Finite Group Databasebeta

← C2×#11747514 #14423552

Subgroups — C2×#11747514 #14423552

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×#6765C211yesmaximal, characteristic
2C2×C5×#897C211yesmaximal, characteristic, complemented
3C22×#6663C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×#91094C211yesmaximal, characteristic, complemented
6C2×C3×#3941C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊#168C211yesmaximal, characteristic, complemented
8#11747514C218yesmaximal, direct product factor
9C2×#65336—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C4×C5×D3C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×D20C2211yescharacteristic
14C22×#1201—21no—
15C22×D5×Dic3—21no—
16C2×#6765—24no—
17C2×#6765—22no—
18C2×#6765—24no—
19C2×#6765C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C2×C5×(C2×D3)⋊C4—21no—
23C2×C5×C4⋊Dic3—21no—
24C5×#897—22no—
25C5×#897C2214yescomplemented
26C22×C3×#168C2211yescharacteristic
27C2×#6663—24no—
28C2×#6663C2214yescomplemented
29C2×#6655—24no—
30C2×#6655C2214yescomplemented
31#91094C2214yescomplemented
32C3×#3941C2214yescomplemented
33(C2×D3)⋊#168C2214yescomplemented
34C2×#4783—51nomaximal, Hall
35C22×#709—31no—
36C2×C5×C22⋊Q8—31no—
37C22×#689—31no—
38C22×#688—31no—
39C2×C22⋊#168—31no—
40#65336—38no—
41C2×#3942—31no—
42C2×#3941D311yescharacteristic, complemented
43C23×C5×D3D411yescharacteristic
44C23×C3×D5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C2×Dic30—21no—
49C2×Dic30—22no—
50C2×Dic30D414yes—
51C2×Dic30C2312yes—
52C22×C5×Dic3—21no—
53C22×C5×Dic3D411yescharacteristic
54C2×C4×C5×D3—22no—
55C2×C4×C5×D3—22no—
56C2×C4×C5×D3D412yes—
57C2×C4×C5×D3C2312yes—
58C2×C5×Dic6—22no—
59C2×C5×Dic6—22no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6C2312yes—
62C2×C3×D20—21no—
63C2×C3×D20—22no—
64C2×C3×D20D414yes—
65C2×C3×D20C2312yes—
66C2×#1201—28no—
67C2×#1201—24no—
68C2×D5×Dic3—28no—
69C2×D5×Dic3—24no—
70#6765—216no—
71#6765—28no—
72#6765—28no—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C2×C3⋊#168—22no—
76C2×C3⋊#168C2312yes—
77C5×(C2×D3)⋊C4—24no—
78C5×C4⋊Dic3—24no—
79C2×C3×#168—22no—
80C2×C3×#168C2312yes—
81#6663—28no—
82#6655—28no—
83C22×#237—51no—
84C22×#214—51no—
85C22×Dic12—51no—
86C2×#897D511yescharacteristic, complemented
87C2×C3×#102—51no—
88C2×(C2×D3)⋊C8—51no—
89C2×#810—51no—
90#4783—58no—
91C22×C5×Q8—31no—
92C23×C4×C5—31no—
93C22×C22⋊D5—61no—
94C2×#709—34no—
95C2×#709—64no—
96C2×#709—62no—
97C2×#709—64no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—61no—
100C22×Dic10—31no—
101C5×C22⋊Q8—34no—
102C5×C22⋊Q8—62no—
103C2×C5×C4⋊C4—61no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×C5×C22⋊C4—61no—
106C2×#689—34no—
107C2×#689—64no—
108C2×#688—34no—
109C2×#688—64no—
110C22×#168—31no—
111C22×#168C2×D311yescharacteristic
112C22⋊#168—34no—
113#3942—34no—
114#3941C2×D314yescomplemented
115C2×#452—151noSylow
116C23×C3×C5C2×D411yescharacteristic
117C22×C5×D3—22no—
118C22×C5×D3—22no—
119C22×C5×D3—22no—
120C22×C5×D3C2×D412yes—
121C22×C3×D5—24no—
122C22×C3×D5—22no—
123C22×C3×D5—42no—
124C22×C3×D5—42no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—42no—
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—24no—
132C2×Dic15—22no—
133Dic30—24no—
134Dic30—22no—
135Dic30C2×D414yes—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—42no—
139C2×C5×Dic3C2×D412yes—
140C4×C5×D3—24no—
141C4×C5×D3—22no—
142C4×C5×D3—22no—
143C5×Dic6—22no—
144C5×Dic6—22no—
145C5×Dic6—42no—
146C3×D20—24no—
147C3×D20—22no—
148C3×D20C2×D414yes—
149#1201—216no—
150D5×Dic3—216no—
151C3⋊#168—22no—
152C3×#168—22no—
153C22×C3×D4—51no—
154C22×#67—101no—
155C23×Dic3—101no—
156C2×#237—54no—
157C2×#237—104no—
158C2×#237—104no—
159C2×#237—102no—
160C22×C4×D3C2×D511yescharacteristic
161C22×Dic6—51no—
162C22×Dic6C2×D511yescharacteristic
163C22×C3×C8—51no—
164C2×C3×C4⋊C4C2×D511yescharacteristic
165C2×#214—54no—
166C2×#214—104no—
167C2×(C2×D3)⋊C4—21no—
168C2×C4⋊Dic3—21no—
169C22×C3⋊C8—51no—
170C2×Dic12—54no—
171C2×Dic12—104no—
172#897—22no—
173#897C2×D514yescomplemented
174C3×#102—54no—
175(C2×D3)⋊C8—54no—
176#810—54no—
177C24×C5—31no—
178C23×D5—21no—
179C2×C5×Q8—32no—
180C2×C5×Q8—61no—
181C2×C5×Q8—62no—
182C2×C5×Q8—62no—
183C22×C4×C5—21no—
184C22×C4×C5—31no—
185C22×C4×C5—32no—
186C22×C4×C5—32no—
187C22×C4×C5—62no—
188C22×C4×C5—62no—
189C22×C4×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—64no—
192C2×C22⋊D5—68no—
193C22×Dic5—61no—
194#709—68no—
195#709—616no—
196#709—68no—
197C2×D20—22no—
198C2×D20—21no—
199C2×D20D1214yes—
200C2×D20C22×D312yes—
201C2×C4×D5—64no—
202C2×C4×D5—68no—
203C2×Dic10—34no—
204C2×Dic10—32no—
205C2×Dic10—62no—
206C2×Dic10—61no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—64no—
209C5×C4⋊C4C22×D312yes—
210C5×C22⋊C4—64no—
211#689—68no—
212#688—68no—
213C2×#168—22no—
214C2×#168—32no—
215C2×#168—62no—
216C2×#168C22×D312yes—
217C22×#41—151no—
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—31no—
221#452—158no—
222C2×#103—151no—
223C2×#102—51no—
224C2×C22⋊C8—151no—
225C22×C3×C5#12012yes—
226C22×C3×C5#13512yes—
227C22×C3×C5#13712yes—
228C22×C3×C5C22×D411yescharacteristic
229C2×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C5×D3—22no—
232C2×C5×D3—44no—
233C2×C3×D5—24no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—48no—
237C3×C4×C5—42no—
238C3×C4×C5#12012yes—
239C3×C4×C5C22×D411yescharacteristic
240C3×C4×C5C22×D411yescharacteristic
241Dic15—24no—
242C5×Dic3—22no—
243C5×Dic3—42no—
244C24×C3—101no—
245C23×D3C22⋊D511yescharacteristic
246C2×C3×D4—54no—
247C2×C3×D4—52no—
248C2×C3×D4—102no—
249C2×C3×D4—101no—
250C22×C3×C4—21no—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—108no—
253C2×#67—104no—
254C22×Dic3—21no—
255C22×Dic3—108no—
256C22×Dic3—101no—
257C22×Dic3—104no—
258C22×Dic3C22⋊D511yescharacteristic
259#237—108no—
260#237—108no—
261#237—1016no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3C22⋊D512yes—
265C2×C4×D3C22×D512yes—
266C2×Dic6—22no—
267C2×Dic6—22no—
268C2×Dic6—21no—
269C2×Dic6—54no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—101no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—52no—
275C2×C3×C8—102no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D512yes—
278#214—108no—
279(C2×D3)⋊C4—24no—
280C4⋊Dic3—24no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—102no—
283Dic12—108no—
284C23×C5—32no—
285C23×C5—62no—
286C23×C5—62no—
287C23×C5—62no—
288C23×C5D3×D411yescharacteristic
289C22×D5—24no—
290C22×D5—22no—
291C22×D5—42no—
292C22×D5—42no—
293C5×Q8—62no—
294C5×Q8—62no—
295C5×Q8—122no—
296C2×C4×C5—22no—
297C2×C4×C5—32no—
298C2×C4×C5—42no—
299C2×C4×C5—62no—
300C2×C4×C5—64no—
301C2×C4×C5—62no—
302C2×C4×C5—62no—
303C2×C4×C5—62no—
304C2×C4×C5—122no—
305C2×C4×C5C2×D1212yes—
306C2×C4×C5D3×D412yes—
307C2×C4×C5D3×D411yescharacteristic
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—616no—
310C2×Dic5—64no—
311C2×Dic5—62no—
312D20—24no—
313D20—22no—
314D20C2×D1214yes—
315C4×D5—616no—
316Dic10—34no—
317Dic10—64no—
318Dic10—62no—
319#168—22no—
320#168—62no—
321C2×#41—154no—
322C2×#41—302no—
323C2×#41—304no—
324C2×#41—304no—
325C22×Q8—31no—
326C22×Q8—151no—
327C22×D4—51no—
328C22×D4—301no—
329C23×C4—31no—
330C23×C4—301no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—51no—
336C22×C8—151no—
337C22⋊Q8—34no—
338C22⋊Q8—62no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4D3×D511yescharacteristic
341C2×C22⋊C4—61no—
342#103—154no—
343#102—54no—
344C22⋊C8—154no—
345C2×C3×C5#45214yescomplemented
346C2×C3×C5C2×#12011yescharacteristic
347C2×C3×C5C2×#13511yescharacteristic
348C2×C3×C5C2×#13711yescharacteristic
349C3×D5—44no—
350C5×D3—42no—
351C23×C3—102no—
352C23×C3—104no—
353C23×C3—202no—
354C23×C3—202no—
355C23×C3C2×C22⋊D511yescharacteristic
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3C2×C22⋊D512yes—
360C3×D4—54no—
361C3×D4—102no—
362C3×D4—104no—
363C2×C3×C4—22no—
364C2×C3×C4—42no—
365C2×C3×C4D4×D512yes—
366C2×C3×C4D4×D512yes—
367C2×C3×C4C2×C22⋊D511yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369#67—1016no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—42no—
373C2×Dic3—1016no—
374C2×Dic3—102no—
375C2×Dic3—104no—
376C2×Dic3C2×C22⋊D512yes—
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—24no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383Dic6—54no—
384Dic6—102no—
385Dic6—104no—
386C3×C8—102no—
387C3⋊C8—102no—
388C22×C5—62no—
389C22×C5—62no—
390C22×C5—62no—
391C22×C5—124no—
392C22×C5#88212yes—
393C22×C5#91212yes—
394C22×C5#91512yes—
395C22×C5C2×D3×D411yescharacteristic
396C2×D5—24no—
397C2×D5—42no—
398C2×D5—42no—
399C2×D5—48no—
400C4×C5—42no—
401C4×C5—62no—
402C4×C5—122no—
403C4×C5#88212yes—
404C4×C5C22×D1211yescharacteristic
405C4×C5C2×D3×D411yescharacteristic
406Dic5—64no—
407C24—31no—
408C24—101no—
409#41—308no—
410#41—308no—
411#41—3016no—
412C2×Q8—32no—
413C2×Q8—61no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—154no—
417C2×Q8—152no—
418C2×Q8—302no—
419C2×Q8—301no—
420C2×D4—54no—
421C2×D4—52no—
422C2×D4—102no—
423C2×D4—101no—
424C2×D4—304no—
425C2×D4—308no—
426C22×C4—21no—
427C22×C4—31no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—61no—
433C22×C4—304no—
434C22×C4—308no—
435C22×C4—301no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—52no—
440C2×C8—102no—
441C2×C8—152no—
442C2×C8—302no—
443C4⋊C4—21no—
444C4⋊C4—64no—
445C4⋊C4C2×D3×D512yes—
446C22⋊C4—64no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—104no—
449C22×C3—208no—
450C22×C3—202no—
451C22×C3—202no—
452C22×C3#408312yes—
453C22×C3#408812yes—
454C22×C3#409612yes—
455C22×C3C22×C22⋊D511yescharacteristic
456C2×D3—22no—
457C2×D3—22no—
458C2×D3—22no—
459C2×D3—44no—
460C3×C4—42no—
461C3×C4#408312yes—
462C3×C4C2×D4×D511yescharacteristic
463C3×C4C2×D4×D511yescharacteristic
464Dic3—22no—
465Dic3—42no—
466Dic3—104no—
467C2×C5—122no—
468C2×C5#478314yescomplemented
469C2×C5C2×#88211yescharacteristic
470C2×C5C2×#91211yescharacteristic
471C2×C5C2×#91511yescharacteristic
472D5—44no—
473C23—32no—
474C23—62no—
475C23—62no—
476C23—62no—
477C23—104no—
478C23—102no—
479C23—202no—
480C23—202no—
481C23D3×C22⋊D511yescharacteristic
482Q8—62no—
483Q8—62no—
484Q8—122no—
485Q8—154no—
486Q8—304no—
487Q8—302no—
488D4—54no—
489D4—104no—
490D4—102no—
491D4—3016no—
492C2×C4—22no—
493C2×C4—32no—
494C2×C4—42no—
495C2×C4—62no—
496C2×C4—64no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—122no—
501C2×C4—3016no—
502C2×C4—304no—
503C2×C4—302no—
504C2×C4D5×D1212yes—
505C2×C4#677712yes—
506C2×C4D3×C22⋊D511yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—102no—
509C8—302no—
510C2×C3—204no—
511C2×C3#6533614yescomplemented
512C2×C3C2×#408311yescharacteristic
513C2×C3C2×#408811yescharacteristic
514C2×C3C2×#409611yescharacteristic
515D3—42no—
516C5C2×#478311yescharacteristic, complemented, Sylow
517C22—62no—
518C22—62no—
519C22—62no—
520C22—104no—
521C22—124no—
522C22—202no—
523C22—208no—
524C22—202no—
525C22#9147512yes—
526C22#9149312yes—
527C22#9151812yes—
528C22C2×D3×C22⋊D511yescharacteristic
529C4—42no—
530C4—62no—
531C4—122no—
532C4—304no—
533C4#9147512yes—
534C4C2×D5×D1211yescharacteristic
535C4C2×#677711yescharacteristic
536C3C2×#6533611yescharacteristic, complemented, Sylow
537C2—122no—
538C2—204no—
539C2#1174751414yesdirect product factor
540C2C2×#9147511yescharacteristic
541C2C2×#9149311yescharacteristic
542C2C2×#9151811yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6765C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#897C2semidirect
3. C22×#6663C2semidirect
4. C22×#6655C2semidirect
5. C2×#91094C2semidirect
6. C2×C3×#3941C2semidirect
7. C2×(C2×D3)⋊#168C2semidirect
8. #11747514C2direct (N × H)
25. C5×#897C22semidirect
28. C2×#6663C22semidirect
30. C2×#6655C22semidirect
31. #91094C22semidirect
32. C3×#3941C22semidirect
33. (C2×D3)⋊#168C22semidirect
42. C2×#3941D3semidirect
86. C2×#897D5semidirect
114. #3941C2×D3semidirect
173. #897C2×D5semidirect
345. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#4783semidirect
511. C2×C3#65336semidirect
516. C5C2×#4783semidirect
536. C3C2×#65336semidirect
539. C2#11747514direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67652
C2×C5×#8972
C22×#66632
C22×#66552
C2×#910942
C2×C3×#39412
C2×(C2×D3)⋊#1682
#117475142
C2×#653363
C2×#47835