD16—121no—
426SD16—121no—
427SD16C5×S411yescharacteristic, direct product factor
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—31no—
431C2×C8—31no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—31no—
435C4⋊C4—31no—
436C4⋊C4—31no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C22⋊C4—31no—
443C22⋊C4—31no—
444C22⋊C4—61no—
445C22⋊C4—61no—
446C22⋊C4—61no—
447C22⋊C4—61no—
448C22⋊C4—61no—
449C42—31no—
450C42—61no—
451C3×C5—41noHall
452C22×C3—81no—
453C2×D3—41no—
454C2×D3—81no—
455C2×D3—162no—
456A4C2×C5×SD1611yescharacteristic, complemented
457C3×C4—41no—
458C3×C4—81no—
459Dic3—41no—
460Dic3—81no—
461C2×C5—31no—
462C2×C5—31no—
463C2×C5—41no—
464C2×C5—62no—
465C2×C5—121no—
466C2×C5—241no—
467C2×C5D4×S411yescharacteristic
468C23—31no—
469C23—41no—
470C23—61no—
471C23—61no—
472C23—61no—
473C23—121no—
474C23—121no—
475C23—122no—
476C23—121no—
477C23—241no—
478C23C5×D3×D411yescharacteristic
479Q8—31no—
480Q8—61no—
481Q8—61no—
482Q8—61no—
483Q8—61no—
484Q8—121no—
485Q8—121no—
486Q8C2×C5×S411yescharacteristic, complemented
487D4—32no—
488D4—32no—
489D4—31no—
490D4—61no—
491D4—61no—
492D4—61no—
493D4—61no—
494D4—122no—
495D4—121no—
496D4—121no—
497D4—121no—
498D4—122no—
499D4—121no—
500D4—241no—
501D4C2×C5×S411yescharacteristic
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—31no—
506C2×C4—31no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—121no—
515C2×C4—122no—
516C2×C4—121no—
517C8—31no—
518C8—61no—
519C8—61no—
520C8C2×C5×S411yescharacteristic, complemented
521C2×C3—41no—
522C2×C3—161no—
523D3—42no—
524D3—161no—
525C5SD16×S411yescharacteristic, direct product factor, Sylow
526C22—21no—
527C22—31no—
528C22—31no—
529C22—32no—
530C22—61no—
531C22—61no—
532C22—61no—
533C22—121no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22—121no—
539C22—121no—
540C22—242no—
541C22—242no—
542C22C5×D3×SD1611yescharacteristic, complemented
543C4—21no—
544C4—32no—
545C4—31no—
546C4—61no—
547C4—61no—
548C4—61no—
549C4—121no—
550C4—121no—
551C4—121no—
552C4C22×C5×S411yescharacteristic
553C3—41noSylow
554C2—31no—
555C2—31no—
556C2—41no—
557C2—62no—
558C2—121no—
559C2—241no—
560C2C5×D4×S411yescharacteristic
subgroupG/H
centerC2×C5D4×S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×SD16D3
socleC23×C5D3×D4
prime radicalC5×D4×S4C2
hypercenterC5×SD16S4
hypocenterA4C2×C5×SD16
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×SD16

Complements

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

NH ≅ G/Ntype
1. C5×Q8×S4C2semidirect
3. C5×A4×SD16C2semidirect
4. C5×#5417C2semidirect
5. C5×#5414C2semidirect
6. C5×#5401C2semidirect
7. C5×C8×S4C2semidirect
10. C5×Q8×A4C22semidirect
17. C5×A4⋊Q8C22semidirect
19. C5×C8×A4C22semidirect
20. C5×A4⋊C8C22semidirect
21. SD16×S4C5direct (N × H)
23. C22×C5×SD16D3semidirect
52. Q8×S4C2×C5semidirect
54. A4×SD16C2×C5semidirect
55. #5417C2×C5semidirect
56. #5414C2×C5semidirect
57. #5401C2×C5semidirect
58. C8×S4C2×C5semidirect
60. C22×C5×Q8C2×D3semidirect
78. C22×C5×C8C2×D3semidirect
111. C5×S4SD16direct (N × H)
123. Q8×A4C22×C5semidirect
130. A4⋊Q8C22×C5semidirect
132. C8×A4C22×C5semidirect
133. A4⋊C8C22×C5semidirect
176. C5×SD16S4direct (N × H)
201. C22×SD16C5×D3semidirect
219. C5×A4C2×SD16semidirect
257. C5×Q8C2×S4semidirect
291. C5×C8C2×S4semidirect
293. C22×Q8C2×C5×D3semidirect
311. C22×C8C2×C5×D3semidirect
347. S4C5×SD16direct (N × H)
374. C22×C5D3×SD16semidirect
427. SD16C5×S4direct (N × H)
456. A4C2×C5×SD16semidirect
486. Q8C2×C5×S4semidirect
520. C8C2×C5×S4semidirect
525. C5SD16×S4direct (N × H)
542. C22C5×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×S42
C5×D4×S42
C5×A4×SD162
C5×#54172
C5×#54142
C5×#54012
C5×C8×S42
C5×D4×SD163
C5×D3×SD164
SD16×S45