Finite Group Databasebeta

← S4×C22⋊Dic5 #14513648

Subgroups — S4×C22⋊Dic5 #14513648

Order 1920.

1314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 1314 conjugacy classes of subgroups — too many to draw. Only its 103 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
2C2×Dic5×S4C212yesmaximal, complemented
3A4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4#11752151C211yesmaximal, characteristic, complemented
5(C2×S4)⋊Dic5C212yesmaximal, complemented
6D4×C22⋊Dic5—31nomaximal, Hall
7C23×C5×A4C2211yescharacteristic
8C22×C5×S4—24no—
9C22×C5×S4C414yescomplemented
10C22×C5×S4C2211yescharacteristic
11C22×C5×S4C2211yescharacteristic
12C2×A4×Dic5C2212yescomplemented
13C2×A4⋊Dic5C2212yescomplemented
14Dic5×S4—24no—
15D3×C22⋊Dic5—41nomaximal
16C22⋊C4×S4—51nomaximal, Hall
17C23×C5×D4—31no—
18C22×C22⋊Dic5—31no—
19C22×C22⋊Dic5D311yescharacteristic, complemented
20C2×D4×Dic5—32no—
21#65536—31no—
22#65536—31no—
23#65510—32no—
24#65509—32no—
25#65509—32no—
26#65501—31no—
27C4×C22⋊Dic5—31no—
28C23×C5×D3—41no—
29C22×C5×A4—22no—
30C22×C5×A4C2×C412yescomplemented
31C22×C5×A4C2311yescharacteristic
32C2×C5×S4—22no—
33C2×C5×S4—28no—
34C2×C5×S4C2×C412yes—
35C2×C5×S4C2×C412yescomplemented
36C2×C5×S4D414yes—
37C2×D3×Dic5—42no—
38A4×Dic5—22no—
39A4⋊Dic5—22no—
40#6719—41no—
41C3×C22⋊Dic5—41no—
42(C2×D3)⋊Dic5—42no—
43C23×S4D511yescharacteristic
44C2×C4×S4—52no—
45A4×C22⋊C4—51no—
46#5432—51no—
47(C2×S4)⋊C4—52no—
48C25×C5—31no—
49C25×C5C2×D311yescharacteristic
50C22×C5×D4—31no—
51C22×C5×D4—31no—
52C22×C5×D4—31no—
53C22×C5×D4—34no—
54C22×C5×D4—34no—
55C22×C5×D4—31no—
56C22×C5×D4—64no—
57C22×C5×D4—64no—
58C23×C4×C5—31no—
59C23×Dic5—32no—
60C23×Dic5C2×D312yescomplemented
61C2×C22⋊Dic5—31no—
62C2×C22⋊Dic5—31no—
63C2×C22⋊Dic5—32no—
64C2×C22⋊Dic5—31no—
65C2×C22⋊Dic5—32no—
66C2×C22⋊Dic5—31no—
67C2×C22⋊Dic5—32no—
68C2×C22⋊Dic5—32no—
69C2×C22⋊Dic5—32no—
70C2×C22⋊Dic5—32no—
71C2×C22⋊Dic5—61no—
72C2×C22⋊Dic5—62no—
73C2×C22⋊Dic5—61no—
74D4×Dic5—64no—
75D4×Dic5—64no—
76C2×C4⋊Dic5—32no—
77C2×C4×Dic5—32no—
78#3963—32no—
79#3963—32no—
80D4×C22⋊C4—151noSylow
81C23×C3×C5—41no—
82C22×C5×D3—41no—
83C22×C5×D3—41no—
84C22×C5×D3—44no—
85C22×C5×D3—84no—
86C2×C5×A4—22no—
87C2×C5×A4C22×C411yescharacteristic
88C2×C5×A4C2×D412yes—
89C5×S4—22no—
90C5×S4C22⋊C414yescomplemented
91C2×Dic15—42no—
92C2×C3×Dic5—42no—
93D3×Dic5—84no—
94C23×A4C2×D511yescharacteristic
95C22×S4—24no—
96C22×S4Dic514yescomplemented
97C22×S4C2×D511yescharacteristic
98C22×S4C2×D511yescharacteristic
99C2×C4×A4—52no—
100C2×SL(2,ℤ/4)—52no—
101C4×S4—104no—
102D3×C22⋊C4—201no—
103C24×C5—22no—
104C24×C5—31no—
105C24×C5—31no—
106C24×C5—31no—
107C24×C5—32no—
108C24×C5—31no—
109C24×C5—34no—
110C24×C5—62no—
111C24×C5—61no—
112C24×C5—64no—
113C24×C5—62no—
114C24×C5—61no—
115C24×C5—122no—
116C24×C5C4×D312yescomplemented
117C24×C5C22×D311yescharacteristic
118C2×C5×D4—32no—
119C2×C5×D4—34no—
120C2×C5×D4—32no—
121C2×C5×D4—34no—
122C2×C5×D4—34no—
123C2×C5×D4—32no—
124C2×C5×D4—34no—
125C2×C5×D4—32no—
126C2×C5×D4—64no—
127C2×C5×D4—68no—
128C2×C5×D4—68no—
129C2×C5×D4—616no—
130C2×C5×D4—62no—
131C2×C5×D4—64no—
132C2×C5×D4—62no—
133C22×C4×C5—31no—
134C22×C4×C5—34no—
135C22×C4×C5—31no—
136C22×C4×C5—64no—
137C22×Dic5—22no—
138C22×Dic5—32no—
139C22×Dic5—32no—
140C22×Dic5—32no—
141C22×Dic5—32no—
142C22×Dic5—62no—
143C22×Dic5—62no—
144C22×Dic5—64no—
145C22×Dic5—62no—
146C22×Dic5—122no—
147C22⋊Dic5—31no—
148C22⋊Dic5—32no—
149C22⋊Dic5—61no—
150C22⋊Dic5—62no—
151C22⋊Dic5—62no—
152C22⋊Dic5—61no—
153C22⋊Dic5—64no—
154C22⋊Dic5—62no—
155C22⋊Dic5—62no—
156C22⋊Dic5—61no—
157C22⋊Dic5—62no—
158C22⋊Dic5—122no—
159C22⋊Dic5—122no—
160C22⋊Dic5S411yescharacteristic, direct product factor
161C4⋊Dic5—64no—
162C4×Dic5—64no—
163C23×D4—31no—
164C2×C4×D4—152no—
165C22×C22⋊C4—51no—
166C22×C22⋊C4—151no—
167#390—152no—
168#386—152no—
169#386—152no—
170#380—151no—
171#379—151no—
172#379—151no—
173C4×C22⋊C4—151no—
174C22×C3×C5—42no—
175C22×C3×C5—41no—
176C22×C3×C5—82no—
177C2×C5×D3—44no—
178C2×C5×D3—42no—
179C2×C5×D3—42no—
180C2×C5×D3—88no—
181C2×C5×D3—82no—
182C5×A4C2×C22⋊C411yescharacteristic, complemented
183Dic15—82no—
184C3×Dic5—82no—
185C23×D3—41no—
186C22×A4—22no—
187C22×A4C2×Dic512yescomplemented
188C22×A4C22×D511yescharacteristic
189C2×S4—22no—
190C2×S4—28no—
191C2×S4C2×Dic512yes—
192C2×S4C2×Dic512yescomplemented
193C2×S4C22⋊D514yes—
194C2×C4×D3—202no—
195C4×A4—102no—
196SL(2,ℤ/4)—102no—
197C3×C22⋊C4—201no—
198#217—201no—
199(C2×D3)⋊C4—202no—
200C23×C5—22no—
201C23×C5—31no—
202C23×C5—32no—
203C23×C5—31no—
204C23×C5—34no—
205C23×C5—32no—
206C23×C5—32no—
207C23×C5—32no—
208C23×C5—32no—
209C23×C5—31no—
210C23×C5—32no—
211C23×C5—62no—
212C23×C5—62no—
213C23×C5—61no—
214C23×C5—62no—
215C23×C5—62no—
216C23×C5—61no—
217C23×C5—62no—
218C23×C5—64no—
219C23×C5—62no—
220C23×C5—62no—
221C23×C5—62no—
222C23×C5—68no—
223C23×C5—61no—
224C23×C5—64no—
225C23×C5—61no—
226C23×C5—64no—
227C23×C5—61no—
228C23×C5—124no—
229C23×C5—122no—
230C23×C5—124no—
231C23×C5—128no—
232C23×C5—124no—
233C23×C5C2×C4×D311yescharacteristic
234C23×C5D3×D412yes—
235C23×C5C2×S411yescharacteristic
236C5×D4—34no—
237C5×D4—38no—
238C5×D4—34no—
239C5×D4—68no—
240C5×D4—62no—
241C5×D4—64no—
242C5×D4—68no—
243C5×D4—62no—
244C2×C4×C5—34no—
245C2×C4×C5—32no—
246C2×C4×C5—32no—
247C2×C4×C5—68no—
248C2×C4×C5—62no—
249C2×Dic5—32no—
250C2×Dic5—62no—
251C2×Dic5—62no—
252C2×Dic5—62no—
253C2×Dic5—62no—
254C2×Dic5—62no—
255C2×Dic5—62no—
256C2×Dic5—62no—
257C2×Dic5—62no—
258C2×Dic5—62no—
259C2×Dic5—62no—
260C2×Dic5—124no—
261C2×Dic5—124no—
262C2×Dic5C2×S412yescomplemented
263C25—31no—
264C25D3×D511yescharacteristic
265C22×D4—31no—
266C22×D4—34no—
267C22×D4—31no—
268C22×D4—31no—
269C22×D4—34no—
270C22×D4—31no—
271C22×D4—64no—
272C22×D4—64no—
273C23×C4—31no—
274C23×C4—52no—
275C23×C4—152no—
276C4×D4—304no—
277C4×D4—304no—
278C2×C4⋊C4—152no—
279C2×C22⋊C4—151no—
280C2×C22⋊C4—151no—
281C2×C22⋊C4—152no—
282C2×C22⋊C4—151no—
283C2×C22⋊C4—152no—
284C2×C22⋊C4—152no—
285C2×C22⋊C4—151no—
286C2×C22⋊C4—152no—
287C2×C22⋊C4—152no—
288C2×C22⋊C4—152no—
289C2×C22⋊C4—301no—
290C2×C22⋊C4—302no—
291C2×C22⋊C4—301no—
292C2×C42—152no—
293#95—152no—
294#95—152no—
295C2×C3×C5—41no—
296C2×C3×C5—42no—
297C2×C3×C5—82no—
298C5×D3—44no—
299C5×D3—82no—
300C23×C3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—44no—
304C22×D3—84no—
305C2×A4—22no—
306C2×A4C22×Dic511yescharacteristic
307C2×A4C2×C22⋊D512yes—
308S4—22no—
309S4C22⋊Dic514yesdirect product factor
310C2×C3×C4—202no—
311C2×Dic3—202no—
312C4×D3—404no—
313C22×C5—22no—
314C22×C5—31no—
315C22×C5—32no—
316C22×C5—31no—
317C22×C5—31no—
318C22×C5—32no—
319C22×C5—32no—
320C22×C5—34no—
321C22×C5—32no—
322C22×C5—62no—
323C22×C5—64no—
324C22×C5—62no—
325C22×C5—61no—
326C22×C5—62no—
327C22×C5—62no—
328C22×C5—64no—
329C22×C5—62no—
330C22×C5—62no—
331C22×C5—62no—
332C22×C5—62no—
333C22×C5—64no—
334C22×C5—62no—
335C22×C5—62no—
336C22×C5—128no—
337C22×C5—122no—
338C22×C5—122no—
339C22×C5—128no—
340C22×C5—122no—
341C22×C5D3×C22⋊C411yescharacteristic, complemented
342C22×C5C4×S412yescomplemented
343C22×C5C22×S411yescharacteristic
344C4×C5—34no—
345C4×C5—62no—
346Dic5—22no—
347Dic5—62no—
348Dic5—122no—
349Dic5—122no—
350C24—22no—
351C24—31no—
352C24—31no—
353C24—31no—
354C24—32no—
355C24—31no—
356C24—34no—
357C24—62no—
358C24—61no—
359C24—64no—
360C24—62no—
361C24—61no—
362C24—122no—
363C24D3×Dic512yescomplemented
364C24C2×D3×D511yescharacteristic
365C2×D4—34no—
366C2×D4—32no—
367C2×D4—32no—
368C2×D4—34no—
369C2×D4—34no—
370C2×D4—32no—
371C2×D4—34no—
372C2×D4—32no—
373C2×D4—64no—
374C2×D4—68no—
375C2×D4—68no—
376C2×D4—616no—
377C2×D4—62no—
378C2×D4—64no—
379C2×D4—62no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—34no—
383C22×C4—64no—
384C22×C4—102no—
385C22×C4—152no—
386C22×C4—152no—
387C22×C4—152no—
388C22×C4—152no—
389C22×C4—302no—
390C22×C4—302no—
391C22×C4—302no—
392C22×C4—304no—
393C22×C4—602no—
394C4⋊C4—304no—
395C22⋊C4—51no—
396C22⋊C4—152no—
397C22⋊C4—151no—
398C22⋊C4—302no—
399C22⋊C4—301no—
400C22⋊C4—302no—
401C22⋊C4—301no—
402C22⋊C4—304no—
403C22⋊C4—302no—
404C22⋊C4—302no—
405C22⋊C4—302no—
406C22⋊C4—301no—
407C22⋊C4—602no—
408C22⋊C4—602no—
409C42—304no—
410C3×C5—41noHall
411C22×C3—41no—
412C22×C3—42no—
413C22×C3—82no—
414C2×D3—44no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—88no—
418C2×D3—82no—
419A4C2×C22⋊Dic511yescharacteristic, complemented
420C3×C4—402no—
421Dic3—402no—
422C2×C5—22no—
423C2×C5—32no—
424C2×C5—31no—
425C2×C5—31no—
426C2×C5—62no—
427C2×C5—64no—
428C2×C5—122no—
429C2×C5C2×C4×S411yescharacteristic
430C2×C5D4×S412yes—
431C23—22no—
432C23—31no—
433C23—32no—
434C23—31no—
435C23—34no—
436C23—32no—
437C23—32no—
438C23—31no—
439C23—32no—
440C23—32no—
441C23—32no—
442C23—62no—
443C23—62no—
444C23—61no—
445C23—62no—
446C23—62no—
447C23—61no—
448C23—62no—
449C23—64no—
450C23—62no—
451C23—62no—
452C23—62no—
453C23—68no—
454C23—61no—
455C23—64no—
456C23—61no—
457C23—61no—
458C23—64no—
459C23—124no—
460C23—122no—
461C23—124no—
462C23—128no—
463C23—124no—
464C23C2×D3×Dic511yescharacteristic
465C23D3×C22⋊D512yes—
466C23D5×S411yescharacteristic
467D4—34no—
468D4—38no—
469D4—34no—
470D4—68no—
471D4—62no—
472D4—64no—
473D4—68no—
474D4—62no—
475C2×C4—34no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—52no—
479C2×C4—68no—
480C2×C4—62no—
481C2×C4—152no—
482C2×C4—302no—
483C2×C4—302no—
484C2×C4—302no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4—302no—
492C2×C4—604no—
493C2×C4—604no—
494C2×C3—41no—
495C2×C3—42no—
496C2×C3—82no—
497D3—44no—
498D3—82no—
499C5C22⋊C4×S411yescharacteristic, complemented, Sylow
500C22—22no—
501C22—31no—
502C22—32no—
503C22—31no—
504C22—31no—
505C22—32no—
506C22—32no—
507C22—34no—
508C22—32no—
509C22—62no—
510C22—64no—
511C22—62no—
512C22—61no—
513C22—62no—
514C22—62no—
515C22—64no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—62no—
520C22—64no—
521C22—62no—
522C22—62no—
523C22—128no—
524C22—122no—
525C22—122no—
526C22—128no—
527C22—122no—
528C22D3×C22⋊Dic511yescharacteristic, complemented
529C22Dic5×S412yescomplemented
530C22C2×D5×S411yescharacteristic
531C4—34no—
532C4—62no—
533C4—102no—
534C4—302no—
535C4—602no—
536C4—602no—
537C3—41noSylow
538C2—22no—
539C2—31no—
540C2—32no—
541C2—31no—
542C2—62no—
543C2—64no—
544C2—122no—
545C2C2×Dic5×S411yescharacteristic
546C2S4×C22⋊D512yes—
subgroupG/H
center, FrattiniC22C2×D5×S4
commutatorC2×C5×A4C22×C4
FittingC25×C5C2×D3
socleC24×C5C22×D3
prime radicalC23×C5×S4C2
cosocleC22×C5×A4C23
hypercenterC23D5×S4
hypocenterC5×A4C2×C22⋊C4
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×Dic5×S4C2semidirect
3. A4×C22⋊Dic5C2semidirect
4. #11752151C2semidirect
5. (C2×S4)⋊Dic5C2semidirect
9. C22×C5×S4C4semidirect
12. C2×A4×Dic5C22semidirect
13. C2×A4⋊Dic5C22semidirect
19. C22×C22⋊Dic5D3semidirect
30. C22×C5×A4C2×C4semidirect
35. C2×C5×S4C2×C4semidirect
60. C23×Dic5C2×D3semidirect
90. C5×S4C22⋊C4semidirect
96. C22×S4Dic5semidirect
116. C24×C5C4×D3semidirect
160. C22⋊Dic5S4direct (N × H)
182. C5×A4C2×C22⋊C4semidirect
187. C22×A4C2×Dic5semidirect
192. C2×S4C2×Dic5semidirect
262. C2×Dic5C2×S4semidirect
309. S4C22⋊Dic5direct (N × H)
341. C22×C5D3×C22⋊C4semidirect
342. C22×C5C4×S4semidirect
363. C24D3×Dic5semidirect
419. A4C2×C22⋊Dic5semidirect
499. C5C22⋊C4×S4semidirect
528. C22D3×C22⋊Dic5semidirect
529. C22Dic5×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×Dic5×S42
A4×C22⋊Dic52
#117521512
(C2×S4)⋊Dic52
D4×C22⋊Dic53
D3×C22⋊Dic54
C22⋊C4×S45