Finite Group Databasebeta

← C2×#11749397 #14423262

Subgroups — C2×#11749397 #14423262

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×D12C211yesmaximal, characteristic
2C22×#6717C211yesmaximal, characteristic, complemented
3C22×C5×#215C211yesmaximal, characteristic, complemented
4C2×C3×#4092C211yesmaximal, characteristic, complemented
5#11749397C218yesmaximal, direct product factor
6C2×#90968C211yesmaximal, characteristic, complemented
7C2×#90966C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic, complemented
9C2×#65458—31nomaximal, Hall
10C23×D3×D5—21no—
11C22×C3×C5×Q8C2211yescharacteristic, complemented
12C22×D60C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1203—21no—
16C2×D5×D12—24no—
17C2×D5×D12—24no—
18C2×D5×D12—22no—
19C2×D5×D12C2214yes—
20C2×#6717—24no—
21C2×#6717C2214yescomplemented
22C22×C3⋊#168C2211yescharacteristic, complemented
23C2×C5×#215—24no—
24C2×C5×#215C2214yescomplemented
25C22×C5×C3⋊C8C2211yescharacteristic, complemented
26C3×#4092—22no—
27C3×#4092C2214yescomplemented
28C2×C3×#685—21no—
29C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
30C2×C3×#683—21no—
31#90968C2214yescomplemented
32#90966C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5046—51nomaximal, Hall
35C22×D4×D5—31no—
36C22×C5×SD16—31no—
37C2×#4092D311yescharacteristic, complemented
38C22×#688—31no—
39C2×#3964—31no—
40#65458—38no—
41C2×#3953—31no—
42C2×#3952—31no—
43C23×D15—21no—
44C23×C5×D3—21no—
45C23×C3×D5D411yescharacteristic
46C22×D3×D5—28no—
47C22×D3×D5—24no—
48C22×D3×D5—44no—
49C22×D3×D5—44no—
50C2×C3×C5×Q8—21no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8C2312yescomplemented
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×D60—21no—
57C2×D60—22no—
58C2×D60D414yes—
59C2×D60C2312yes—
60C2×C5×D12—21no—
61C2×C5×D12—22no—
62C2×C5×D12D414yes—
63C2×C5×D12C2312yes—
64C22×C3×Dic5—21no—
65C22×C3×Dic5D411yescharacteristic
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5D412yes—
69C2×C3×C4×D5C2312yes—
70C2×#1203—28no—
71C2×#1203—24no—
72D5×D12—216no—
73D5×D12—28no—
74D5×D12—28no—
75#6717—28no—
76C2×C3⋊#168—22no—
77C2×C3⋊#168C2312yescomplemented
78C5×#215—28no—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yescomplemented
81C3×#685—24no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yescomplemented
84C3×#683—24no—
85C23×D12—51no—
86C2×C3×C22⋊Q8—51no—
87C22×#215—51no—
88C22×#215D511yescharacteristic, complemented
89C2×#830—51no—
90#5046—58no—
91C2×#809—51no—
92C2×#809—51no—
93C24×D5—61no—
94C22×C5×Q8C2×D311yescharacteristic, complemented
95C22×C5×D4—31no—
96C22×C22⋊D5—61no—
97C2×D4×D5—34no—
98C2×D4×D5—64no—
99C2×D4×D5—64no—
100C2×D4×D5—62no—
101C22×D20—31no—
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×SD16—34no—
104C2×C5×SD16—64no—
105C22×C5×C8—31no—
106#4092—22no—
107#4092C2×D314yescomplemented
108C2×#688—34no—
109C2×#688—64no—
110C2×#685—21no—
111C2×C4⋊Dic5C2×D311yescharacteristic, complemented
112C2×#683—21no—
113C22×#168—31no—
114#3964—34no—
115#3953—34no—
116#3952—34no—
117C2×#450—151noSylow
118C23×C3×C5C2×D411yescharacteristic
119C22×D15—24no—
120C22×D15—22no—
121C22×D15—42no—
122C22×D15—42no—
123C22×C5×D3—24no—
124C22×C5×D3—22no—
125C22×C5×D3—42no—
126C22×C5×D3—42no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5SD1614yescomplemented
130C22×C3×D5C2×D412yes—
131C2×D3×D5—216no—
132C2×D3×D5—48no—
133C2×D3×D5—432no—
134C2×D3×D5—48no—
135C3×C5×Q8—22no—
136C3×C5×Q8—22no—
137C3×C5×Q8—42no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—42no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144D60—24no—
145D60—22no—
146D60C2×D414yes—
147C5×D12—24no—
148C5×D12—22no—
149C5×D12C2×D414yes—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—42no—
153C2×C3×Dic5C2×D412yes—
154C3×C4×D5—24no—
155C3×C4×D5—22no—
156C3×C4×D5—22no—
157#1203—216no—
158C3⋊#168—22no—
159C5×C3⋊C8—22no—
160C24×D3—101no—
161C22×C3×Q8C2×D511yescharacteristic, complemented
162C23×C3×C4—51no—
163C22×D12—51no—
164C22×D12—54no—
165C22×D12—104no—
166C22×D12—102no—
167C22×D12—101no—
168C22×D12—104no—
169C22×D12C2×D511yescharacteristic
170C3×C22⋊Q8—54no—
171C3×C22⋊Q8—102no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C4⋊C4—101no—
174C2×C3×C22⋊C4—101no—
175C2×#215—24no—
176C2×#215—54no—
177C2×#215—104no—
178C2×#215C2×D514yescomplemented
179C22×C3⋊C8—51no—
180C22×C3⋊C8C2×D511yescharacteristic, complemented
181#830—54no—
182#809—54no—
183#809—54no—
184C24×C5—61no—
185C23×D5—68no—
186C23×D5—61no—
187C23×D5—64no—
188C23×D5—124no—
189C23×D5—124no—
190C23×D5#6711yescharacteristic
191C2×C5×Q8—21no—
192C2×C5×Q8—22no—
193C2×C5×Q8—22no—
194C2×C5×Q8C22×D312yescomplemented
195C2×C5×D4—34no—
196C2×C5×D4—32no—
197C2×C5×D4—62no—
198C2×C5×D4—61no—
199C22×C4×C5—21no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—68no—
202C2×C22⋊D5—64no—
203C22×Dic5—21no—
204C22×Dic5#6711yescharacteristic
205D4×D5—68no—
206D4×D5—68no—
207D4×D5—616no—
208C2×D20—34no—
209C2×D20—32no—
210C2×D20—62no—
211C2×D20—61no—
212C2×C4×D5—22no—
213C2×C4×D5—22no—
214C2×C4×D5#6712yes—
215C2×C4×D5C22×D312yes—
216C5×SD16—68no—
217C2×C5×C8—32no—
218C2×C5×C8—62no—
219#688—68no—
220#685—24no—
221C4⋊Dic5—21no—
222C4⋊Dic5C22×D312yescomplemented
223#683—24no—
224C2×#168—32no—
225C2×#168—62no—
226C23×D4—151no—
227C22×SD16—31no—
228C22×SD16—151no—
229C2×C22⋊Q8—51no—
230#450—158no—
231C2×#102—151no—
232C2×#102—151no—
233C2×C22⋊C8—151no—
234C22×C3×C5#12012yes—
235C22×C3×C5C2×SD1612yes—
236C22×C3×C5AGL(1,ℤ/8)12yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—24no—
239C2×D15—42no—
240C2×D15—42no—
241C2×D15—48no—
242C2×C5×D3—24no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C2×C5×D3—48no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5—28no—
249C2×C3×D5C2×SD1614yescomplemented
250D3×D5—432no—
251C3×C4×C5—42no—
252C3×C4×C5#12012yes—
253C3×C4×C5C22×D411yescharacteristic
254C3×C4×C5C22×D411yescharacteristic
255C3×Dic5—22no—
256C3×Dic5—42no—
257C24×C3—51no—
258C23×D3—21no—
259C23×D3—104no—
260C23×D3—108no—
261C23×D3—101no—
262C23×D3—204no—
263C23×D3—204no—
264C2×C3×Q8—21no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8C22×D512yescomplemented
268C22×C3×C4—21no—
269C22×C3×C4—51no—
270C22×C3×C4—52no—
271C22×C3×C4—52no—
272C22×C3×C4—102no—
273C22×C3×C4—102no—
274C22×C3×C4—101no—
275C22×C3×C4C22×D511yescharacteristic
276C2×D12—21no—
277C2×D12—22no—
278C2×D12—54no—
279C2×D12—52no—
280C2×D12—108no—
281C2×D12—1016no—
282C2×D12—104no—
283C2×D12—108no—
284C2×D12—101no—
285C2×D12—102no—
286C2×D12—108no—
287C2×D12C22⋊D514yes—
288C2×D12C22×D512yes—
289C3×C4⋊C4—52no—
290C3×C4⋊C4—104no—
291C3×C4⋊C4—101no—
292C3×C22⋊C4—104no—
293#215—28no—
294#215—108no—
295C2×C3⋊C8—22no—
296C2×C3⋊C8—52no—
297C2×C3⋊C8—102no—
298C2×C3⋊C8C22×D512yescomplemented
299C23×C5—64no—
300C23×C5—62no—
301C23×C5—122no—
302C23×C5—122no—
303C23×C5C2×#6711yescharacteristic
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—616no—
307C22×D5—64no—
308C22×D5—62no—
309C22×D5—1232no—
310C22×D5—128no—
311C22×D5—122no—
312C22×D5—122no—
313C22×D5—128no—
314C22×D5#21514yescomplemented
315C22×D5C2×#6712yes—
316C5×Q8—22no—
317C5×Q8—22no—
318C5×Q8—42no—
319C5×D4—34no—
320C5×D4—64no—
321C5×D4—62no—
322C2×C4×C5—22no—
323C2×C4×C5—42no—
324C2×C4×C5D3×D412yes—
325C2×C4×C5D3×D412yes—
326C2×C4×C5C2×#6711yescharacteristic
327C2×C4×C5C23×D311yescharacteristic
328C22⋊D5—616no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—42no—
332C2×Dic5C2×#6712yes—
333D20—34no—
334D20—64no—
335D20—62no—
336C4×D5—24no—
337C4×D5—22no—
338C4×D5—22no—
339C5×C8—62no—
340#168—62no—
341C25—301no—
342C22×Q8D3×D511yescharacteristic, complemented
343C22×D4—31no—
344C22×D4—154no—
345C22×D4—151no—
346C22×D4—302no—
347C22×D4—301no—
348C22×D4—304no—
349C22×D4—304no—
350C23×C4—51no—
351C2×SD16—34no—
352C2×SD16—64no—
353C2×SD16—154no—
354C2×SD16—304no—
355C22×C8—31no—
356C22×C8—151no—
357C22⋊Q8—54no—
358C22⋊Q8—102no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—101no—
361C2×C22⋊C4—101no—
362#102—154no—
363#102—154no—
364C22⋊C8—154no—
365C2×C3×C5#45014yescomplemented
366C2×C3×C5C2×#12011yescharacteristic
367C2×C3×C5C22×SD1611yescharacteristic
368C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
369D15—44no—
370C3×D5—24no—
371C5×D3—44no—
372C23×C3—52no—
373C23×C3—54no—
374C23×C3—102no—
375C23×C3—102no—
376C23×C3D4×D511yescharacteristic
377C22×D3—22no—
378C22×D3—24no—
379C22×D3—42no—
380C22×D3—42no—
381C22×D3—1016no—
382C22×D3—102no—
383C22×D3—104no—
384C22×D3—208no—
385C22×D3—208no—
386C22×D3—2032no—
387C22×D3—202no—
388C22×D3—202no—
389C3×Q8—22no—
390C3×Q8—22no—
391C3×Q8—42no—
392C2×C3×C4—22no—
393C2×C3×C4—42no—
394C2×C3×C4—52no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4—104no—
399C2×C3×C4—102no—
400C2×C3×C4—202no—
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4D4×D512yes—
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405D12—22no—
406D12—24no—
407D12—54no—
408D12—1016no—
409D12—102no—
410D12—104no—
411D12C2×C22⋊D514yes—
412C3⋊C8—22no—
413C3⋊C8—102no—
414C22×C5—64no—
415C22×C5—122no—
416C22×C5—128no—
417C22×C5—122no—
418C22×C5#93712yes—
419C22×C5C2×#21512yes—
420C22×C5#94912yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—22no—
423C2×D5—28no—
424C2×D5—22no—
425C2×D5—64no—
426C2×D5—1232no—
427C2×D5—122no—
428C2×D5—128no—
429C2×D5—122no—
430C2×D5C2×#21514yescomplemented
431C4×C5—42no—
432C4×C5#93712yes—
433C4×C5C2×D3×D411yescharacteristic
434C4×C5C2×D3×D411yescharacteristic
435Dic5—22no—
436Dic5—42no—
437C24—51no—
438C24—61no—
439C24—304no—
440C24—308no—
441C24—301no—
442C24—604no—
443C24—604no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8C2×D3×D512yescomplemented
448C2×D4—34no—
449C2×D4—32no—
450C2×D4—61no—
451C2×D4—62no—
452C2×D4—154no—
453C2×D4—152no—
454C2×D4—304no—
455C2×D4—308no—
456C2×D4—308no—
457C2×D4—3016no—
458C2×D4—308no—
459C2×D4—301no—
460C2×D4—302no—
461C22×C4—21no—
462C22×C4—51no—
463C22×C4—52no—
464C22×C4—52no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4C2×D3×D511yescharacteristic
469SD16—68no—
470SD16—308no—
471C2×C8—32no—
472C2×C8—62no—
473C2×C8—152no—
474C2×C8—302no—
475C4⋊C4—52no—
476C4⋊C4—104no—
477C4⋊C4—101no—
478C22⋊C4—104no—
479C3×C5C2×#45011yescharacteristic, complemented, Hall
480C22×C3—54no—
481C22×C3—102no—
482C22×C3—102no—
483C22×C3—108no—
484C22×C3D5×SD1612yes—
485C22×C3#406012yes—
486C22×C3#408312yes—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—24no—
489C2×D3—42no—
490C2×D3—42no—
491C2×D3—48no—
492C2×D3—104no—
493C2×D3—2032no—
494C2×D3—202no—
495C2×D3—202no—
496C2×D3—208no—
497C3×C4—42no—
498C3×C4—102no—
499C3×C4—202no—
500C3×C4#408312yes—
501C3×C4C2×D4×D511yescharacteristic
502C3×C4C22×C22⋊D511yescharacteristic
503C2×C5—124no—
504C2×C5#504614yescomplemented
505C2×C5C2×#93711yescharacteristic
506C2×C5C22×#21511yescharacteristic
507C2×C5C2×#94911yescharacteristic
508D5—24no—
509D5—124no—
510C23—54no—
511C23—52no—
512C23—62no—
513C23—64no—
514C23—102no—
515C23—102no—
516C23—122no—
517C23—122no—
518C23—3016no—
519C23—302no—
520C23—304no—
521C23—608no—
522C23—6032no—
523C23—608no—
524C23—602no—
525C23—602no—
526C23D5×#6711yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—42no—
530D4—34no—
531D4—62no—
532D4—64no—
533D4—154no—
534D4—3016no—
535D4—302no—
536D4—304no—
537C2×C4—22no—
538C2×C4—42no—
539C2×C4—52no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—104no—
544C2×C4—102no—
545C2×C4—202no—
546C2×C4D5×#6711yescharacteristic
547C2×C4D3×C22⋊D512yes—
548C2×C4#679012yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—302no—
552C2×C3—104no—
553C2×C3#6545814yescomplemented
554C2×C3C2×D5×SD1611yescharacteristic
555C2×C3C2×#406011yescharacteristic
556C2×C3C2×#408311yescharacteristic
557D3—44no—
558D3—204no—
559C5C2×#504611yescharacteristic, complemented, Sylow
560C22—54no—
561C22—64no—
562C22—108no—
563C22—102no—
564C22—102no—
565C22—128no—
566C22—122no—
567C22—122no—
568C22—304no—
569C22—6032no—
570C22—608no—
571C22—602no—
572C22—602no—
573C22D5×#21512yes—
574C22#9150212yes—
575C22#9157712yes—
576C22C2×D5×#6711yescharacteristic
577C4—42no—
578C4—102no—
579C4—202no—
580C4#9157712yes—
581C4C2×D3×C22⋊D511yescharacteristic
582C4C2×#679011yescharacteristic
583C3C2×#6545811yescharacteristic, complemented, Sylow
584C2—104no—
585C2—124no—
586C2—604no—
587C2#1174939714yesdirect product factor
588C2C2×D5×#21511yescharacteristic
589C2C2×#9150211yescharacteristic
590C2C2×#9157711yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC22×D5×D12C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#450
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#6717C2semidirect
3. C22×C5×#215C2semidirect
4. C2×C3×#4092C2semidirect
5. #11749397C2direct (N × H)
6. C2×#90968C2semidirect
7. C2×#90966C2semidirect
8. C2×#90955C2semidirect
11. C22×C3×C5×Q8C22semidirect
21. C2×#6717C22semidirect
22. C22×C3⋊#168C22semidirect
24. C2×C5×#215C22semidirect
25. C22×C5×C3⋊C8C22semidirect
27. C3×#4092C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
31. #90968C22semidirect
32. #90966C22semidirect
33. #90955C22semidirect
37. C2×#4092D3semidirect
53. C2×C3×C5×Q8C23semidirect
77. C2×C3⋊#168C23semidirect
80. C2×C5×C3⋊C8C23semidirect
83. C3×C4⋊Dic5C23semidirect
88. C22×#215D5semidirect
94. C22×C5×Q8C2×D3semidirect
107. #4092C2×D3semidirect
111. C2×C4⋊Dic5C2×D3semidirect
129. C22×C3×D5SD16semidirect
161. C22×C3×Q8C2×D5semidirect
178. C2×#215C2×D5semidirect
180. C22×C3⋊C8C2×D5semidirect
194. C2×C5×Q8C22×D3semidirect
222. C4⋊Dic5C22×D3semidirect
249. C2×C3×D5C2×SD16semidirect
267. C2×C3×Q8C22×D5semidirect
298. C2×C3⋊C8C22×D5semidirect
314. C22×D5#215semidirect
342. C22×Q8D3×D5semidirect
365. C2×C3×C5#450semidirect
430. C2×D5C2×#215semidirect
447. C2×Q8C2×D3×D5semidirect
479. C3×C5C2×#450semidirect
504. C2×C5#5046semidirect
553. C2×C3#65458semidirect
559. C5C2×#5046semidirect
583. C3C2×#65458semidirect
587. C2#11749397direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D122
C22×#67172
C22×C5×#2152
C2×C3×#40922
#117493972
C2×#909682
C2×#909662
C2×#909552
C2×#654583
C2×#50465