Finite Group Databasebeta

← C2×#11756747 #14514432

Subgroups — C2×#11756747 #14514432

Order 1920.

1690 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1690 conjugacy classes of subgroups — too many to draw. Only its 143 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×A4×Dic10C211yesmaximal, characteristic, complemented
2C2×C4⋊(C5⋊S4)C211yesmaximal, characteristic, complemented
3C2×C4×C5×S4C211yesmaximal, characteristic, complemented
4C2×#91902C212yesmaximal, complemented
5C2×#91901C212yesmaximal, complemented
6#11756747C218yesmaximal, direct product factor
7C2×#65886—31nomaximal, Hall
8C22×C5⋊S4C2212yes—
9C22×C5×S4C2211yescharacteristic
10C2×C4×C5×A4C2211yescharacteristic
11C2×#6769—41nomaximal
12C2×A4×Dic5C2212yes—
13A4×Dic10C2214yescomplemented
14C4⋊(C5⋊S4)C2214yescomplemented
15C2×C5×SL(2,ℤ/4)C2211yescharacteristic
16C4×C5×S4C2214yescomplemented
17#91902C2218yescomplemented
18#91901C2218yescomplemented
19C2×#5919—51nomaximal, Hall
20C22×#709—31no—
21C23×Dic10D311yescharacteristic, complemented
22C2×C4×C5×D4—31no—
23C2×#4085—32no—
24C2×#4076—31no—
25C2×#4070—31no—
26#65886—38no—
27#65886—38no—
28C2×#4042—32no—
29C2×#4031—32no—
30C2×#4027—32no—
31C2×#4021—31no—
32C2×C4×Dic10—31no—
33C22×C5×A4C2311yescharacteristic
34C2×C5⋊S4—24no—
35C2×C5⋊S4C2314yes—
36C2×C5×S4—22no—
37C2×C5×S4C2312yes—
38C2×D60—41no—
39C2×C4×C5×D3—41no—
40C2×C3×Dic10—41no—
41C4×C5×A4C2312yes—
42C2×#1203—42no—
43C2×#1200—42no—
44#6769—48no—
45A4×Dic5C2314yes—
46C5×SL(2,ℤ/4)C2312yes—
47C2×Q8×A4—51no—
48#5919—58no—
49C2×C4⋊S4—52no—
50C2×C4⋊S4—51no—
51C2×C4×S4—52no—
52C2×C4×S4D511yescharacteristic, complemented
53C22×C5×D4—31no—
54C23×C4×C5—31no—
55C23×C4×C5C2×D311yescharacteristic
56C22×C22⋊D5—32no—
57C22×C22⋊D5—32no—
58C23×Dic5C2×D312yes—
59C2×#709—38no—
60C2×#709—61no—
61C2×#709—62no—
62C2×#709—64no—
63C2×#709—61no—
64C22×D20—31no—
65C22×C4×D5—32no—
66C22×Dic10—31no—
67C22×Dic10—31no—
68C22×Dic10—32no—
69C22×Dic10—34no—
70C22×Dic10C2×D314yescomplemented
71C4×C5×D4—34no—
72C4×C5×D4—34no—
73C2×C5×C4⋊C4—31no—
74C2×C5×C22⋊C4—31no—
75C2×C5×C22⋊C4—31no—
76C2×C42×C5—31no—
77C2×C22⋊Dic5—32no—
78#4085—38no—
79#4085—38no—
80#4076—34no—
81#4076—34no—
82C2×#685—32no—
83C2×#685—32no—
84C2×#685—32no—
85C2×C4⋊Dic5—31no—
86#4070—38no—
87C2×#683—32no—
88C2×#683—32no—
89C2×C4×Dic5—32no—
90#4042—316no—
91#4031—316no—
92#4027—38no—
93#4027—38no—
94#4021—38no—
95C4×Dic10—38no—
96C2×#548—151noSylow
97C22×D15—42no—
98C22×C5×D3—41no—
99C2×C5×A4#4112yescomplemented
100C2×C5×A4C2411yescharacteristic
101C5⋊S4—24no—
102C5×S4—22no—
103C2×C3×C4×C5—41no—
104D60—44no—
105C2×C5×Dic3—41no—
106C4×C5×D3—44no—
107C2×C3×Dic5—42no—
108C3×Dic10—44no—
109#1203—48no—
110#1200—48no—
111C22×S4—52no—
112C22×S4C2×D511yescharacteristic
113C2×#239—201no—
114Q8×A4—54no—
115C2×C4×A4—52no—
116C2×C4×A4C2×D511yescharacteristic
117C2×SL(2,ℤ/4)C2×D511yescharacteristic
118C4⋊S4—58no—
119C4⋊S4—54no—
120C4×S4—58no—
121C4×S4C2×D514yescomplemented
122C24×C5—31no—
123C24×C5C22×D311yescharacteristic
124C23×D5—32no—
125C2×C5×D4—32no—
126C2×C5×D4—32no—
127C2×C5×D4—62no—
128C2×C5×D4—62no—
129C22×C4×C5—31no—
130C22×C4×C5—31no—
131C22×C4×C5—32no—
132C22×C4×C5—31no—
133C22×C4×C5—31no—
134C22×C4×C5—31no—
135C22×C4×C5—34no—
136C22×C4×C5—61no—
137C22×C4×C5—62no—
138C22×C4×C5—61no—
139C22×C4×C5C22×D312yes—
140C2×C22⋊D5—38no—
141C2×C22⋊D5—34no—
142C2×C22⋊D5—34no—
143C2×C22⋊D5—62no—
144C2×C22⋊D5—64no—
145C2×C22⋊D5—64no—
146C2×C22⋊D5—64no—
147C2×C22⋊D5—62no—
148C22×Dic5—32no—
149C22×Dic5—32no—
150C22×Dic5—34no—
151C22×Dic5—32no—
152C22×Dic5C22×D314yes—
153#709—68no—
154#709—616no—
155#709—68no—
156C2×D20—34no—
157C2×D20—61no—
158C2×D20—62no—
159C2×D20—61no—
160C2×C4×D5—38no—
161C2×C4×D5—62no—
162C2×C4×D5—64no—
163C2×C4×D5—62no—
164C2×Dic10—31no—
165C2×Dic10—32no—
166C2×Dic10—34no—
167C2×Dic10—34no—
168C2×Dic10—34no—
169C2×Dic10—38no—
170C2×Dic10—64no—
171C2×Dic10—62no—
172C2×Dic10—61no—
173C2×Dic10S411yescharacteristic, complemented
174C5×C4⋊C4—34no—
175C5×C22⋊C4—32no—
176C5×C22⋊C4—34no—
177C5×C22⋊C4—32no—
178C42×C5—34no—
179C22⋊Dic5—38no—
180#685—38no—
181#685—38no—
182#685—38no—
183C4⋊Dic5—34no—
184#683—38no—
185#683—38no—
186C4×Dic5—38no—
187C22×#41—151no—
188C23×Q8—51no—
189#548—158no—
190#548—158no—
191C2×#124—151no—
192C2×#124—152no—
193C2×C22⋊Q8—152no—
194C2×C22⋊Q8—151no—
195C2×#121—152no—
196C2×#121—151no—
197C2×C4×Q8—151no—
198C2×C4×D4—31no—
199C2×C4×D4—152no—
200C22×C3×C5—41no—
201C2×D15—44no—
202C2×D15—84no—
203C2×C5×D3—42no—
204C2×C5×D3—82no—
205C5×A4C2×#4111yescharacteristic, complemented
206C3×C4×C5—42no—
207C3×Dic5—44no—
208C5×Dic3—42no—
209C22×A4C22×D511yescharacteristic
210C2×S4—22no—
211C2×S4—54no—
212C2×S4—104no—
213C2×S4C22×D512yes—
214C2×C3×Q8—201no—
215#239—208no—
216C2×D12—201no—
217C2×D12—202no—
218C2×C4×D3—41no—
219C2×C4×D3—202no—
220C4×A4—54no—
221C4×A4C22×D512yes—
222SL(2,ℤ/4)C22×D512yes—
223C23×C5—31no—
224C23×C5—31no—
225C23×C5—32no—
226C23×C5—32no—
227C23×C5—61no—
228C23×C5—62no—
229C23×C5—62no—
230C23×C5—61no—
231C23×C5#23912yescomplemented
232C23×C5C23×D311yescharacteristic
233C22×D5—34no—
234C22×D5—62no—
235C22×D5—64no—
236C22×D5—64no—
237C22×D5—62no—
238C5×D4—64no—
239C5×D4—62no—
240C5×D4—62no—
241C2×C4×C5—31no—
242C2×C4×C5—32no—
243C2×C4×C5—32no—
244C2×C4×C5—32no—
245C2×C4×C5—32no—
246C2×C4×C5—32no—
247C2×C4×C5—32no—
248C2×C4×C5—61no—
249C2×C4×C5—64no—
250C2×C4×C5—61no—
251C2×C4×C5—62no—
252C2×C4×C5—62no—
253C2×C4×C5—61no—
254C2×C4×C5—64no—
255C2×C4×C5C2×S411yescharacteristic
256C22⋊D5—68no—
257C22⋊D5—68no—
258C22⋊D5—64no—
259C22⋊D5—64no—
260C22⋊D5—68no—
261C2×Dic5—32no—
262C2×Dic5—34no—
263C2×Dic5—34no—
264C2×Dic5—34no—
265C2×Dic5—34no—
266C2×Dic5—62no—
267C2×Dic5—64no—
268C2×Dic5C2×S412yes—
269D20—64no—
270D20—64no—
271C4×D5—68no—
272C4×D5—68no—
273Dic10—34no—
274Dic10—38no—
275Dic10—64no—
276Dic10C2×S414yescomplemented
277C2×#41—158no—
278C2×#41—301no—
279C2×#41—302no—
280C2×#41—304no—
281C2×#41—301no—
282C22×Q8—54no—
283C22×Q8—151no—
284C22×Q8—151no—
285C22×Q8—152no—
286C22×Q8—154no—
287C22×D4—31no—
288C22×D4—151no—
289C22×D4—152no—
290C22×D4—152no—
291C23×C4—31no—
292C23×C4—52no—
293C23×C4—152no—
294C23×C4D3×D511yescharacteristic
295#124—158no—
296#124—1516no—
297C22⋊Q8—1516no—
298C22⋊Q8—158no—
299#121—154no—
300#121—158no—
301#121—158no—
302#121—154no—
303C4×Q8—158no—
304C4×D4—34no—
305C4×D4—34no—
306C4×D4—158no—
307C4×D4—158no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—152no—
310C2×C4⋊C4—152no—
311C2×C4⋊C4—151no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—31no—
314C2×C22⋊C4—152no—
315C2×C22⋊C4—152no—
316C2×C22⋊C4—152no—
317C2×C22⋊C4—152no—
318C2×C42—31no—
319C2×C42—152no—
320C2×C3×C5—42no—
321C2×C3×C5—41no—
322D15—84no—
323C5×D3—82no—
324C22×D3—41no—
325C22×D3—202no—
326C2×A4#70912yescomplemented
327C2×A4C23×D511yescharacteristic
328S4—22no—
329S4—104no—
330C3×Q8—204no—
331C2×C3×C4—41no—
332C2×C3×C4—202no—
333C2×Dic3—41no—
334D12—204no—
335D12—208no—
336C4×D3—44no—
337C4×D3—208no—
338C22×C5—32no—
339C22×C5—31no—
340C22×C5—32no—
341C22×C5—32no—
342C22×C5—31no—
343C22×C5—31no—
344C22×C5—61no—
345C22×C5—62no—
346C22×C5—62no—
347C22×C5—62no—
348C22×C5—122no—
349C22×C5—122no—
350C22×C5C2×#23911yescharacteristic, complemented
351C22×C5C22×S411yescharacteristic
352C2×D5—64no—
353C2×D5—64no—
354C2×D5—64no—
355C2×D5—124no—
356C2×D5—124no—
357C4×C5—32no—
358C4×C5—62no—
359C4×C5—62no—
360C4×C5—62no—
361C4×C5C22×S412yes—
362Dic5—34no—
363Dic5—64no—
364Dic5C22×S414yes—
365C24—31no—
366C24—152no—
367C24C2×D3×D511yescharacteristic
368#41—308no—
369#41—3016no—
370#41—308no—
371C2×Q8—51no—
372C2×Q8—152no—
373C2×Q8—154no—
374C2×Q8—154no—
375C2×Q8—154no—
376C2×Q8—158no—
377C2×Q8—151no—
378C2×Q8—301no—
379C2×Q8—302no—
380C2×Q8—304no—
381C2×D4—32no—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—62no—
385C2×D4—154no—
386C2×D4—154no—
387C2×D4—158no—
388C2×D4—154no—
389C2×D4—301no—
390C2×D4—302no—
391C2×D4—302no—
392C2×D4—304no—
393C2×D4—302no—
394C2×D4—304no—
395C2×D4—304no—
396C2×D4—301no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—32no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—34no—
404C22×C4—54no—
405C22×C4—61no—
406C22×C4—62no—
407C22×C4—61no—
408C22×C4—158no—
409C22×C4—152no—
410C22×C4—152no—
411C22×C4—154no—
412C22×C4—152no—
413C22×C4—302no—
414C22×C4—304no—
415C22×C4—302no—
416C22×C4C2×D3×D512yes—
417C4⋊C4—34no—
418C4⋊C4—158no—
419C4⋊C4—158no—
420C4⋊C4—154no—
421C22⋊C4—32no—
422C22⋊C4—34no—
423C22⋊C4—32no—
424C22⋊C4—158no—
425C22⋊C4—158no—
426C22⋊C4—158no—
427C22⋊C4—158no—
428C42—34no—
429C42—158no—
430C3×C5—41noHall
431C22×C3—41no—
432C2×D3—42no—
433C2×D3—82no—
434C2×D3—204no—
435C2×D3—404no—
436A4C2×#70911yescharacteristic, complemented
437C3×C4—42no—
438C3×C4—204no—
439Dic3—42no—
440C2×C5—31no—
441C2×C5—31no—
442C2×C5—32no—
443C2×C5—122no—
444C2×C5#591912yescomplemented
445C2×C5C23×S411yescharacteristic
446D5—124no—
447C23—31no—
448C23—31no—
449C23—32no—
450C23—32no—
451C23—61no—
452C23—62no—
453C23—62no—
454C23—61no—
455C23—154no—
456C23—302no—
457C23—304no—
458C23—304no—
459C23—302no—
460C23#676912yescomplemented
461C23C22×D3×D511yescharacteristic
462Q8—54no—
463Q8—158no—
464Q8—154no—
465Q8—304no—
466D4—64no—
467D4—62no—
468D4—62no—
469D4—304no—
470D4—308no—
471D4—308no—
472D4—308no—
473D4—304no—
474D4—304no—
475D4—304no—
476C2×C4—31no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—52no—
484C2×C4—61no—
485C2×C4—64no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—64no—
491C2×C4—154no—
492C2×C4—154no—
493C2×C4—152no—
494C2×C4—154no—
495C2×C4—154no—
496C2×C4—308no—
497C2×C4—308no—
498C2×C4—302no—
499C2×C4—304no—
500C2×C4D5×S411yescharacteristic
501C2×C3—41no—
502C2×C3—42no—
503D3—82no—
504D3—404no—
505C5C2×#591911yescharacteristic, complemented, Sylow
506C22—32no—
507C22—31no—
508C22—31no—
509C22—31no—
510C22—32no—
511C22—32no—
512C22—61no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—122no—
517C22—122no—
518C22—304no—
519C22—304no—
520C22—304no—
521C22—604no—
522C22—604no—
523C22C2×#676911yescharacteristic, complemented
524C22C2×D5×S411yescharacteristic
525C4—32no—
526C4—54no—
527C4—62no—
528C4—62no—
529C4—62no—
530C4—154no—
531C4—304no—
532C4C2×D5×S412yes—
533C3—41noSylow
534C2—31no—
535C2—31no—
536C2—32no—
537C2—122no—
538C2—604no—
539C2#1175674712yesdirect product factor
540C2C22×D5×S411yescharacteristic
subgroupG/H
centerC22C2×D5×S4
commutator, cosocleC2×C5×A4C24
FrattiniC2C22×D5×S4
FittingC23×C4×C5C2×D3
socleC24×C5C22×D3
hypercenterC2×C4D5×S4
hypocenterC5×A4C2×#41
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×A4×Dic10C2semidirect
2. C2×C4⋊(C5⋊S4)C2semidirect
3. C2×C4×C5×S4C2semidirect
4. C2×#91902C2semidirect
5. C2×#91901C2semidirect
6. #11756747C2direct (N × H)
13. A4×Dic10C22semidirect
14. C4⋊(C5⋊S4)C22semidirect
16. C4×C5×S4C22semidirect
17. #91902C22semidirect
18. #91901C22semidirect
21. C23×Dic10D3semidirect
52. C2×C4×S4D5semidirect
70. C22×Dic10C2×D3semidirect
99. C2×C5×A4#41semidirect
121. C4×S4C2×D5semidirect
173. C2×Dic10S4semidirect
205. C5×A4C2×#41semidirect
231. C23×C5#239semidirect
276. Dic10C2×S4semidirect
326. C2×A4#709semidirect
350. C22×C5C2×#239semidirect
436. A4C2×#709semidirect
444. C2×C5#5919semidirect
460. C23#6769semidirect
505. C5C2×#5919semidirect
523. C22C2×#6769semidirect
539. C2#11756747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×Dic102
C2×C4⋊(C5⋊S4)2
C2×C4×C5×S42
C2×#919022
C2×#919012
#117567472
C2×#658863
C2×#67694
C2×#59195