Finite Group Databasebeta

← C2×#11748711 #14320477

Subgroups — C2×#11748711 #14320477

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
2C22×C3×#685C211yesmaximal, characteristic
3C22×#6665C211yesmaximal, characteristic
4C22×#6665C211yesmaximal, characteristic
5C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
6C2×#91115C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748711C218yesmaximal, direct product factor
9C2×#65279—31nomaximal, Hall
10C24×C3×D5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C2×C5×Dic3⋊C4—24no—
18C2×C5×Dic3⋊C4C2214yescomplemented
19C2×C3×#685—24no—
20C2×C3×#685C2214yes—
21C2×#6665—24no—
22C2×#6665C418yescomplemented
23C2×#6665C2214yes—
24C2×#6665C2214yes—
25C2×Dic3×Dic5—24no—
26C2×Dic3×Dic5C2214yescomplemented
27#91115C2214yescomplemented
28#90994C2214yescomplemented
29C2×#4944—51nomaximal, Hall
30C22×C5×C4⋊C4—31no—
31C22×#685—31no—
32C22×#685—31no—
33C22×#685D311yescharacteristic
34C22×C4×Dic5—31no—
35C2×#3963—31no—
36C2×#3963—31no—
37#65279—38no—
38C24×C3×C5C2311yescharacteristic
39C23×C3×D5—22no—
40C23×C3×D5—22no—
41C23×C3×D5—22no—
42C23×C3×D5—22no—
43C23×C3×D5—22no—
44C23×C3×D5—22no—
45C23×C3×D5C2×C414yes—
46C23×C3×D5C2312yes—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5C2312yes—
51C22×Dic15—22no—
52C22×Dic15—22no—
53C22×Dic15—22no—
54C22×Dic15—22no—
55C22×Dic15—22no—
56C22×Dic15C2×C414yes—
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3—22no—
62C22×C5×Dic3—22no—
63C22×C5×Dic3C2×C414yes—
64C22×C5×Dic3D414yes—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2312yes—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5D414yes—
70C22×C3×Dic5C2312yes—
71C5×Dic3⋊C4—28no—
72C3×#685—28no—
73#6665—28no—
74#6665C2×C4116yescomplemented
75Dic3×Dic5—28no—
76C22×C3×C22⋊C4—51no—
77C22×#217—51no—
78C22×#217—51no—
79C22×Dic3⋊C4D511yescharacteristic, complemented
80C22×C4×Dic3—51no—
81C2×C3⋊#95—51no—
82C2×C3⋊#95—51no—
83#4944—58no—
84C24×D5C2×D311yescharacteristic
85C23×C4×C5—31no—
86C23×C4×C5—31no—
87C23×C4×C5C2×D311yescharacteristic
88C23×Dic5—31no—
89C23×Dic5—31no—
90C23×Dic5C2×D311yescharacteristic
91C2×C5×C4⋊C4—34no—
92C2×C5×C4⋊C4—64no—
93C2×#685—24no—
94C2×#685—38no—
95C2×#685—34no—
96C2×#685—34no—
97C2×#685—64no—
98C2×#685C2×D314yes—
99C2×C4×Dic5—34no—
100C2×C4×Dic5—64no—
101#3963—34no—
102#3963—34no—
103C2×#388—151noSylow
104C23×C3×C5C22×C412yes—
105C23×C3×C5C2×D412yes—
106C23×C3×C5C2×D412yes—
107C23×C3×C5#4112yes—
108C23×C3×C5#4112yes—
109C23×C3×C5#4112yes—
110C23×C3×C5#4112yes—
111C23×C3×C5C2411yescharacteristic
112C22×C3×D5—28no—
113C22×C3×D5—28no—
114C22×C3×D5—28no—
115C22×C3×D5—22no—
116C22×C3×D5—22no—
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—44no—
122C22×C3×D5—44no—
123C22×C3×D5—44no—
124C22×C3×D5—44no—
125C22×C3×D5C22×C414yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×Dic15—28no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—44no—
137C2×Dic15C22×C414yes—
138C2×C5×Dic3—28no—
139C2×C5×Dic3—28no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C22×C414yes—
145C2×C5×Dic3C2×D414yes—
146C2×C3×Dic5—28no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5C2×D414yes—
150C25×C3—51no—
151C23×C3×C4—51no—
152C23×C3×C4C2×D511yescharacteristic
153C23×Dic3—51no—
154C23×Dic3—51no—
155C23×Dic3C2×D511yescharacteristic
156C23×Dic3C2×D511yescharacteristic
157C2×C3×C22⋊C4—54no—
158C2×C3×C22⋊C4—104no—
159C2×#217—58no—
160C2×#217—54no—
161C2×#217—54no—
162C2×#217—104no—
163C2×Dic3⋊C4—24no—
164C2×Dic3⋊C4C2×D514yescomplemented
165C2×C4×Dic3—54no—
166C2×C4×Dic3—104no—
167C3⋊#95—54no—
168C3⋊#95—54no—
169C24×C5C22×D311yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5C4×D314yes—
177C23×D5C22×D312yes—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—34no—
182C22×C4×C5—34no—
183C22×C4×C5—32no—
184C22×C4×C5—32no—
185C22×C4×C5—62no—
186C22×C4×C5—62no—
187C22×C4×C5—62no—
188C22×C4×C5—62no—
189C22×C4×C5C22×D312yes—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—34no—
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5—62no—
196C22×Dic5—62no—
197C22×Dic5—62no—
198C22×Dic5—62no—
199C22×Dic5—62no—
200C22×Dic5#6714yes—
201C22×Dic5C22×D312yes—
202C5×C4⋊C4—68no—
203#685—28no—
204#685—316no—
205#685—68no—
206C4×Dic5—68no—
207C22×C4⋊C4—31no—
208C22×C22⋊C4—51no—
209C22×C22⋊C4—151no—
210C22×C22⋊C4—151no—
211C22×C42—151no—
212#388—158no—
213C2×#95—151no—
214C2×#95—151no—
215C22×C3×C5#11714yes—
216C22×C3×C5C4×D414yes—
217C22×C3×C5C4×D414yes—
218C22×C3×C5#12114yes—
219C22×C3×C5#12314yes—
220C22×C3×C5#12414yes—
221C22×C3×C5#12614yes—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C22×D411yescharacteristic
224C22×C3×C5C22×D411yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C2×C3×D5—24no—
230C2×C3×D5—24no—
231C2×C3×D5—24no—
232C2×C3×D5—42no—
233C2×C3×D5—42no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—416no—
237C3×C4×C5—42no—
238Dic15—24no—
239Dic15—42no—
240C3×Dic5—24no—
241C5×Dic3—24no—
242C5×Dic3—24no—
243C24×C3—54no—
244C24×C3—52no—
245C24×C3—102no—
246C24×C3—102no—
247C24×C3—102no—
248C24×C3—102no—
249C24×C3—102no—
250C24×C3—102no—
251C24×C3C22×D511yescharacteristic
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—54no—
256C22×C3×C4—52no—
257C22×C3×C4—102no—
258C22×C3×C4—102no—
259C22×C3×C4C22×D512yes—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—54no—
265C22×Dic3—52no—
266C22×Dic3—52no—
267C22×Dic3—102no—
268C22×Dic3—102no—
269C22×Dic3—102no—
270C22×Dic3—102no—
271C22×Dic3—102no—
272C22×Dic3C4×D514yes—
273C22×Dic3C22⋊D514yes—
274C22×Dic3C22×D512yes—
275C22×Dic3C22×D512yes—
276C3×C22⋊C4—108no—
277#217—516no—
278#217—108no—
279Dic3⋊C4—28no—
280C4×Dic3—108no—
281C23×C5C2×C4×D312yes—
282C23×C5#23512yes—
283C23×C5D3×D412yes—
284C23×C5#23712yes—
285C23×C5#23712yes—
286C23×C5#23712yes—
287C23×C5C2×#6712yes—
288C23×C5C23×D311yescharacteristic
289C22×D5—28no—
290C22×D5—28no—
291C22×D5—28no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5—22no—
297C22×D5—22no—
298C22×D5—44no—
299C22×D5—44no—
300C22×D5—44no—
301C22×D5—44no—
302C22×D5C2×C4×D314yes—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—34no—
307C2×C4×C5—34no—
308C2×C4×C5—44no—
309C2×C4×C5—68no—
310C2×C4×C5—68no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×Dic5—28no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—34no—
319C2×Dic5—68no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—124no—
326C2×Dic5C2×#6714yes—
327C25—51no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—51no—
331C23×C4—151no—
332C23×C4—151no—
333C23×C4D3×D511yescharacteristic
334C2×C4⋊C4—34no—
335C2×C4⋊C4—64no—
336C2×C22⋊C4—54no—
337C2×C22⋊C4—104no—
338C2×C22⋊C4—154no—
339C2×C22⋊C4—158no—
340C2×C22⋊C4—154no—
341C2×C22⋊C4—304no—
342C2×C42—154no—
343C2×C42—304no—
344#95—154no—
345#95—154no—
346C2×C3×C5#38818yescomplemented
347C2×C3×C5C2×#11711yescharacteristic
348C2×C3×C5C2×C4×D411yescharacteristic
349C2×C3×C5C2×C4×D411yescharacteristic
350C2×C3×C5C2×#12111yescharacteristic
351C2×C3×C5C2×#12311yescharacteristic
352C2×C3×C5C2×#12411yescharacteristic
353C2×C3×C5C2×#12611yescharacteristic
354C3×D5—44no—
355C23×C3—54no—
356C23×C3—102no—
357C23×C3—102no—
358C23×C3—102no—
359C23×C3—102no—
360C23×C3—102no—
361C23×C3—102no—
362C23×C3—108no—
363C23×C3—108no—
364C23×C3—108no—
365C23×C3—204no—
366C23×C3—204no—
367C23×C3—204no—
368C23×C3—204no—
369C23×C3C2×C4×D512yes—
370C23×C3#70912yes—
371C23×C3D4×D512yes—
372C23×C3#71112yes—
373C23×C3#71312yes—
374C23×C3#71312yes—
375C23×C3C2×C22⋊D512yes—
376C23×C3C23×D511yescharacteristic
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—44no—
381C2×C3×C4—54no—
382C2×C3×C4—102no—
383C2×C3×C4—102no—
384C2×C3×C4—108no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—28no—
390C2×Dic3—28no—
391C2×Dic3—54no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—108no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—204no—
399C2×Dic3C2×C4×D514yes—
400C2×Dic3C2×C22⋊D514yes—
401C22×C5#87714yes—
402C22×C5#87914yes—
403C22×C5#67⋊C414yes—
404C22×C5#88514yes—
405C22×C5C4×#6714yes—
406C22×C5#93514yes—
407C22×C5#93814yes—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C2×#23511yescharacteristic
410C22×C5C2×D3×D411yescharacteristic
411C22×C5C2×#23711yescharacteristic
412C22×C5C2×#23711yescharacteristic
413C22×C5C2×#23711yescharacteristic
414C22×C5C22×#6711yescharacteristic
415C2×D5—24no—
416C2×D5—24no—
417C2×D5—24no—
418C2×D5—416no—
419C2×D5—42no—
420C2×D5—42no—
421C2×D5—42no—
422C2×D5—42no—
423C4×C5—42no—
424C4×C5—64no—
425C4×C5—64no—
426Dic5—24no—
427Dic5—64no—
428Dic5—122no—
429C24—54no—
430C24—52no—
431C24—102no—
432C24—102no—
433C24—102no—
434C24—102no—
435C24—102no—
436C24—102no—
437C24C2×D3×D511yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—34no—
442C22×C4—34no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—54no—
446C22×C4—52no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—154no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4—302no—
457C22×C4—302no—
458C22×C4—302no—
459C22×C4—302no—
460C22×C4—302no—
461C22×C4C2×D3×D512yes—
462C4⋊C4—68no—
463C22⋊C4—108no—
464C22⋊C4—1516no—
465C22⋊C4—308no—
466C42—308no—
467C3×C5C2×#38811yescharacteristic, complemented, Hall
468C22×C3—104no—
469C22×C3—104no—
470C22×C3—104no—
471C22×C3—202no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—202no—
475C22×C3—2016no—
476C22×C3#403814yes—
477C22×C3#403914yes—
478C22×C3#404014yes—
479C22×C3#404414yes—
480C22×C3C4×C22⋊D514yes—
481C22×C3#408514yes—
482C22×C3#409314yes—
483C22×C3C22×C4×D511yescharacteristic
484C22×C3C2×#70911yescharacteristic
485C22×C3C2×D4×D511yescharacteristic
486C22×C3C2×#71111yescharacteristic
487C22×C3C2×#71311yescharacteristic
488C22×C3C2×#71311yescharacteristic
489C22×C3C22×C22⋊D511yescharacteristic
490C3×C4—42no—
491C3×C4—104no—
492Dic3—24no—
493Dic3—24no—
494Dic3—104no—
495Dic3—202no—
496C2×C5#494418yescomplemented
497C2×C5C2×#87711yescharacteristic
498C2×C5C2×#87911yescharacteristic
499C2×C5C2×#67⋊C411yescharacteristic
500C2×C5C2×#88511yescharacteristic
501C2×C5C2×C4×#6711yescharacteristic
502C2×C5C2×#93511yescharacteristic
503C2×C5C2×#93811yescharacteristic
504D5—44no—
505C23—54no—
506C23—108no—
507C23—108no—
508C23—108no—
509C23—102no—
510C23—102no—
511C23—102no—
512C23—102no—
513C23—102no—
514C23—102no—
515C23—204no—
516C23—204no—
517C23—204no—
518C23—204no—
519C23#676512yes—
520C23#676612yes—
521C23#677312yes—
522C23C4×D3×D512yes—
523C23#678012yes—
524C23D5×#6712yes—
525C23D3×C22⋊D512yes—
526C23C22×D3×D511yescharacteristic
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—34no—
531C2×C4—34no—
532C2×C4—44no—
533C2×C4—54no—
534C2×C4—68no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—68no—
540C2×C4—108no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—154no—
544C2×C4—308no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—604no—
551C2×C3—204no—
552C2×C3#6527918yescomplemented
553C2×C3C2×#403811yescharacteristic
554C2×C3C2×#403911yescharacteristic
555C2×C3C2×#404011yescharacteristic
556C2×C3C2×#404411yescharacteristic
557C2×C3C2×C4×C22⋊D511yescharacteristic
558C2×C3C2×#408511yescharacteristic
559C2×C3C2×#409311yescharacteristic
560C5C2×#494411yescharacteristic, complemented, Sylow
561C22—104no—
562C22—104no—
563C22—104no—
564C22—202no—
565C22—202no—
566C22—202no—
567C22—2016no—
568C22—202no—
569C22#9136214yes—
570C22#9139414yes—
571C22#9140714yes—
572C22#9144114yes—
573C22#9144414yes—
574C22#9145514yes—
575C22#9156514yes—
576C22C2×#676511yescharacteristic
577C22C2×#676611yescharacteristic
578C22C2×#677311yescharacteristic
579C22C2×C4×D3×D511yescharacteristic
580C22C2×#678011yescharacteristic
581C22C2×D5×#6711yescharacteristic
582C22C2×D3×C22⋊D511yescharacteristic
583C4—42no—
584C4—64no—
585C4—64no—
586C4—104no—
587C4—304no—
588C4—602no—
589C3C2×#6527911yescharacteristic, complemented, Sylow
590C2—204no—
591C2#1174871118yesdirect product factor
592C2C2×#9136211yescharacteristic
593C2C2×#9139411yescharacteristic
594C2C2×#9140711yescharacteristic
595C2C2×#9144111yescharacteristic
596C2C2×#9144411yescharacteristic
597C2C2×#9145511yescharacteristic
598C2C2×#9156511yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×Dic3⋊C4C2semidirect
5. C22×Dic3×Dic5C2semidirect
6. C2×#91115C2semidirect
7. C2×#90994C2semidirect
8. #11748711C2direct (N × H)
18. C2×C5×Dic3⋊C4C22semidirect
22. C2×#6665C4semidirect
26. C2×Dic3×Dic5C22semidirect
27. #91115C22semidirect
28. #90994C22semidirect
74. #6665C2×C4semidirect
79. C22×Dic3⋊C4D5semidirect
164. C2×Dic3⋊C4C2×D5semidirect
346. C2×C3×C5#388semidirect
467. C3×C5C2×#388semidirect
496. C2×C5#4944semidirect
552. C2×C3#65279semidirect
560. C5C2×#4944semidirect
589. C3C2×#65279semidirect
591. C2#11748711direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×Dic3⋊C42
C22×C3×#6852
C22×#66652
C22×Dic3×Dic52
C2×#911152
C2×#909942
#117487112
C2×#652793
C2×#49445