Finite Group Databasebeta

← C2×#11752573 #14483564

Subgroups — C2×#11752573 #14483564

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C5×#870C211yesmaximal, characteristic, complemented
3C2×C3×C4×D20C211yesmaximal, characteristic
4C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#91407C212yesmaximal
6C2×#91394C212yesmaximal, complemented
7C2×#91366C212yesmaximal, complemented
8C2×#91360C211yesmaximal, characteristic, complemented
9C2×#91360C211yesmaximal, characteristic, complemented
10C2×#91358C211yesmaximal, characteristic, complemented
11C2×#91346C212yesmaximal, complemented
12#11752573C2116yesmaximal, direct product factor
13C2×#66028—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×D5×Dic3C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×#6712C2212yes—
22C2×C4×Dic15C2212yes—
23C4×Dic30C2218yescomplemented
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2212yes—
27C2×C5×Dic3⋊C4C2212yes—
28C5×#870C2218yescomplemented
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C3×C4×D20C2218yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6668C2212yes—
36C2×#6665C2212yes—
37C2×#6665C2212yes—
38C2×#6665C2212yes—
39C2×Dic3×Dic5C2212yes—
40D5×C4⋊Dic3C2218yescomplemented
41#91407C22116yes—
42#91394C22116yescomplemented
43#91366C22116yescomplemented
44#91360C2218yescomplemented
45#91360C2218yescomplemented
46#91358C2218yescomplemented
47#91346C22116yescomplemented
48C2×#5541—51nomaximal, Hall
49C2×C5×#125—31no—
50#66028—316no—
51C2×#4044—32no—
52C2×#4043—31no—
53C2×#4043—31no—
54C2×#4040—32no—
55C2×#4038—32no—
56C2×#4038—31no—
57C2×D5×C4⋊C4—31no—
58C2×#4036—32no—
59C2×C4×D20D311yescharacteristic
60C2×C4×Dic10—31no—
61C23×C3×D5C2311yescharacteristic
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2312yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2312yes—
71C22×C5×Dic3C2312yes—
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74C2×C3×D20—24no—
75C2×C3×D20C2314yes—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5—24no—
78C2×C3×C4×D5C2314yes—
79C2×C3×C4×D5C2314yes—
80C2×D5×Dic3—28no—
81C2×D5×Dic3C2318yes—
82C3×C42×C5C2314yes—
83C4⋊Dic15C2314yes—
84#6712C2318yes—
85C4×Dic15C2318yes—
86C5×C4⋊Dic3C2314yes—
87C5×C4⋊Dic3C2314yes—
88C5×Dic3⋊C4C2318yes—
89C5×Dic3⋊C4C2318yes—
90C3×#685C2314yes—
91C3×#685C2314yes—
92C3×C4⋊Dic5C2314yes—
93Dic3⋊Dic5C2318yes—
94Dic3⋊Dic5C2318yes—
95#6668C2318yes—
96#6665C2318yes—
97#6665C2318yes—
98#6665C2318yes—
99Dic3×Dic5C2318yes—
100C2×C3×C4×D4—51no—
101C2×#935—52no—
102C2×#926—51no—
103C22×C4⋊Dic3—51no—
104C2×#924—51no—
105C2×#924—51no—
106#5541—516no—
107C2×#889—52no—
108C2×#879—52no—
109C2×#877—52no—
110C2×#870D511yescharacteristic, complemented
111C2×C4×Dic6—51no—
112C22×D20C2×D311yescharacteristic
113C22×C4×D5—32no—
114C22×C4×D5C2×D311yescharacteristic
115C22×C4×D5C2×D311yescharacteristic
116C22×Dic10—31no—
117C5×#125—38no—
118C2×C5×C4⋊C4—32no—
119C2×C5×C4⋊C4—31no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C42×C5C2×D311yescharacteristic
123C2×#685—32no—
124C2×#685—32no—
125C2×#685—32no—
126C2×#685C2×D311yescharacteristic
127C2×#685C2×D311yescharacteristic
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×#683—32no—
133C2×#683—32no—
134C2×C4×Dic5—32no—
135C2×C4×Dic5—32no—
136#4044—316no—
137#4043—38no—
138#4043—38no—
139#4040—316no—
140#4038—38no—
141#4038—316no—
142D5×C4⋊C4—38no—
143#4036—316no—
144C4×D20C2×D318yes—
145C4×Dic10—38no—
146C2×#552—151noSylow
147C23×C3×C5C2411yescharacteristic
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5#4114yes—
154C22×C3×D5C2412yes—
155C22×C3×D5C2412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5#4114yes—
159C2×C3×C4×C5C2412yes—
160C2×C3×C4×C5C2412yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—24no—
163C2×Dic15—24no—
164C2×Dic15C2414yes—
165C2×Dic15C2414yes—
166Dic30—28no—
167C2×C5×Dic3—24no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3C2414yes—
170C2×C5×Dic3C2414yes—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C2412yes—
174C2×C3×Dic5C2412yes—
175C3×D20—28no—
176C3×C4×D5—28no—
177C3×C4×D5—28no—
178D5×Dic3—216no—
179C22×C3×D4—51no—
180C23×C3×C4—51no—
181C23×C3×C4—51no—
182C23×Dic3—52no—
183C22×Dic6—51no—
184C3×C4×D4—58no—
185C2×C3×C4⋊C4—51no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—51no—
188C2×C3×C42C2×D511yescharacteristic
189C2×#217—52no—
190C2×#217—52no—
191C2×#217—52no—
192#935—516no—
193#926—58no—
194C2×C4⋊Dic3—51no—
195C2×C4⋊Dic3—52no—
196C2×C4⋊Dic3—58no—
197C2×C4⋊Dic3C2×D511yescharacteristic
198C2×C4⋊Dic3C2×D511yescharacteristic
199#924—58no—
200#924—58no—
201C2×Dic3⋊C4—52no—
202C2×Dic3⋊C4—52no—
203C2×Dic3⋊C4—52no—
204C2×Dic3⋊C4C2×D512yes—
205C2×Dic3⋊C4C2×D512yes—
206C2×C4×Dic3—52no—
207C2×C4×Dic3—52no—
208#889—516no—
209#879—516no—
210#877—516no—
211#870C2×D518yescomplemented
212C4×Dic6—58no—
213C23×D5C22×D311yescharacteristic
214C23×D5C22×D311yescharacteristic
215C22×C4×C5—32no—
216C22×C4×C5—32no—
217C22×C4×C5C22×D311yescharacteristic
218C22×C4×C5C22×D311yescharacteristic
219C22×C4×C5C22×D311yescharacteristic
220C22×Dic5—32no—
221C22×Dic5—32no—
222C22×Dic5C22×D311yescharacteristic
223C22×Dic5C22×D311yescharacteristic
224C2×D20—24no—
225C2×D20C22×D314yes—
226C2×C4×D5—24no—
227C2×C4×D5—24no—
228C2×C4×D5—38no—
229C2×C4×D5—68no—
230C2×C4×D5C22×D314yes—
231C2×C4×D5C22×D314yes—
232C2×Dic10—34no—
233C2×Dic10—64no—
234C5×C4⋊C4—38no—
235C5×C4⋊C4—38no—
236C5×C4⋊C4—34no—
237C5×C4⋊C4—34no—
238C42×C5C22×D314yes—
239#685—38no—
240#685—38no—
241#685—38no—
242#685C22×D314yes—
243#685C22×D314yes—
244C4⋊Dic5—34no—
245C4⋊Dic5—38no—
246C4⋊Dic5—38no—
247C4⋊Dic5C22×D314yes—
248#683—38no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5—38no—
252#552—1516no—
253C2×#126—152no—
254C2×#125—31no—
255C2×#125—152no—
256C2×#123—152no—
257C2×C22⋊Q8—151no—
258C2×C22⋊Q8—151no—
259C2×C4×Q8—151no—
260C2×C4×D4—51no—
261C2×#117—152no—
262C2×#117—151no—
263C22×C4⋊C4—151no—
264C22×C3×C5C2×#4112yes—
265C22×C3×C5C2×#4112yes—
266C22×C3×C52−1+412yes—
267C22×C3×C5C2511yescharacteristic
268C2×C3×D5—28no—
269C2×C3×D5—22no—
270C2×C3×D5—22no—
271C2×C3×D5—22no—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—44no—
275C2×C3×D5C2×#4114yes—
276C3×C4×C5—22no—
277C3×C4×C5—22no—
278C3×C4×C5C2×#4114yes—
279Dic15—24no—
280Dic15—24no—
281C3×Dic5—22no—
282C3×Dic5—22no—
283C5×Dic3—24no—
284C5×Dic3—24no—
285C24×C3—51no—
286C24×C3—51no—
287C2×C3×D4—54no—
288C2×C3×D4—104no—
289C22×C3×C4—51no—
290C22×C3×C4—51no—
291C22×C3×C4—54no—
292C22×C3×C4—54no—
293C22×C3×C4—104no—
294C22×C3×C4—104no—
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D511yescharacteristic
298C22×Dic3—52no—
299C22×Dic3—52no—
300C22×Dic3—58no—
301C22×Dic3—108no—
302C22×Dic3C22×D512yes—
303C22×Dic3C22×D512yes—
304C2×Dic6—54no—
305C2×Dic6—104no—
306C3×C4⋊C4—54no—
307C3×C22⋊C4—54no—
308C3×C22⋊C4—54no—
309C3×C42C22×D514yes—
310#217—58no—
311#217—58no—
312#217—58no—
313C4⋊Dic3—54no—
314C4⋊Dic3—58no—
315C4⋊Dic3C22×D514yes—
316C4⋊Dic3C22×D514yes—
317Dic3⋊C4—58no—
318Dic3⋊C4—58no—
319Dic3⋊C4—58no—
320Dic3⋊C4C22×D518yes—
321Dic3⋊C4C22×D518yes—
322C4×Dic3—58no—
323C4×Dic3—58no—
324C23×C5C23×D311yescharacteristic
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5#23514yes—
331C22×D5C23×D312yes—
332C22×D5C23×D312yes—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—34no—
336C2×C4×C5—34no—
337C2×C4×C5—64no—
338C2×C4×C5—64no—
339C2×C4×C5#23714yes—
340C2×C4×C5C23×D312yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—34no—
346C2×Dic5—34no—
347C2×Dic5—64no—
348C2×Dic5—64no—
349C2×Dic5C23×D312yes—
350C2×Dic5C23×D312yes—
351D20—28no—
352C4×D5—28no—
353C4×D5—28no—
354C4×D5—616no—
355Dic10—68no—
356C22×Q8—151no—
357C22×D4—51no—
358C23×C4—51no—
359C23×C4—51no—
360C23×C4—152no—
361#126—1516no—
362#125—38no—
363#125—1516no—
364#123—1516no—
365C22⋊Q8—158no—
366C22⋊Q8—158no—
367C4×Q8—158no—
368C4×D4—58no—
369#117—1516no—
370#117—158no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—32no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—158no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4—152no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—152no—
382C2×C22⋊C4—51no—
383C2×C22⋊C4—51no—
384C2×C22⋊C4—152no—
385C2×C22⋊C4—152no—
386C2×C22⋊C4—152no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42D3×D511yescharacteristic
390C2×C3×C5#55214yescomplemented
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394C3×D5—24no—
395C3×D5—42no—
396C23×C3—54no—
397C23×C3—52no—
398C23×C3—52no—
399C23×C3—102no—
400C23×C3—102no—
401C23×C3—102no—
402C23×C3—102no—
403C23×C3—102no—
404C23×C3C23×D511yescharacteristic
405C3×D4—108no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—52no—
409C2×C3×C4—52no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—108no—
413C2×C3×C4—108no—
414C2×C3×C4#71314yes—
415C2×C3×C4C23×D512yes—
416C2×C3×C4C23×D512yes—
417C2×C3×C4C23×D512yes—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—54no—
421C2×Dic3—54no—
422C2×Dic3—1016no—
423C2×Dic3—104no—
424C2×Dic3—104no—
425C2×Dic3C23×D514yes—
426C2×Dic3C23×D514yes—
427Dic6—108no—
428C22×C5C2×#23512yes—
429C22×C5C2×#23712yes—
430C22×C5#101012yes—
431C22×C5C24×D311yescharacteristic
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—28no—
435C2×D5—22no—
436C2×D5—22no—
437C2×D5—22no—
438C2×D5—44no—
439C2×D5C2×#23514yes—
440C4×C5—22no—
441C4×C5—22no—
442C4×C5—64no—
443C4×C5—64no—
444C4×C5C2×#23714yes—
445Dic5—22no—
446Dic5—22no—
447Dic5—64no—
448Dic5—64no—
449C24—51no—
450C24—51no—
451C2×Q8—154no—
452C2×Q8—304no—
453C2×D4—54no—
454C2×D4—104no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—51no—
458C22×C4—51no—
459C22×C4—54no—
460C22×C4—54no—
461C22×C4—104no—
462C22×C4—104no—
463C22×C4—158no—
464C22×C4—152no—
465C22×C4—152no—
466C22×C4—308no—
467C22×C4C2×D3×D511yescharacteristic
468C22×C4C2×D3×D511yescharacteristic
469C22×C4C2×D3×D511yescharacteristic
470C4⋊C4—34no—
471C4⋊C4—34no—
472C4⋊C4—38no—
473C4⋊C4—38no—
474C4⋊C4—54no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—154no—
479C4⋊C4—158no—
480C22⋊C4—54no—
481C22⋊C4—54no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—158no—
485C42—158no—
486C42—158no—
487C42C2×D3×D514yes—
488C3×C5C2×#55211yescharacteristic, complemented, Hall
489C22×C3—54no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—108no—
493C22×C3—102no—
494C22×C3—102no—
495C22×C3—102no—
496C22×C3—204no—
497C22×C3C2×#71312yes—
498C22×C3D5×#4112yes—
499C22×C3#415012yes—
500C22×C3C24×D511yescharacteristic
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—102no—
504C3×C4—102no—
505C3×C4C2×#71314yes—
506Dic3—24no—
507Dic3—24no—
508Dic3—104no—
509Dic3—104no—
510C2×C5#554114yescomplemented
511C2×C5C22×#23511yescharacteristic
512C2×C5C22×#23711yescharacteristic
513C2×C5C2×#101011yescharacteristic
514D5—24no—
515D5—42no—
516C23—54no—
517C23—52no—
518C23—52no—
519C23—102no—
520C23—102no—
521C23—102no—
522C23—102no—
523C23—102no—
524C23C22×D3×D511yescharacteristic
525Q8—308no—
526D4—108no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—64no—
534C2×C4—64no—
535C2×C4—102no—
536C2×C4—102no—
537C2×C4—108no—
538C2×C4—108no—
539C2×C4—154no—
540C2×C4—154no—
541C2×C4—3016no—
542C2×C4—304no—
543C2×C4—304no—
544C2×C4#676614yes—
545C2×C4C22×D3×D512yes—
546C2×C4C22×D3×D512yes—
547C2×C4C22×D3×D512yes—
548C2×C3—104no—
549C2×C3—202no—
550C2×C3#6602814yescomplemented
551C2×C3C22×#71311yescharacteristic
552C2×C3C2×D5×#4111yescharacteristic
553C2×C3C2×#415011yescharacteristic
554C5C2×#554111yescharacteristic, complemented, Sylow
555C22—54no—
556C22—108no—
557C22—102no—
558C22—102no—
559C22—102no—
560C22—102no—
561C22—102no—
562C22—204no—
563C22C2×#676612yes—
564C22#9200112yes—
565C22D5×#23512yes—
566C22C23×D3×D511yescharacteristic
567C4—22no—
568C4—22no—
569C4—64no—
570C4—64no—
571C4—102no—
572C4—102no—
573C4—304no—
574C4—304no—
575C4C2×#676614yes—
576C3C2×#6602811yescharacteristic, complemented, Sylow
577C2—104no—
578C2—202no—
579C2#1175257314yesdirect product factor
580C2C22×#676611yescharacteristic
581C2C2×#9200111yescharacteristic
582C2C2×D5×#23511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#552
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic30C2semidirect
2. C2×C5×#870C2semidirect
4. C2×D5×C4⋊Dic3C2semidirect
6. C2×#91394C2semidirect
7. C2×#91366C2semidirect
8. C2×#91360C2semidirect
9. C2×#91360C2semidirect
10. C2×#91358C2semidirect
11. C2×#91346C2semidirect
12. #11752573C2direct (N × H)
23. C4×Dic30C22semidirect
28. C5×#870C22semidirect
40. D5×C4⋊Dic3C22semidirect
42. #91394C22semidirect
43. #91366C22semidirect
44. #91360C22semidirect
45. #91360C22semidirect
46. #91358C22semidirect
47. #91346C22semidirect
110. C2×#870D5semidirect
211. #870C2×D5semidirect
390. C2×C3×C5#552semidirect
488. C3×C5C2×#552semidirect
510. C2×C5#5541semidirect
550. C2×C3#66028semidirect
554. C5C2×#5541semidirect
576. C3C2×#66028semidirect
579. C2#11752573direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C5×#8702
C2×C3×C4×D202
C2×D5×C4⋊Dic32
C2×#914072
C2×#913942
C2×#913662
C2×#913602
C2×#913582
C2×#913462
#117525732
C2×#660283
C2×#55415