Finite Group Databasebeta

← C2×#11752048 #14412145

Subgroups — C2×#11752048 #14412145

Order 1920.

1512 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6780C211yesmaximal, characteristic
2C2×D3×#704C212yesmaximal, complemented
3C2×#91242C211yesmaximal, characteristic, complemented
4C2×C3×#4013C211yesmaximal, characteristic, complemented
5#11752048C218yesmaximal, direct product factor
6C2×#91175C212yesmaximal, complemented
7C2×#65777—31nomaximal, Hall
8C23×Dic15C411yescharacteristic
9C22×C5×#67C411yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C22×#1204C2211yescharacteristic
12C22×#1201C411yescharacteristic
13C22×D3×Dic5C2211yescharacteristic
14C2×#6780—22no—
15C2×#6780—24no—
16C2×#6780—22no—
17C2×#6780C414yes—
18C2×#6780C2214yes—
19C22×D5×Dic3C411yescharacteristic
20C2×#6762C2212yes—
21C2×C3×#704C2212yes—
22C2×#6739—22no—
23D3×#704—24no—
24D3×#704C2218yescomplemented
25C2×D3×#170—22no—
26#91242C2214yescomplemented
27C3×#4013C2214yescomplemented
28#91175C2218yescomplemented
29C2×#4745—51nomaximal, Hall
30C22×#711—31no—
31C22×#704—32no—
32C2×#4013—31no—
33C2×#4013D311yescharacteristic, complemented
34#65777—38no—
35C2×#4005—32no—
36C24×C3×C5C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C22×Dic15—22no—
40C22×Dic15—21no—
41C22×Dic15—21no—
42C22×Dic15C2×C414yes—
43C22×Dic15C2×C411yescharacteristic
44C22×Dic15C2×C411yescharacteristic
45C2×C5×#67—22no—
46C2×C5×#67—22no—
47C2×C5×#67C2×C414yes—
48C22×C5×Dic3C2×C411yescharacteristic
49C2×C3×C22⋊D5—22no—
50C2×C3×C22⋊D5—22no—
51C2×C3×C22⋊D5C2×C412yes—
52C2×C3×C22⋊D5C2312yes—
53C22×C3×Dic5C2311yescharacteristic
54C2×#1204—22no—
55C2×#1204—22no—
56C2×#1204C2×C412yes—
57C2×#1204C2312yes—
58C2×#1201—22no—
59C2×#1201—22no—
60C2×#1201C2×C414yes—
61C2×D3×Dic5C2×C412yes—
62C2×D3×Dic5D412yes—
63C2×D3×Dic5D414yes—
64C2×D3×Dic5D412yes—
65C2×D3×Dic5C2312yes—
66#6780—28no—
67#6780—28no—
68#6780—28no—
69#6780—28no—
70C2×D5×Dic3—22no—
71C2×D5×Dic3—21no—
72C2×D5×Dic3—21no—
73C2×D5×Dic3C2×C414yes—
74#6762—22no—
75#6762C2314yes—
76C2×C3⋊#170—22no—
77C3×#704—22no—
78C3×#704C2314yes—
79C2×C3×#170—22no—
80#6739—28no—
81D3×#170—28no—
82C22×#237—51no—
83C2×D3×M16—52no—
84C2×C3×#100—51no—
85C2×#833—51no—
86C2×#824—52no—
87#4745—58no—
88C22×C5×D4—31no—
89C22×C22⋊D5—31no—
90C22×C22⋊D5C2×D311yescharacteristic
91C23×Dic5—31no—
92C23×Dic5—31no—
93C2×#711—34no—
94C2×#711—34no—
95C2×#711—62no—
96C2×#711—62no—
97C2×#711—64no—
98C22×C4×D5—31no—
99C22×Dic10—31no—
100C2×#704—32no—
101C2×#704—38no—
102C2×#704—62no—
103C2×#704—64no—
104C2×#704C2×D312yes—
105C22×#170—62no—
106#4013—34no—
107#4013C2×D314yescomplemented
108#4005—38no—
109C2×#413—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—42no—
113C23×C3×C5C22×C411yescharacteristic
114C23×C3×C5C22×C412yes—
115C22×C5×D3—42no—
116C22×C5×D3C22⋊C412yes—
117C22×C5×D3C22⋊C412yes—
118C22×C5×D3C22×C412yes—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5—42no—
122C22×C3×D5C22×C412yes—
123C2×Dic15—21no—
124C2×Dic15—21no—
125C2×Dic15—24no—
126C2×Dic15—24no—
127C2×Dic15C22⋊C412yes—
128C2×Dic15C22⋊C411yescharacteristic
129C2×Dic15C22⋊C411yescharacteristic
130C2×Dic15C22×C412yes—
131C2×Dic15C22×C412yes—
132C5×#67—28no—
133C2×C5×Dic3—21no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3C22×C412yes—
136C3×C22⋊D5—24no—
137C3×C22⋊D5—24no—
138C2×C3×Dic5C22×C411yescharacteristic
139C2×C3×Dic5C2×D412yes—
140C2×C3×Dic5C2×D412yes—
141C2×C3×Dic5C2411yescharacteristic
142#1204—24no—
143#1204—24no—
144#1201—28no—
145D3×Dic5C22⋊C414yes—
146D3×Dic5C22⋊C414yes—
147D3×Dic5C2×D414yes—
148D3×Dic5C2×D414yes—
149D5×Dic3—24no—
150D5×Dic3—24no—
151C3⋊#170—24no—
152C3×#170—24no—
153C22×C3×D4—51no—
154C22×#67—51no—
155C22×#67AGL(1,𝔽5)11yescharacteristic
156C23×Dic3—51no—
157C23×Dic3—51no—
158C2×#237—54no—
159C2×#237—54no—
160C2×#237—102no—
161C2×#237—102no—
162C2×#237—104no—
163C22×C4×D3—51no—
164C22×Dic6—51no—
165C2×C3×M16—52no—
166C2×#208—52no—
167D3×M16—58no—
168D3×M16—104no—
169C2×ΓL(1,𝔽25)—102no—
170C2×D3×C8—102no—
171C3×#100—54no—
172#833—54no—
173#824—58no—
174C24×C5—31no—
175C24×C5C4×D311yescharacteristic
176C23×D5C4×D311yescharacteristic
177C2×C5×D4—34no—
178C2×C5×D4—62no—
179C2×C5×D4—62no—
180C22×C4×C5—31no—
181C2×C22⋊D5—22no—
182C2×C22⋊D5—22no—
183C2×C22⋊D5—34no—
184C2×C22⋊D5—62no—
185C2×C22⋊D5—62no—
186C2×C22⋊D5C4×D312yes—
187C2×C22⋊D5C22×D312yes—
188C22×Dic5—31no—
189C22×Dic5—32no—
190C22×Dic5—32no—
191C22×Dic5—34no—
192C22×Dic5—32no—
193C22×Dic5—32no—
194C22×Dic5—31no—
195C22×Dic5—34no—
196C22×Dic5—62no—
197C22×Dic5—61no—
198C22×Dic5—61no—
199C22×Dic5C22×D311yescharacteristic
200#711—68no—
201#711—68no—
202#711—68no—
203#711—68no—
204C2×C4×D5—34no—
205C2×C4×D5—62no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×Dic10—32no—
209C2×Dic10—32no—
210C2×Dic10—62no—
211C2×Dic10—62no—
212#704—22no—
213#704—34no—
214#704—68no—
215#704—62no—
216#704C22×D314yes—
217C2×#170—22no—
218C2×#170—68no—
219C2×#170—62no—
220C22×#41—151no—
221C22×M16—152no—
222#413—158no—
223C2×#101—152no—
224C2×#100—51no—
225C2×#100—151no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—42no—
229C22×C3×C5—42no—
230C22×C3×C5—42no—
231C22×C3×C5C2×C22⋊C411yescharacteristic
232C22×C3×C5C2×C22⋊C411yescharacteristic
233C22×C3×C5C23×C411yescharacteristic
234C2×C5×D3—24no—
235C2×C5×D3—42no—
236C2×C5×D3—42no—
237C2×C5×D3C2×C22⋊C414yes—
238C2×C3×D5—22no—
239C2×C3×D5—42no—
240C2×C3×D5—42no—
241C2×C3×D5—42no—
242Dic15—22no—
243Dic15C2×C22⋊C412yes—
244Dic15C2×C22⋊C412yes—
245C3×Dic5C2×C22⋊C412yes—
246C3×Dic5C22×D412yes—
247C5×Dic3—22no—
248C24×C3—51no—
249C24×C3C2×AGL(1,𝔽5)11yescharacteristic
250C23×D3C2×AGL(1,𝔽5)11yescharacteristic
251C2×C3×D4—52no—
252C2×C3×D4—52no—
253C2×C3×D4—102no—
254C2×C3×D4—102no—
255C22×C3×C4—51no—
256C2×#67—22no—
257C2×#67—22no—
258C2×#67—54no—
259C2×#67—102no—
260C2×#67—102no—
261C2×#67C2×AGL(1,𝔽5)14yes—
262C22×Dic3—51no—
263C22×Dic3—51no—
264C22×Dic3—54no—
265C22×Dic3—54no—
266C22×Dic3—102no—
267C22×Dic3—101no—
268C22×Dic3—101no—
269C22×Dic3—102no—
270C22×Dic3—101no—
271C22×Dic3—101no—
272C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
273#237—108no—
274#237—108no—
275#237—108no—
276#237—108no—
277C2×C4×D3—52no—
278C2×C4×D3—52no—
279C2×C4×D3—54no—
280C2×C4×D3—52no—
281C2×C4×D3—52no—
282C2×Dic6—52no—
283C2×Dic6—52no—
284C2×Dic6—102no—
285C2×Dic6—102no—
286C3×M16—54no—
287C3×M16—102no—
288C2×C3×C8—102no—
289#208—54no—
290#208—102no—
291C2×C3⋊C8—102no—
292ΓL(1,𝔽25)—108no—
293D3×C8—108no—
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—32no—
297C23×C5—32no—
298C23×C5—32no—
299C23×C5—42no—
300C23×C5—122no—
301C23×C5C2×C4×D312yes—
302C23×C5C2×C4×D311yescharacteristic
303C22×D5—21no—
304C22×D5—21no—
305C22×D5—42no—
306C22×D5C2×C4×D312yes—
307C5×D4—68no—
308C2×C4×C5—32no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C22⋊D5—24no—
312C22⋊D5—24no—
313C22⋊D5—68no—
314C2×Dic5—32no—
315C2×Dic5—31no—
316C2×Dic5—31no—
317C2×Dic5—32no—
318C2×Dic5—34no—
319C2×Dic5—34no—
320C2×Dic5—34no—
321C2×Dic5—34no—
322C2×Dic5—32no—
323C2×Dic5—64no—
324C2×Dic5—64no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5C2×C4×D311yescharacteristic
328C2×Dic5D3×D412yes—
329C2×Dic5D3×D412yes—
330C2×Dic5C23×D311yescharacteristic
331C4×D5—64no—
332C4×D5—64no—
333Dic10—64no—
334Dic10—64no—
335#170—24no—
336#170—64no—
337C2×#41—154no—
338C2×#41—154no—
339C2×#41—302no—
340C2×#41—304no—
341C2×#41—302no—
342C22×Q8—151no—
343C22×D4—31no—
344C22×D4—51no—
345C22×D4—151no—
346C23×C4—151no—
347C23×C4—151no—
348C23×C4—151no—
349C2×M16—52no—
350C2×M16—158no—
351C2×M16—152no—
352C2×M16—302no—
353C2×M16—304no—
354C22×C8—302no—
355#101—158no—
356#100—54no—
357#100—154no—
358C2×C3×C5—21no—
359C2×C3×C5—21no—
360C2×C3×C5—42no—
361C2×C3×C5#41312yescomplemented
362C2×C3×C5C22×C22⋊C411yescharacteristic
363C3×D5—42no—
364C5×D3—24no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—42no—
368C23×C3—52no—
369C23×C3—101no—
370C23×C3—101no—
371C23×C3—202no—
372C23×C3C22×AGL(1,𝔽5)12yes—
373C23×C3C22×AGL(1,𝔽5)11yescharacteristic
374C22×D3—42no—
375C22×D3C22⋊AGL(1,𝔽5)12yes—
376C22×D3C22⋊AGL(1,𝔽5)12yes—
377C22×D3C22×AGL(1,𝔽5)12yes—
378C3×D4—104no—
379C3×D4—104no—
380C2×C3×C4—52no—
381C2×C3×C4—52no—
382C2×C3×C4—51no—
383C2×C3×C4—51no—
384#67—28no—
385#67—108no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—52no—
389C2×Dic3—51no—
390C2×Dic3—51no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—104no—
394C2×Dic3—104no—
395C2×Dic3—104no—
396C2×Dic3—104no—
397C2×Dic3—101no—
398C2×Dic3—101no—
399C2×Dic3C22×AGL(1,𝔽5)12yes—
400C4×D3—54no—
401C4×D3—54no—
402C4×D3—54no—
403C4×D3—54no—
404Dic6—104no—
405Dic6—104no—
406C3×C8—104no—
407C3⋊C8—104no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—34no—
411C22×C5—42no—
412C22×C5—42no—
413C22×C5—42no—
414C22×C5—64no—
415C22×C5—122no—
416C22×C5—122no—
417C22×C5D3×C22⋊C411yescharacteristic
418C22×C5D3×C22⋊C411yescharacteristic
419C22×C5C22×C4×D311yescharacteristic
420C2×D5—22no—
421C2×D5—42no—
422C2×D5—42no—
423C2×D5—42no—
424C4×C5—62no—
425Dic5—32no—
426Dic5—32no—
427Dic5—62no—
428Dic5D3×C22⋊C412yes—
429Dic5C2×D3×D412yes—
430C24—31no—
431C24—51no—
432C24D3×AGL(1,𝔽5)11yescharacteristic
433#41—308no—
434#41—308no—
435#41—308no—
436#41—308no—
437C2×Q8—152no—
438C2×Q8—152no—
439C2×Q8—302no—
440C2×Q8—302no—
441C2×D4—34no—
442C2×D4—52no—
443C2×D4—52no—
444C2×D4—62no—
445C2×D4—62no—
446C2×D4—102no—
447C2×D4—102no—
448C2×D4—154no—
449C2×D4—302no—
450C2×D4—302no—
451C22×C4—31no—
452C22×C4—51no—
453C22×C4—154no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4—154no—
457C22×C4—152no—
458C22×C4—152no—
459C22×C4—151no—
460C22×C4—154no—
461C22×C4—151no—
462C22×C4—302no—
463C22×C4—301no—
464C22×C4—301no—
465C22×C4—302no—
466C22×C4—301no—
467C22×C4—301no—
468M16—54no—
469M16—102no—
470M16—154no—
471M16—308no—
472M16—302no—
473C2×C8—102no—
474C2×C8—308no—
475C2×C8—302no—
476C3×C5C2×#41311yescharacteristic, complemented, Hall
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—102no—
483C22×C3—202no—
484C22×C3—202no—
485C22×C3—202no—
486C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
487C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
488C22×C3C23×AGL(1,𝔽5)11yescharacteristic
489C2×D3—24no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3C2×C22⋊AGL(1,𝔽5)14yes—
493C3×C4—52no—
494C3×C4—52no—
495Dic3—22no—
496Dic3—52no—
497Dic3—52no—
498Dic3—102no—
499C2×C5—21no—
500C2×C5—21no—
501C2×C5—42no—
502C2×C5—64no—
503C2×C5#474512yescomplemented
504C2×C5C2×D3×C22⋊C411yescharacteristic
505D5—42no—
506C23—21no—
507C23—21no—
508C23—32no—
509C23—32no—
510C23—32no—
511C23—42no—
512C23—52no—
513C23—101no—
514C23—101no—
515C23—122no—
516C23—202no—
517C23C2×D3×AGL(1,𝔽5)12yes—
518C23C2×D3×AGL(1,𝔽5)11yescharacteristic
519Q8—304no—
520Q8—304no—
521D4—68no—
522D4—104no—
523D4—104no—
524D4—308no—
525C2×C4—32no—
526C2×C4—52no—
527C2×C4—52no—
528C2×C4—51no—
529C2×C4—51no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—154no—
533C2×C4—154no—
534C2×C4—154no—
535C2×C4—154no—
536C2×C4—152no—
537C2×C4—151no—
538C2×C4—151no—
539C2×C4—152no—
540C2×C4—152no—
541C2×C4—304no—
542C2×C4—304no—
543C2×C4—304no—
544C2×C4—304no—
545C2×C4—301no—
546C2×C4—301no—
547C8—104no—
548C8—304no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—42no—
552C2×C3—202no—
553C2×C3#6577712yescomplemented
554C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
555D3—24no—
556C5C2×#474511yescharacteristic, complemented, Sylow
557C22—22no—
558C22—22no—
559C22—34no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—64no—
564C22—102no—
565C22—122no—
566C22—122no—
567C22—202no—
568C22—202no—
569C22—202no—
570C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
571C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
572C22C22×D3×AGL(1,𝔽5)11yescharacteristic
573C4—52no—
574C4—52no—
575C4—62no—
576C4—152no—
577C4—152no—
578C4—302no—
579C3C2×#6577711yescharacteristic, complemented, Sylow
580C2—21no—
581C2—21no—
582C2—42no—
583C2—64no—
584C2—202no—
585C2#1175204812yesdirect product factor
586C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6780C2
cosocleC2×C3×Dic5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#413
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×D3×#704C2semidirect
3. C2×#91242C2semidirect
4. C2×C3×#4013C2semidirect
5. #11752048C2direct (N × H)
6. C2×#91175C2semidirect
24. D3×#704C22semidirect
26. #91242C22semidirect
27. C3×#4013C22semidirect
28. #91175C22semidirect
33. C2×#4013D3semidirect
107. #4013C2×D3semidirect
361. C2×C3×C5#413semidirect
476. C3×C5C2×#413semidirect
503. C2×C5#4745semidirect
553. C2×C3#65777semidirect
556. C5C2×#4745semidirect
579. C3C2×#65777semidirect
585. C2#11752048direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67802
C2×D3×#7042
C2×#912422
C2×C3×#40132
#117520482
C2×#911752
C2×#657773
C2×#47455