Finite Group Databasebeta

← C2×#11749049 #14423537

Subgroups — C2×#11749049 #14423537

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×C3×#711C211yesmaximal, characteristic
2C22×#6716C211yesmaximal, characteristic, complemented
3C2×#91360C211yesmaximal, characteristic, complemented
4C22×#6662C211yesmaximal, characteristic, complemented
5C2×C5×#832C211yesmaximal, characteristic, complemented
6#11749049C218yesmaximal, direct product factor
7C2×#90970C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65072—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×Dic30C2211yescharacteristic
12C22×C3×C22⋊D5—21no—
13C23×C3×Dic5—21no—
14C2×C3×#711—24no—
15C2×C3×#711—22no—
16C2×C3×#711—24no—
17C2×C3×#711C2214yes—
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C2×#6716—24no—
21C2×#6716C2214yescomplemented
22C22×C3⋊#168C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic
25C2×Dic3⋊Dic5—21no—
26C2×#6665—21no—
27#91360—22no—
28#91360C2214yescomplemented
29C2×#6662—24no—
30C2×#6662C2214yescomplemented
31C5×#832C2214yescomplemented
32#90970C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5239—51nomaximal, Hall
35C22×#711D311yescharacteristic
36C22×#687—31no—
37C22×Dic20—31no—
38C2×#4043—31no—
39C2×C5×#102—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65072—38no—
43C24×C3×C5—21no—
44C23×C3×D5D411yescharacteristic
45C2×C3×C5×D4—21no—
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4D414yes—
48C2×C3×C5×D4C2312yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C2×Dic30—22no—
52C2×Dic30—22no—
53C2×Dic30—21no—
54C2×Dic30C2312yes—
55C22×C5×Dic3—21no—
56C2×C3×C22⋊D5—28no—
57C2×C3×C22⋊D5—24no—
58C22×C3×Dic5—28no—
59C22×C3×Dic5—21no—
60C22×C3×Dic5—24no—
61C22×C3×Dic5D411yescharacteristic
62C3×#711—216no—
63C3×#711—28no—
64C3×#711—28no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5D412yes—
68C2×C3×C4×D5C2312yes—
69C2×C3×Dic10—21no—
70C2×C3×Dic10—22no—
71C2×C3×Dic10D414yes—
72C2×C3×Dic10C2312yes—
73#6716—28no—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C5×C4⋊Dic3—21no—
77C5×C4⋊Dic3C2312yes—
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2312yes—
80Dic3⋊Dic5—24no—
81#6665—24no—
82#6662—28no—
83C22×C3×#41—51no—
84C22×#216—51no—
85C22×#214—51no—
86C2×#924—51no—
87#5239—58no—
88C2×#835—51no—
89C2×#832D511yescharacteristic, complemented
90C2×#830—51no—
91C22×C5×D4C2×D311yescharacteristic
92C22×C22⋊D5—21no—
93C23×Dic5—21no—
94C2×#711—24no—
95C2×#711—22no—
96C2×#711—24no—
97C2×#711C2×D314yes—
98C22×C4×D5C2×D311yescharacteristic
99C22×Dic10—31no—
100C22×Dic10C2×D311yescharacteristic
101C22×C5×C8—31no—
102C2×C5×C4⋊C4—31no—
103C2×#687—34no—
104C2×#687—64no—
105C2×#685—61no—
106C2×C4⋊Dic5—61no—
107C22×#168—31no—
108C2×Dic20—34no—
109C2×Dic20—64no—
110#4043—34no—
111#4043—62no—
112C5×#102—34no—
113#3952—34no—
114#3942—34no—
115C2×#452—151noSylow
116C23×C3×C5—24no—
117C23×C3×C5—22no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5C2×D411yescharacteristic
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5C2×D412yes—
125C3×C5×D4—24no—
126C3×C5×D4—22no—
127C3×C5×D4C2×D414yes—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—42no—
134Dic30—22no—
135Dic30—22no—
136Dic30—42no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—42no—
139C3×C22⋊D5—216no—
140C2×C3×Dic5—216no—
141C2×C3×Dic5—24no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5C2×D412yes—
145C3×C4×D5—24no—
146C3×C4×D5—22no—
147C3×C4×D5—22no—
148C3×Dic10—24no—
149C3×Dic10—22no—
150C3×Dic10C2×D414yes—
151C3⋊#168—22no—
152C5×C3⋊C8—22no—
153C2×C3×#41—54no—
154C2×C3×#41—102no—
155C2×C3×#41—104no—
156C2×C3×#41—104no—
157C22×C3×Q8—51no—
158C22×C3×D4—101no—
159C22×C3×D4C2×D511yescharacteristic
160C23×C3×C4—51no—
161C23×C3×C4—101no—
162C22×Dic6—51no—
163C2×#217—101no—
164C2×#216—54no—
165C2×#216—104no—
166C2×#214—54no—
167C2×#214—104no—
168C2×C4⋊Dic3C2×D511yescharacteristic
169#924—54no—
170#924—102no—
171C2×Dic3⋊C4—101no—
172C22×C3⋊C8—51no—
173C22×C3⋊C8C2×D511yescharacteristic
174#835—54no—
175#832C2×D514yescomplemented
176#830—54no—
177C24×C5—21no—
178C23×D5#6711yescharacteristic
179C2×C5×D4—21no—
180C2×C5×D4—22no—
181C2×C5×D4#6714yes—
182C2×C5×D4C22×D312yes—
183C22×C4×C5—61no—
184C22×C4×C5C22×D311yescharacteristic
185C2×C22⋊D5—28no—
186C2×C22⋊D5—24no—
187C22×Dic5—28no—
188C22×Dic5—21no—
189C22×Dic5—24no—
190C22×Dic5—61no—
191C22×Dic5#6711yescharacteristic
192#711—216no—
193#711—28no—
194#711—28no—
195C2×C4×D5—22no—
196C2×C4×D5—22no—
197C2×C4×D5#6712yes—
198C2×C4×D5C22×D312yes—
199C2×Dic10—22no—
200C2×Dic10—21no—
201C2×Dic10—32no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C2×Dic10—61no—
205C2×Dic10#6714yes—
206C2×Dic10C22×D312yes—
207C2×C5×C8—32no—
208C2×C5×C8—62no—
209C5×C4⋊C4—32no—
210C5×C4⋊C4—61no—
211#687—68no—
212#685—64no—
213C4⋊Dic5—64no—
214C2×#168—32no—
215C2×#168—62no—
216Dic20—68no—
217C22×#41—51no—
218C22×Q16—151no—
219C22×SD16—151no—
220C2×C22⋊Q8—151no—
221#452—158no—
222C2×#103—151no—
223C2×#102—31no—
224C2×C22⋊C8—151no—
225C22×C3×C5—24no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—48no—
229C22×C3×C5#12012yes—
230C22×C3×C5#13512yes—
231C22×C3×C5#13712yes—
232C22×C3×C5C22×D411yescharacteristic
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—24no—
242C3×Dic5—22no—
243C5×Dic3—42no—
244C24×C3—21no—
245C24×C3—51no—
246C3×#41—108no—
247C3×#41—1016no—
248C3×#41—108no—
249C2×C3×Q8—54no—
250C2×C3×Q8—52no—
251C2×C3×Q8—102no—
252C2×C3×Q8—101no—
253C2×C3×D4—22no—
254C2×C3×D4—21no—
255C2×C3×D4—104no—
256C2×C3×D4—108no—
257C2×C3×D4D2014yes—
258C2×C3×D4C22×D512yes—
259C22×C3×C4—51no—
260C22×C3×C4—52no—
261C22×C3×C4—52no—
262C22×C3×C4—104no—
263C22×C3×C4—108no—
264C22×C3×C4—101no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—21no—
269C22×Dic3—101no—
270C2×Dic6—52no—
271C2×Dic6—102no—
272C2×Dic6—102no—
273C2×Dic6—101no—
274#217—104no—
275#216—108no—
276#214—108no—
277C4⋊Dic3—21no—
278C4⋊Dic3C22×D512yes—
279Dic3⋊C4—104no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—102no—
283C2×C3⋊C8C22×D512yes—
284C23×C5—24no—
285C23×C5—22no—
286C23×C5—42no—
287C23×C5—42no—
288C23×C5C2×#6711yescharacteristic
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—22no—
292C22×D5C2×#6712yes—
293C5×D4—24no—
294C5×D4—22no—
295C5×D4C2×#6714yes—
296C2×C4×C5—62no—
297C2×C4×C5—122no—
298C2×C4×C5C2×#6712yes—
299C2×C4×C5C2×#6711yescharacteristic
300C2×C4×C5C2×#6712yes—
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—216no—
303C2×Dic5—216no—
304C2×Dic5—24no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—62no—
308C2×Dic5—122no—
309C2×Dic5C2×#6712yes—
310C4×D5—24no—
311C4×D5—22no—
312C4×D5—22no—
313Dic10—24no—
314Dic10—22no—
315Dic10—62no—
316Dic10—62no—
317Dic10—122no—
318Dic10C2×#6714yes—
319C5×C8—62no—
320#168—62no—
321C2×#41—54no—
322C2×#41—102no—
323C2×#41—104no—
324C2×#41—104no—
325C22×Q8—51no—
326C22×Q8—151no—
327C22×D4—101no—
328C22×D4D3×D511yescharacteristic
329C23×C4—51no—
330C23×C4—101no—
331C2×Q16—154no—
332C2×Q16—304no—
333C2×SD16—154no—
334C2×SD16—304no—
335C22×C8—31no—
336C22×C8—151no—
337C22⋊Q8—154no—
338C22⋊Q8—302no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—301no—
341C2×C22⋊C4—301no—
342#103—154no—
343#102—34no—
344C22⋊C8—154no—
345C2×C3×C5—44no—
346C2×C3×C5#45214yescomplemented
347C2×C3×C5C2×#12011yescharacteristic
348C2×C3×C5C2×#13511yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C3×D5—42no—
351C23×C3—22no—
352C23×C3—24no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—52no—
356C23×C3—102no—
357C23×C3—102no—
358C23×C3—102no—
359C23×C3D4×D511yescharacteristic
360C3×Q8—54no—
361C3×Q8—102no—
362C3×Q8—104no—
363C3×D4—22no—
364C3×D4—24no—
365C3×D4—1016no—
366C3×D4C2×D2014yes—
367C2×C3×C4—52no—
368C2×C3×C4—1016no—
369C2×C3×C4—102no—
370C2×C3×C4—102no—
371C2×C3×C4—104no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—104no—
375C2×C3×C4C2×D2012yes—
376C2×C3×C4D4×D512yes—
377C2×C3×C4D4×D511yescharacteristic
378C2×C3×C4C23×D511yescharacteristic
379C2×Dic3—22no—
380C2×Dic3—42no—
381C2×Dic3—102no—
382C2×Dic3—202no—
383Dic6—102no—
384Dic6—102no—
385Dic6—202no—
386C3⋊C8—22no—
387C3⋊C8—102no—
388C22×C5—24no—
389C22×C5—48no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5#95012yes—
393C22×C5#95112yes—
394C22×C5#95312yes—
395C22×C5C22×#6711yescharacteristic
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—44no—
400C4×C5—122no—
401C4×C5#95312yes—
402C4×C5C22×#6711yescharacteristic
403C4×C5C22×#6711yescharacteristic
404Dic5—24no—
405Dic5—22no—
406Dic5—122no—
407C24—21no—
408C24—51no—
409#41—108no—
410#41—1016no—
411#41—108no—
412C2×Q8—54no—
413C2×Q8—52no—
414C2×Q8—102no—
415C2×Q8—101no—
416C2×Q8—152no—
417C2×Q8—301no—
418C2×Q8—302no—
419C2×Q8—302no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—104no—
423C2×D4—108no—
424C2×D4#120214yes—
425C2×D4C2×D3×D512yes—
426C22×C4—51no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—61no—
430C22×C4—104no—
431C22×C4—108no—
432C22×C4—101no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—301no—
436C22×C4C2×D3×D511yescharacteristic
437Q16—308no—
438SD16—308no—
439C2×C8—32no—
440C2×C8—62no—
441C2×C8—152no—
442C2×C8—302no—
443C4⋊C4—32no—
444C4⋊C4—61no—
445C4⋊C4—304no—
446C22⋊C4—304no—
447C3×C5C2×#45211yescharacteristic, complemented, Hall
448C22×C3—24no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—48no—
452C22×C3—102no—
453C22×C3—102no—
454C22×C3—102no—
455C22×C3—204no—
456C22×C3#402812yes—
457C22×C3#405812yes—
458C22×C3#406112yes—
459C22×C3C2×D4×D511yescharacteristic
460C3×C4—102no—
461C3×C4—104no—
462C3×C4#402812yes—
463C3×C4C22×D2011yescharacteristic
464C3×C4C2×D4×D511yescharacteristic
465Dic3—42no—
466Dic3—202no—
467C2×C5—44no—
468C2×C5#523914yescomplemented
469C2×C5C2×#95011yescharacteristic
470C2×C5C2×#95111yescharacteristic
471C2×C5C2×#95311yescharacteristic
472D5—42no—
473C23—22no—
474C23—24no—
475C23—42no—
476C23—42no—
477C23—52no—
478C23—102no—
479C23—102no—
480C23—102no—
481C23D5×#6711yescharacteristic
482Q8—54no—
483Q8—102no—
484Q8—104no—
485Q8—302no—
486Q8—302no—
487Q8—602no—
488D4—22no—
489D4—24no—
490D4—1016no—
491D4C2×#120214yes—
492C2×C4—52no—
493C2×C4—62no—
494C2×C4—1016no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—104no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—104no—
501C2×C4—122no—
502C2×C4—302no—
503C2×C4—602no—
504C2×C4C2×#120212yes—
505C2×C4D5×#6712yes—
506C2×C4D5×#6711yescharacteristic
507C2×C4C22×D3×D511yescharacteristic
508C8—62no—
509C8—302no—
510C2×C3—44no—
511C2×C3—202no—
512C2×C3#6507214yescomplemented
513C2×C3C2×#402811yescharacteristic
514C2×C3C2×#405811yescharacteristic
515C2×C3C2×#406111yescharacteristic
516C5C2×#523911yescharacteristic, complemented, Sylow
517C22—24no—
518C22—48no—
519C22—42no—
520C22—42no—
521C22—102no—
522C22—102no—
523C22—102no—
524C22—204no—
525C22#9148412yes—
526C22#9149012yes—
527C22#9156412yes—
528C22C2×D5×#6711yescharacteristic
529C4—102no—
530C4—104no—
531C4—122no—
532C4—602no—
533C4#9156412yes—
534C4C22×#120211yescharacteristic
535C4C2×D5×#6711yescharacteristic
536C3C2×#6507211yescharacteristic, complemented, Sylow
537C2—44no—
538C2—202no—
539C2#1174904914yesdirect product factor
540C2C2×#9148411yescharacteristic
541C2C2×#9149011yescharacteristic
542C2C2×#9156411yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×C3×#711C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6716C2semidirect
3. C2×#91360C2semidirect
4. C22×#6662C2semidirect
5. C2×C5×#832C2semidirect
6. #11749049C2direct (N × H)
7. C2×#90970C2semidirect
8. C2×#90955C2semidirect
21. C2×#6716C22semidirect
28. #91360C22semidirect
30. C2×#6662C22semidirect
31. C5×#832C22semidirect
32. #90970C22semidirect
33. #90955C22semidirect
89. C2×#832D5semidirect
175. #832C2×D5semidirect
346. C2×C3×C5#452semidirect
447. C3×C5C2×#452semidirect
468. C2×C5#5239semidirect
512. C2×C3#65072semidirect
516. C5C2×#5239semidirect
536. C3C2×#65072semidirect
539. C2#11749049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C22×#67162
C2×#913602
C22×#66622
C2×C5×#8322
#117490492
C2×#909702
C2×#909552
C2×#650723
C2×#52395