Finite Group Databasebeta

← C2×#11748165 #14423549

Subgroups — C2×#11748165 #14423549

Order 1920.

1520 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic
2C22×#6706C211yesmaximal, characteristic, complemented
3C2×#91360C211yesmaximal, characteristic, complemented
4C22×#6663C211yesmaximal, characteristic, complemented
5C2×C5×#816C211yesmaximal, characteristic, complemented
6C2×C3×#3952C211yesmaximal, characteristic, complemented
7C2×#90969C211yesmaximal, characteristic, complemented
8#11748165C218yesmaximal, direct product factor
9C2×#65099—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1202—21no—
15C22×#1200—21no—
16C2×#6773—24no—
17C2×#6773—24no—
18C2×#6773—22no—
19C2×#6773C2214yes—
20C22×C3×C5×C8C2211yescharacteristic
21C2×#6706—24no—
22C2×#6706C2214yescomplemented
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C2×Dic3⋊Dic5—21no—
26C2×#6665—21no—
27#91360—22no—
28#91360C2214yescomplemented
29C2×#6663—24no—
30C2×#6663C2214yescomplemented
31C5×#816C2214yescomplemented
32C3×#3952C2214yescomplemented
33#90969C2214yescomplemented
34C2×#4733—51nomaximal, Hall
35C22×#713—31no—
36C22×#689—31no—
37C22×#677—31no—
38C2×#4043—31no—
39C2×C5×#103—31no—
40C2×#3952D311yescharacteristic, complemented
41C2×#3941—31no—
42#65099—38no—
43C23×D15—21no—
44C23×C3×D5D411yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C2×D60—21no—
48C2×D60—22no—
49C2×D60D414yes—
50C2×D60C2312yes—
51C2×Dic30—22no—
52C2×Dic30—22no—
53C2×Dic30—21no—
54C2×Dic30C2312yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6D414yes—
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5D412yes—
65C2×C3×C4×D5C2312yes—
66C2×#1202—28no—
67C2×#1202—24no—
68C2×#1200—28no—
69C2×#1200—24no—
70#6773—216no—
71#6773—28no—
72#6773—28no—
73C2×C3×C5×C8—22no—
74C2×C3×C5×C8C2312yes—
75#6706—28no—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C3×#168—22no—
79C2×C3×#168C2312yes—
80Dic3⋊Dic5—24no—
81#6665—24no—
82#6663—28no—
83C22×#235—51no—
84C2×#924—51no—
85C22×Dic12—51no—
86C22×#204—51no—
87C2×C3×C22⋊C8—51no—
88C2×#821—51no—
89C2×#816D511yescharacteristic, complemented
90#4733—58no—
91C22×C5×Q8—31no—
92C2×#713—34no—
93C2×#713—64no—
94C2×#713—64no—
95C2×#713—62no—
96C22×D20—31no—
97C22×D20—61no—
98C22×C4×D5—61no—
99C22×C4×D5C2×D311yescharacteristic
100C22×Dic10—31no—
101C22×C5×C8C2×D311yescharacteristic
102C2×C5×C4⋊C4—31no—
103C2×#689—34no—
104C2×#689—64no—
105C2×#685—61no—
106C2×C4⋊Dic5—61no—
107C22×#168C2×D311yescharacteristic
108C2×#677—34no—
109C2×#677—64no—
110#4043—34no—
111#4043—62no—
112C5×#103—34no—
113#3952C2×D314yescomplemented
114#3941—34no—
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×D15—24no—
118C22×D15—22no—
119C22×D15—42no—
120C22×D15—42no—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5C2×D412yes—
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D412yes—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C2×Dic15—42no—
131D60—24no—
132D60—22no—
133D60C2×D414yes—
134Dic30—22no—
135Dic30—22no—
136Dic30—42no—
137C2×C5×Dic3—24no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—42no—
141C5×Dic6—24no—
142C5×Dic6—22no—
143C5×Dic6C2×D414yes—
144C2×C3×Dic5—22no—
145C2×C3×Dic5C2×D412yes—
146C3×C4×D5—24no—
147C3×C4×D5—22no—
148C3×C4×D5—22no—
149#1202—216no—
150#1200—216no—
151C3×C5×C8—22no—
152C3×#168—22no—
153C23×C3×C4—51no—
154C22×#67—101no—
155C2×#235—54no—
156C2×#235—104no—
157C2×#235—102no—
158C2×#235—104no—
159C22×D12—51no—
160C22×C4×D3—101no—
161C22×Dic6—51no—
162C22×Dic6C2×D511yescharacteristic
163C22×C3×C8—51no—
164C22×C3×C8C2×D511yescharacteristic
165C2×#217—101no—
166C2×C4⋊Dic3C2×D511yescharacteristic
167#924—54no—
168#924—102no—
169C2×Dic3⋊C4—101no—
170C2×Dic12—54no—
171C2×Dic12—104no—
172C2×#204—54no—
173C2×#204—104no—
174C3×C22⋊C8—54no—
175#821—54no—
176#816C2×D514yescomplemented
177C23×D5—61no—
178C23×D5D1211yescharacteristic
179C2×C5×Q8—34no—
180C2×C5×Q8—32no—
181C2×C5×Q8—61no—
182C2×C5×Q8—62no—
183C22×C4×C5—61no—
184C22×C4×C5—61no—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—61no—
187C22×Dic5D1211yescharacteristic
188#713—68no—
189#713—68no—
190#713—616no—
191C2×D20—34no—
192C2×D20—32no—
193C2×D20—68no—
194C2×D20—64no—
195C2×D20—61no—
196C2×D20—62no—
197C2×C4×D5—22no—
198C2×C4×D5—22no—
199C2×C4×D5—68no—
200C2×C4×D5—64no—
201C2×C4×D5D1212yes—
202C2×C4×D5C22×D312yes—
203C2×Dic10—32no—
204C2×Dic10—62no—
205C2×Dic10—62no—
206C2×Dic10—61no—
207C2×C5×C8—22no—
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—61no—
211#689—68no—
212#685—64no—
213C4⋊Dic5—64no—
214C2×#168—22no—
215C2×#168C22×D312yes—
216#677—68no—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—31no—
223C2×#102—151no—
224C2×C22⋊C8—51no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×D15—24no—
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—48no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—22no—
236C2×C3×D5—44no—
237C3×C4×C5#12012yes—
238C3×C4×C5C22×D411yescharacteristic
239C3×C4×C5C22×D411yescharacteristic
240Dic15—42no—
241C3×Dic5—22no—
242C5×Dic3—24no—
243C5×Dic3—42no—
244C24×C3—51no—
245C23×D3—101no—
246C22×C3×C4—51no—
247C22×C3×C4—52no—
248C22×C3×C4—52no—
249C22×C3×C4—102no—
250C22×C3×C4—102no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—104no—
253C2×#67—108no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C22×Dic3—101no—
257#235—108no—
258#235—1016no—
259#235—108no—
260C2×D12—54no—
261C2×D12—52no—
262C2×D12—102no—
263C2×D12—101no—
264C2×C4×D3—104no—
265C2×C4×D3—108no—
266C2×Dic6—21no—
267C2×Dic6—22no—
268C2×Dic6—52no—
269C2×Dic6—102no—
270C2×Dic6—102no—
271C2×Dic6—101no—
272C2×Dic6D2014yes—
273C2×Dic6C22×D512yes—
274C2×C3×C8—22no—
275C2×C3×C8—52no—
276C2×C3×C8—102no—
277C2×C3×C8C22×D512yes—
278#217—104no—
279C4⋊Dic3—21no—
280C4⋊Dic3C22×D512yes—
281Dic3⋊C4—104no—
282Dic12—108no—
283#204—108no—
284C23×C5C2×D1211yescharacteristic
285C22×D5—22no—
286C22×D5—22no—
287C22×D5—22no—
288C22×D5—64no—
289C22×D5—62no—
290C22×D5—122no—
291C22×D5—122no—
292C22×D5C2×D1212yes—
293C5×Q8—34no—
294C5×Q8—64no—
295C5×Q8—62no—
296C2×C4×C5—64no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5—122no—
300C2×C4×C5C2×D1211yescharacteristic
301C2×C4×C5D3×D412yes—
302C2×C4×C5D3×D412yes—
303C2×C4×C5C23×D311yescharacteristic
304C2×Dic5—22no—
305C2×Dic5—62no—
306C2×Dic5—122no—
307C2×Dic5C2×D1212yes—
308D20—34no—
309D20—616no—
310D20—64no—
311D20—62no—
312C4×D5—24no—
313C4×D5—22no—
314C4×D5—22no—
315C4×D5—616no—
316Dic10—62no—
317Dic10—62no—
318Dic10—122no—
319C5×C8—22no—
320#168—22no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—31no—
326C22×Q8—151no—
327C22×D4—151no—
328C22×D4—301no—
329C23×C4—51no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—51no—
336C22×C8D3×D511yescharacteristic
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—34no—
343#102—154no—
344C22⋊C8—54no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349D15—44no—
350C3×D5—42no—
351C23×C3—52no—
352C23×C3—102no—
353C23×C3—102no—
354C23×C3—102no—
355C23×C3D4×D511yescharacteristic
356C22×D3—102no—
357C22×D3—104no—
358C22×D3—202no—
359C22×D3—202no—
360C2×C3×C4—52no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—104no—
365C2×C3×C4C2×D2012yes—
366C2×C3×C4D4×D511yescharacteristic
367C2×C3×C4D4×D512yes—
368C2×C3×C4C23×D511yescharacteristic
369#67—1016no—
370C2×Dic3—22no—
371C2×Dic3—24no—
372C2×Dic3—22no—
373C2×Dic3—42no—
374C2×Dic3—102no—
375C2×Dic3—202no—
376D12—54no—
377D12—102no—
378D12—104no—
379C4×D3—1016no—
380Dic6—22no—
381Dic6—24no—
382Dic6—102no—
383Dic6—102no—
384Dic6—202no—
385Dic6C2×D2014yes—
386C3×C8—22no—
387C3×C8—102no—
388C22×C5#88212yes—
389C22×C5#90412yes—
390C22×C5#90912yes—
391C22×C5C22×D1211yescharacteristic
392C2×D5—22no—
393C2×D5—22no—
394C2×D5—22no—
395C2×D5—44no—
396C2×D5—64no—
397C2×D5—122no—
398C2×D5—122no—
399C2×D5—128no—
400C4×C5—64no—
401C4×C5—122no—
402C4×C5#88212yes—
403C4×C5C2×D3×D411yescharacteristic
404C4×C5C2×D3×D411yescharacteristic
405Dic5—22no—
406Dic5—122no—
407C24—51no—
408C24—301no—
409#41—308no—
410#41—308no—
411#41—3016no—
412C2×Q8—34no—
413C2×Q8—32no—
414C2×Q8—61no—
415C2×Q8—62no—
416C2×Q8—152no—
417C2×Q8—301no—
418C2×Q8—302no—
419C2×Q8—302no—
420C2×D4—154no—
421C2×D4—152no—
422C2×D4—304no—
423C2×D4—308no—
424C2×D4—301no—
425C2×D4—302no—
426C22×C4—51no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—61no—
430C22×C4—61no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—304no—
434C22×C4—308no—
435C22×C4—301no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—22no—
440C2×C8—52no—
441C2×C8—102no—
442C2×C8C2×D3×D512yes—
443C4⋊C4—32no—
444C4⋊C4—61no—
445C4⋊C4—304no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—102no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—204no—
452C22×C3#402812yes—
453C22×C3#406212yes—
454C22×C3#406412yes—
455C22×C3C2×D4×D511yescharacteristic
456C2×D3—104no—
457C2×D3—202no—
458C2×D3—202no—
459C2×D3—208no—
460C3×C4—102no—
461C3×C4#402812yes—
462C3×C4C22×D2011yescharacteristic
463C3×C4C2×D4×D511yescharacteristic
464Dic3—24no—
465Dic3—42no—
466Dic3—202no—
467C2×C5#473314yescomplemented
468C2×C5C2×#88211yescharacteristic
469C2×C5C2×#90411yescharacteristic
470C2×C5C2×#90911yescharacteristic
471D5—42no—
472D5—124no—
473C23—52no—
474C23—102no—
475C23—102no—
476C23—102no—
477C23—304no—
478C23—302no—
479C23—602no—
480C23—602no—
481C23D5×D1211yescharacteristic
482Q8—34no—
483Q8—64no—
484Q8—62no—
485Q8—302no—
486Q8—302no—
487Q8—602no—
488D4—154no—
489D4—3016no—
490D4—304no—
491D4—302no—
492C2×C4—52no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—102no—
497C2×C4—104no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—122no—
501C2×C4—3016no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4D5×D1211yescharacteristic
505C2×C4D3×D2012yes—
506C2×C4#679012yes—
507C2×C4C22×D3×D511yescharacteristic
508C8—22no—
509C8—102no—
510C2×C3—202no—
511C2×C3#6509914yescomplemented
512C2×C3C2×#402811yescharacteristic
513C2×C3C2×#406211yescharacteristic
514C2×C3C2×#406411yescharacteristic
515D3—204no—
516C5C2×#473311yescharacteristic, complemented, Sylow
517C22—102no—
518C22—102no—
519C22—102no—
520C22—204no—
521C22—304no—
522C22—602no—
523C22—602no—
524C22—608no—
525C22#9126112yes—
526C22#9126912yes—
527C22#9147612yes—
528C22C2×D5×D1211yescharacteristic
529C4—64no—
530C4—102no—
531C4—122no—
532C4—602no—
533C4#9147612yes—
534C4C2×D3×D2011yescharacteristic
535C4C2×#679011yescharacteristic
536C3C2×#6509911yescharacteristic, complemented, Sylow
537C2—202no—
538C2—604no—
539C2#1174816514yesdirect product factor
540C2C2×#9126111yescharacteristic
541C2C2×#9126911yescharacteristic
542C2C2×#9147611yescharacteristic
subgroupG/H
centerC23D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×#6773C2
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#6706C2semidirect
3. C2×#91360C2semidirect
4. C22×#6663C2semidirect
5. C2×C5×#816C2semidirect
6. C2×C3×#3952C2semidirect
7. C2×#90969C2semidirect
8. #11748165C2direct (N × H)
22. C2×#6706C22semidirect
28. #91360C22semidirect
30. C2×#6663C22semidirect
31. C5×#816C22semidirect
32. C3×#3952C22semidirect
33. #90969C22semidirect
40. C2×#3952D3semidirect
89. C2×#816D5semidirect
113. #3952C2×D3semidirect
176. #816C2×D5semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
467. C2×C5#4733semidirect
511. C2×C3#65099semidirect
516. C5C2×#4733semidirect
536. C3C2×#65099semidirect
539. C2#11748165direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67732
C22×#67062
C2×#913602
C22×#66632
C2×C5×#8162
C2×C3×#39522
C2×#909692
#117481652
C2×#650993
C2×#47335